IG Y Satellite Report Series Number 1 IGY WORLD DATA CENTER A ROCKETS AND SATELLITES NATIONAL ACADEMY OF SCIENCES PROCESSED OBSERVATIONAL DATA FOR USSR SATELLITES 1957 ALPHA AND 1957 BETA (Special Report No. 10 of the Smithsonian Astrophysical Observatory) KCADEMY oT, LIBRARY* MAY 1 2 i958 NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, D. C. L 21 IGY World Data Center kWfJ -Rockets and Satellites National Academy of Sciences Washington, D . C . (J.GY Satellite Geriea Number 1 March 1, 1958 PROCESSED OBSERVATIONAL DATA FOR USSR SATELLITES 1957 ALPHA AND 1957 BETA by R.MV. Adams, N. McCumber, and M. Brinkman WWEMY OF 5> LIBRARY MAY 1 2 i958 Smithsonian Institution Astrophysical Observatory (Special Report No. 10) Project Director: Fred L. Whipple Associate Director: J. Allen Hynek Cambridge, Massachusetts K£ Preface This is the first of a series of reports on satellite observations and experiments. The new ness of the program, operational problems attend ant upon new endeavors, and the related problems in organizing the IGY World Data Center A for Rockets and Satellites have precluded earlier compilation and issuance of this document. It is expected that the Rocket and Satellite Center will be able regularly and promptly to compile and issue documents of interest to all World Data Centers, IGY participating committees, and the scientific community. This publication represents a compilation of the first preliminary reports from the observations of the earth satellites 1957 alpha and 1957 beta. Although these data may be superceded by subsequent reports, they are being provided in the interest of presenting a complete record. Additional earlier information, contained in Smithsonian Special Re ports Numbers 1-9, are being published by the Government Printing Office, and will be available in June 1958. IGY World Data Center A Rockets and Satellites Washington, D. C. March 1, 1958 PROCESSED OBSERVATIONAL DATA FOR USSR SATELLITES 1957 ALPHA AND 1957 BETA By R. M. Adams*, N. Mc Cumber**, and M. Brinkman*** Astrophysical Observatory, Smithsonian Institution TABLE OF CONTENTS Page 1. Introduction 1 2. Sources of Data. 1 3. Processing of Data 2 4. Catalogue of Observations 3 4.1 Satellite 1957 al 4.2 Satellite 1957 a2 4.3 Satellite 1957 Beta 5. Station Coordinate List 106 6. Acknowledgements 120 Chief, Computations and Analysis Section, Optical Satellite Tracking Program. Mathematician, Computations and Analysis Section, Optical Satellite Tracking Program. Computer, Computations and Analysis Section, Optical Satellite Tracking Program. -1 PROCESSED OBSERVATIONAL DATA FOR USSR SATELLITES 1957 ALPHA AND 1957 BETA. 1. Introduction The information contained In this report la pre sented in partial fulfillment of obligations of research contracts of the Astro physical Observatory of the Smith sonian Institution with the U. S. National Committee for the International Geophysical Year of the National Aca demy of Sciences, and the National Science Foundation, This report presents a collection of observational data, received and processed by the Smithsonian Astrophyslcal Observatory, for the two Soviet artificial earth satellites, launched on October 4, 1957 and November 3, 1957 respec tively. The data cover the total lifetime of the com ponents til, a2, and probably a3 from the Satellite 1957 Alpha launching. For the sedond Soviet Satellite, 1957 Beta, the data extend from the day of launching to the middle of February 1958. At the time of this report, 1957 Beta is still in orbit and is expected to stay in orbit until mid April 1958. 2. Sources of Data Since the first Soviet satellites were launched before all precision optical tracking stations were activated, the task of providing the observations, necessary to com pute ephemerldes and predictions, has fallen to a large extent on the MOONWATCH network and other observing agencies such as astronomical observatories, , radar stations, and various other organizations and individuals. Observations are received by the Smithsonian Astrophysical Observatory in a number of ways. MOONWATCH 6bservations made in the United States are normally tele phoned in and then confirmed by letter. Observations made in foreign countries are sent by the IOY communi cations system (AOIWARN) , if possible. When this is not possible, the observations are sent by air mail. Obser vations made by civilian, industrial, and military research institutions are received through teletype channels as well, A considerable number of observations are also furnished through Project Space Track of the Geophysics Research Directorate at the Air Force Cambridge Research Center, ARDC, as well as by Interested amateurs and pri vate Individuals. 3. Processing of Data As observational data are received, they are sifted, processed, and put into form for use in IBM 704 programs. The limited staff mfekes it impossible to process all ob servations which are received. A major portion of the usable observations have been processed, however, and it is planned to process others as time permits. As of this date approximately 4500 visual and photo graphic observations of the Russian earth satellites have been received at the Smithsonian Astrophysical Observatory. About 2980 of these have been processed for use in the IBM computer programs. The unprocessed observations fall into two groups: (a) those that will be processed as soon as time permits; (b) those that are not accurate enough to be used.. The unprocessed observations in group (a) are, in general, additional sightings on days for which a. large number of observations have already been processed. To be usable, an observation must be accurate to at least one second of time and the position given must be exact to one de gree of arc. The following is a breakdown of all observations: 1957 al * 1957 a2 and 03 50* 1957 P 1610 Processed Unprocessed: Usable Not usable 1320 470 300 0 500 250 Total 2090 50 2360 : 14 of the observations were rejected after processing. -3- Twelve reports of falling objects seen between 30 No vember and 11 December, and twenty-six reports of similar objects seen between 20 December and 8 January, have been received. These have been investigated as possible obser vations of burnouts of al and a2, but analysis makes it highly unlikely that any of these observations could have been of the demise of al or a2 , \ No attempt has been made to process radio and radar sightings unless they were made during a period when there were no visual sightings. In the following lists, all radar and radio observations are labeled as such The observations of 1957 ot2 have been analyzed by Dr. Luigi Jacchla and published on Harvard Announcement Card 1402. The results of this analysis have been noted in the column preceding the observation number in Section 4.2 of this report. Observations labeled a2 appear to be of the satellite itself Those labeled a3 are observations that do not lie on the a2 curve but Instead seem to form an orbit of their own. Possibly these "a3" observations are of the nose cone of the carrier rocket In both cases, doubtful observations have been designated by a question mark. 4. Catalogue of Observations All processed observations have been listed by date of observation. The report is subdivided into three sec tions containing the observations of 1957 al, 1957 a2 and 1957 3 respectively a The possible observations of a3 have been grouped with the a2 data. A serial number is assigned to the observation at the time that it is processed Observation numbers for 1957 al begin with 00100 and continue in numerical order, skipping the numbers from 00138 to 00199 and from 00261 to 00299Observation numbers for 1957 a2 begin with 00100, For 1957 3, the numbering of observations made in 1957 begins with 00001; for observations made in 1958, the numbering begins again with 00001 A few observations have been discarded as obviously incorrect; their numbers have not been re assigned. Some observers have corrected their data for atmos pheric refraction. These observations are indicated by an asterisk before the altitude. All MOONWATCH observations -4- are uncorrected, All positions are given in the form used for the IBM computers. The headings of the tables have the following meanings; Symbol a Term Right ascension Hours, minutes, seconds . Declination Degrees, minutes, seconds. Azimuth Degrees, minutes, seconds; measured clockwise from north. Degrees, minutes, seconds; measured upward from the horizon. Dimenslonless. Angular elevation MAG. Units Apparent magnitude Some stations report their data in degrees and fractions of a degree; in these instances conversions have been made. It is important to note the manner in which three particular stations report their data, since these stations have pro vided a large fraction of the observations received. Pic du Midi gives time to Is and positions to Ofl. White Sands records time to units and the error does not exceed one millisecond. Positions are given to Of001. 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Station Coordinate List Every station has been given a registration number of four digits (xxxx), which appears in the table with the ob servation and identifies its source. The coordinates of the stations are listed by station number in the tabular material below. The registration numbers have been assigned by a code designed to indicate the type of station, its geographical location, and the kind of observations made. However, classi fication has been difficult since pertinent facts are often missing and some stations make several different kinds of observations (e.g., visual and photographic!). The first of the four digits (Oxxx) of station: denotes the type Oxxx : MOONWATCH (visual) 2xxx : Astronomical observatories (visual and photographic) 3xxxA 5xxx/ . 6xxxf* 7xxxj Non-MOONWATCH (visual and photographic) 4xxx : Radio and radar 8xxx : Alternate observation sites; the names of all MOONWATCH stations in this ca tegory are followed by MW. Precision Optical Tracking Stations 9xxx : When ambiguities remain, the station name listed in the table of observations is followed by symbols with the following meanings : MW: SS: BN: PT: MOONWATCH Project Super-Schmidt camera Baker-Nunn satellite camera PHOTOTRACK Project The second of the four digits (0x00) indicates the geo graphical location of the station. With a few exceptions, due to operational reasons, their meanings are as follows: -107xOxx and xlxx x2xx and x3xx United States, including all terri tories and possessions except Alaska Japan x5xx Africa, Alaska, Canada. In this cate gory, the third of the 4 digits is also used to distinguish the location as follows: x40x to x44x: Africa x45x to x49x: Canada Asia x6xx United Kingdom and Eire x7xx Europe (except British Isles) x8xx South America x9xx World-wide x4xx -108- Station Coordinates Station No. 0001 p002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0038 0039 0040 0041 0042 0043 Station Sylacauga, Ala. Phoenix, Ariz. Tucson, Arizona Altaville, Calif. Los Altos, Calif. Oakland, Calif. Sacramento A, Calif. San Francisco, Calif. Santa Barbara, Calif. Stockton, Calif. Walnut Creek, Calif. Whittier, Calif. Denver, Colo. Washington, D.C. Lakeland, Pla. West Palm Beach, Fla. Hapeville, Qa. BolBe, Idaho Idaho Falls, Idaho Chicago, 111. Danville, 111. Lemont, Illinois Peoria, 111. Indianapolis, Ind. Terre Haute, Ind. Manhattan, Kans. Wichita, Kansas Wilmore, Ky. New Orleans, La. New Orleans, La. Silver Spring, Md. Detroit, Mich. Lansing, Mich. St. Paul Minneapolis A, Minn Kansas City, Mo. Lincoln, Nebr*. Dover, N. J. Red Bank, N* J* Alburquerque, New Mex. Las Cruces, New Mex. Los Alamos, New Mex. Longitude East <> 11 Latitude • 1 273 247 249 239 237 237 238 237 240 238 237 24l 255 2Q2 278 279 275 243 247 272 272 272 270 273 272 263 262 275 269 269 282 276 275 266 44 56 03 20 52 48 43 32 18 47 55 58 03 47 03 55 42 32 49 21 22 00 24 50 36 31 45 20 59 53 59 47 31 50 47.4 33 33 32 38 37 37 38 37 34 37 37 33 39 38 28 26 33 43 43 41 40 41 40 39 39 39 37 37 29 29 39 42 42 44 09 27 13 10 23 47 38 46 24 54 55 44.6 OS 41 54 40 31 09 4A 51 57 56 05 28 44 55 57 48 19 40 38 45 44 36 03.61 181 335 227 366 29 30 180 76 12 11 10 149 1625 69 61 5 323 1006 1423 218 189 229 238 223 155 311 413 282 2 2 140 183 261 306 265 263 285 285 253 253 253 25 20 28 55 21 09 40 08 48 15 39 40 40 40 35 32 35 02 50 57 17 05 19 52 02 18 30 40 03 42 30 259 355 267 0 1520 1186 2256 51 34 25 07 30 36 30 25 24 29.5 20 30 58 26 19 09 38 10 09 19 06.1 37 35 01.1 24 10 40 1 ]Meters 11 59 07 56 00 25.8 10 30 17 30 40 44 52 45 37.3 02 ?9 30 47 27 36 30 26 17 50 57 -109- Statlon Coordinates Station Ho. Station Longitude East • 0044 0045 0046 0047 0048 0049 0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0064 0065 0066 0068 OO69 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 Buffalo, No Y. Millbrook, N. Y. New York City, N. Y. Rochester, N. Yo Charlotte, N. C. Greensboro A, N. C. Cincinnati, Ohio Columbus, Ohio Cleveland A, Ohio North Canton, Ohio Tulsa, Okla. BrytarAthyn, Pa. Chambersburg, Pa, Harrisburg, Pa. Philadelphia, Pa. Pittsburgh, Pa. State College, Pa. Yankton, S. Dak. Chattanooga, Term. Arnarillo, Tex. Bryan, Tex. Edinburgh, Tex. Port Worth, Tex. Forth Worth, Texas Waco, Tex. Arlington, Va. Harrisonburgh, Va. Hoanoke, Va. Milwaukee A, Wise. Struthere, Ohio Porthland, Oreg. Port Bel voir, Va. Sunnyvale, Calif. Athens, Ga» St. Louis, Mo, Schenectady, N. Y. Dayton, Ohio Big Spring, Tex. Dodson, Tex. Chicago, 111. (cont'd.) 281 286 286 282 279 280 275 276 278 278 264 284 282 283 284, 280 282 262 274 258 263 261 262 262 262 282 281 280 271 279 237 282 237 276 269 285 275 258 259 272 1 24 22 01 26 12 07 17 58 12 32 03 56 22 05 59 00 06 36 44 03 39 49 37 38 47 53 08 04 51 30 22 48 30 40 48 58 44 33 43 23 n 33 15 11 30 57-58 24.757 45 16 40.6 10 20 18 36 34 23 28 58.630 39 50 14.57 30 05-62 27 42 35 09.5 57 10 27 30 35.9 Latitude 0 1 42 41 40 43 35 36 39 39 41 40 36 40 39 40 39 40 40 42 35 35 32 26 32 32 31 38 38 37 42 4l 45 38 37 33 38 42 39 32 34 41 58 51 54 06 13 04 11 58 29 55 03 08 55 15 57 29 44 52 01 11 38 18 44 42 37 51 28 19 58 07 29 45 22 57 37 53 50 15 42 51 Height Meteor* » 229 243 259 154 195 265 270 229 220 366 204 85 201 41 128 42 32 28 381 00 393 42 379 229 02.41 1125 30 92 14.708 20.4 28 186 40 27.25 182 30 30 27 00 38.53 29.881 45 46 54.9 30 20 07.53 30 19 30 27 06 59.1 32.4 52 11 59 463 343 294 305 9 85 17 245 152 235 229 754 58.4 8? -110- Statlon Coordinates Station No. 0086 0087 0088 0089 0090 0091 0092 0093 0094 0096 0097 0098 0099 0100 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 Station (cont'd.) Longitude East 0 • H Spokane A, Wash. 242 287 New Haven A, Conn. Baltimore, Md. 283 San Antonio, Tex. 261 Biloxi, Miss. 271 274 Panama City, Fla. Rantoul, 111. 271 Waco (Connally ARB), 262 1 ex . 272 Evansville, Ind. 261 San Antonio (Randloph AFB), Tex. Bristol, Term. 277 China Lake, Calif. 242 Cambridge, Mass, 288 Los Angeles, Calif. 24l Dayton (Wright-Patterson274 AFB), Ohio Alamogordo, New Mex. 254 Alburquerque ( Kir t land 253 AFB), N. Mex. El Paso (Biggs AFB), 253 38 03 24 30 08 25 50 55 59 10 35 48.9 28 56.2 30 Latitude n • 47 41 39 29 30 30 40 31 Height Meters 37 19 24 27 23 06 17 38 37 58 28 24.9 27 50.7 30^ 706 12 144 256 7 5 237 149 28 08.80 42 33 37 58 14.86 29 32 06 129 232 50 20 52 45 55 36 35 42 33 39 527 701 24 61 31 13-2 14.25 43 35 39 22 59 47 03 25.2 47.6 41 02 58.045 23 30.837 32 52 24.273 '1335 1618 35 03 18.25 37 31 50 San Angelo (Goodfellow 259 32 13 31 27 19 AFB), Tex. Phoenix (Williams AFB), 248 19 33 17 Ariz. Yuma , Ariz . 245 24 53 32 39 09 Patterson, N. J. 285 51 40 54 Santa Monica, Calif. 241 20 34 04 30 Lawton, Okla. 26l 35 48 34 39 45 Clinton, Miss. 269 40 03 0 787 32 20 20.78 Cary, N. C. 281 14 17 35 47 41 Van Nuys, Calif. 241 24 45 34 14 22 Honolulu, Pacific 202 20 45 21 18 13 Truk, Pacific 151 51 7 28 Wake, Pacific 166 39 19 16 30 Yap, Pacific 138 08 9 31 Pago Pago, Pacific 189 19 10 -14 16 50 Culver City, Calif. 241 24 06 34 09 01.8 Norwalk, Conn. 286 34 35 41 09 21 St. Petersburg, Fla. 277 16 27 46 40 Madison, Wise. 270 33 39 43 03 57 581 65 30 2800 1175 353 152 276 94 2 4 16 3 30 15 317 -Ill- Station Coordinates (cont'd.) Station No. 0123 0124 0125 0126 0127 0128 0199 0130 0131 0132 0133 0134 0135 0136 0194 0197 0198 0199 0200 0201 0202 0204 0205 0206 0207 0208 0209 0210 0211 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 0223 0224 0225 0226 Station Memphis, Term. New Britian, Conn. San Antonio (Lackland AFB), Tex. Bartlesvllle, Okla. Reno, Nev. Salem, 111. Dallas, Tex. Tempe, Ariz. Hapeville, 0a. Decatur, Ga. San Diego, Calif. San Jose, Calif. Oklahoma City, Okla. Wichita Palls, Tex. New Haven B, Conn. Greensboro B, N. C. Milwaukee B, Wise. St. Haul B, Minn. Aidta, Japan Asahlkawa Ashiya Chunichi Pukuoka I Pukuoka II Pukuoka III Gifu Hashimoto Hi ga shima t suyama Hiroshima Hon Jo Hofu Puchu Ichinomiya Ikoma Isahaya Kago shima Kanagawa Kanaya Machi, Japan Kanazawa Kashiwabara Kiryu Konko Kumamoto Kure Longitude East n Latitude 270 08 46.6 284 13 45 261 23 09.I 35 09 26 41 41 25 29 22 46.7 264 240 271 263 248 275 275 242 238 262 261 287 280 272 266 140 142 135 136 130 130 130 136 135 139 132 139 131 133 136 135 130 130 139 135 136 135 139 133 130 132 36 39 38 32 33 33 33 32 37 35 33 41 36 42 44 39 43 34 35 33 33 33 35 34 36 34 36 34 34 35 34 32 31 35 34 36 34 36 34 32 34 04 12 02 14 06 38 42 45 11 29 26 05 11 01 45 07 21 18 54 25 21 24 47 37 23 28 11 33 14 48 40 03 31 21 15 41 48 19 37 44 33 00 29 24 57 13-7 13 20 55 15.1 59-4 02 50 55 14 40 33 59 04 03 54 10 05 56 25 42 23 08 47 16 10 01 15 54 40 34 44 ■ 1 42 33 38 51 25 39 47 42 23 33 49 19 04 59 58 41 46 43 10 37 34 33 25 19 02 22 14 03 34 17 40 51 31 26 03 32 30 24 32 46 14 Height Meters H 45 10 11 27 25.9 01 50 85 61 213 213 1372 174 172 347 270 323 125 122 360 303 41 25.5 30.7 42 27 42 23 25 50 10 49 02 22 08 25 13 25 32 34 41 34 34 46 45 24 22 31 57 57 6 113 14 22 16 14 23 339 125 31 3 56 10 30 8 634 70 13 51 40 80 66 110 4 17 5 -112- Station Coordinates (cont'd.) Station No. 0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 0238 0239 02|0 0241 0243 0244 0245 0246 0247 0248 0249 0250 0251 0252 0253 0254 0255 0256 0257 0258 0259 0260 0261 0262 0263 0264 0265 0266 0267 0268 0269 0270 0271 0272 0273 Station Kurume Machi Hanazuru Mitaka Mlyazakl Mlzukaldo NOunt Fuji I Musashlno Nagano Nagasaki I Nagoya Nakatsu Nligata Oita, Japan Osaka Osaka Yomlurl Otaru Saga Sapporo Sendai Shlzuoka Suva Tadotsu Takada Takamatsu Tohoku Univ. Tokushima ^cryama Toyohashi Uwajima Yamagata Yokkalchl, Japan Kyoto Atsuta Chlba Hlmejl Kasukabe Kochi Kyushu Univ. Hie Mlzusawa Nagasaki II Otsu Takaoka Utsunomlya Yatsushiro Mt. Fuji II Longitude East 0 1 it Latitude 139 139 139 131 139 138 139 137 129 136 131 139 131 135 135 141 130 141 140 138 138 133 138 134 140 134 137 137 132 140 136 135 136 139 134 139 133 130 136 141 129 135 137 139 130 138 35 35 35 31 36 35 35 35 32 35 33 37 33 34 34 43 33 43 38 34 36 34 37 34 38 34 36 34 33 38 35 35 35 35 34 35 33 33 34 30 32 35 36 36 32 35 31 08 32 25 59 48 34 50 51 59 11 02 11 31 30 00 17 22 51 23 07 45 15 02 52 35 11 24 33 20 39 42 54 58 41 44 30 30 37 07 52 52 01 51 36 48 48 46 30 24 18 50.3 3? 44 56 11 53 21 57 01 30 23 59 13 56 18 43 16 22 13 38 32 07 37 32 59 00 24 17 14 24 34 35 41 19 51 20 08 39 45 15 57.5 Height Meters n 45 09 40 55 00 21 42 30 46 08 36 55 36 38 41 11 14 04 15 58 00 16 06 20 16 07 42 45 12 15 00 01 08 51 50 58 33 19 58 08 47 00 44 33 30 25 18 23 20 23 56 20.8 58 50 53 57 10 05 06 36 51 27 35 49 22 25 13 20 38 28 28 34 13 09 49 16 15 01 05 29 25 36 25 55 10 04 05 24 23 56 21 50.6 52 25 50 8 12 815 75 500 15 50 5 24 4 24 30 10 5 20 45 20 762 5 23 5 47 1 65 16 2 151 3 55 10 10 25 5 30 8 3 62 25 90 8 130 3 1040 -113- Statlon Coordinates Station No. 0400 0401 0402 0403 0404 0600 0601 0602 0603 0604 0800 0801 0802 0803 0804 0805 0806 0807 0608 0809 0900 0901 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Station Lwiro, Belgian Congo Bloemfontein, Union of S. Africa Cape Town, Union of S. Africa Johannesburg, Union of S. Africa Pretoria, Union of S. Africa Adelaide, Australia Perth Sydney Woomera Melbourne Buenos Aires Buenos Aires Merlo Pcia, Bs. As. Cordoba Antofagasta, Chile Santiago (Romero) Santiago (Heilmaier) Arequipa , Peru Montevideo, Uruguay Quito, Ecuador Puebla, Pue, Mex. Curacao, Emmas tad, Netherlands, Antilles Univ. of Alabama Obs. Lowell Obs. Univ. of Arizona Obs. Leuschner Obs. Lick Observatory Mt. Palomar Obs. Mt. Wilson Obs. Wesleyan Univ. Obs. Yale Univ. Obs. Georgetown College Obs. U. Sr Naval Obs. Agnes Scott College Oba Northwestern Univ. Obs. Univ. of Illinois Obs., A Univ. of Indiana, Obs. (cont'd,) Longitude East 0 n i 28 45 26 13 35.50 Latitude 0 1 Height Meters 11 - 2 16 -29 06 19.56 18 28 37.984 -33 56 00.440 1707 1494 7 28 04 30 -26 10 55.3 1806 28 13 43.5 -25 47 18 1542 138 115 151 136 144 301 301 301 295 289 289 289 288 303 281 261 291 36 51 05 46 58 33 33 15 48 34 18 21 27 50 32 49 03 14 10 41 272 248 249 237 238 243 241 287 287 282 282 275 272 271 27 18 03 44 21 08 56 20 04 55 56 42 19 46 27 51 05 16 16 10 25 27 51 26 03 21 32 31.5 IS 55.96 39 03 12 03 48 46 55 00 15 28 273 28 45 -34 -32 -33 -31 -37 -34 -34 -34 -31 -23 -33 -33 -16 -34 - 0 19 12 55 00 54 06 49 36 37 40 25 39 33 25 23 55 10 03 09 14 07 43 13 54 19.26 10 56 16 11 42 21 05 10 47 04 2200 6 33 35 32 37 37 33 34 41 41 38 38 33 42 40 12 12 13 52 20 21 12 33 19 54 55 55 03 06 33 30.5 59.4 23.5 25.3 22.4 59.5 18 22.3 26 14.0 54.5 27.2 20.2 87 2210 757 °A 1283 1Z06 1742 65 40 62 86 315 175 236 39 09 56 55 5 15 155 29 23 103 25 439 10 573 864 2377 38 238 114- Station Coordinates (cont'd.) Station No. 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 Station Univ. of Iowa, Obs. Maria Mithhell Obs. Mt. Holyoke College Obs. Wellesley College Obs. Univ. of Michigan Obs. McMath-Hulbert Obs. Univ. of Minnesota, Obs. Univ. of Mississippi, Obs. Washington Univ. Obs. Princeton Univ. Obs. Dudley Obs. Cornell Univ. Obs. Columbia Univ. Obs. Syracuse Univ. Obs. Cincinnati Obs. Warner and Swasey Obs., A Ohio State Univ. Obs. Ohio Wesleyan Univ. Obs. Univ. of Pittsburgh, Obs. Haverford College Obs. Univ. of Pennsylvania Obs., A Lehigh Univ. Obs. Swarthmore College Obs. McDonald Obs. Univ. of Virginia Obs. Univ. of Wisconsin Obs. Yerkes Obs. Sacramento Peak Obs. Colgate Univ. Obs. Rensselaer Polytechnic Obs. Univ. of Illinois Obs., B Univ. of Illinois Obs. C Univ. of Illinois Obs. D Univ. of Illinois Obs. E Warner and Swasey (Nassau Sta. ), B Longitude East Latitude 0 1 Height 1Meters H 268 289 287 288 276 276 266 270 28 53 25 41 16 44 45 28 00 43 15 40 11 10 44 12 41 41 42 42 42 42 44 34 39 16 15 17 16 39 58 22 44 50 18.2 37.1 48.7 47.7 40 12.6 221 20 76 61 282 296 260 161 269 285 286 283 286 283 275 278 41 21 13 31 02 51 34 25 40 06 13 26 30 40 39 55 38 40 42 42 40 43 39 41 38 20 39 27 48 02 08 32 57.0 47.7 12.8 10.4 34.6 13-1 19.8 13.1 178 43 70 270 25 160 247 247 276 59 21 276 56 40 279 58 40 39 59 50.4 40 15 04 40 28 58.1 233 270 370 284 4l 49 284 43 17 40 00 40.1 39 58 02.1 116 74 284 284 255 281 270 271 254 284 286 40 39 30 38 43 42 32 42 42 37 38 58 28 35 26 10 28 19 01 36 40 40 32 41 47.261 14.893 36 54 40 02 04 34 47 49 43 23.2 110 63 16.2 2081 17.0 259 01.2 292 36.8 12.6 334 14.870 2823 44.2 271 46 36.7 40 06 16.2 271 46 24.0 40 05 54.3 271 40 22.8 40 01 04.6 271 49 55 40 08 28 278 55 36 40 35 -115- Statlon Coordinates Station Mo. 2052 2053 2054 2400 2401 2450 2451 2600 2601 2650 2651 2652 2653 2654 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2800 2801 2900 Station Agasslz Station, Har. Princeton Obs. of Instruction Boston Univ. Obs. Boyden Station, Bloemfontein Union Obs. Johannesburg Dominion Obs., Ottawa David Dunlap Obs. , Univ. of Toronto Mt. Stromlo Obs. Sydney Obs. Royal Greenwhich Obs., Herstmonceux Armagh Obs., A Dunsink Obs., A Royal Obs. Edinburgh Dunsink (santry), B Vienna Univ. Obs. Bratislava-Koliba Obs. Ondrejov Obs. Copenhagen Univ. Obs. Helsinki Univ. Obs. Pic du Midi Obs. National Obs. , Athens Sonnenborgh Obs., Utrecht A Stockholm Obs. Harestua Obs. Observatoire de Saint Michel Skalnate" Pleso (Haute Tatra) Obs. Univ. Obs., Bonn National Obs., Cordoba National Obs., Santiago Manila Obs., Phillippines (cont'd.) Longitude East n Latitude 288 26 21 285 20 35.8 42 25 18 40 20 57.8 183 65 288 53 37.5 26 24 21 42 21 00.6 -29 02 18 36 1387 28 04 30 284 17 00.8 280 34 40.5 -26 10 55.3 45 23 38.1 43 51 46 1806 87 244 149 00 20 151 12 14.6 0 20 16 -35 19 16 -33 51 41.1 50 52 01.3 768 44 32 • Height Meters H 11.1 13.1 30 64 86 146 55.1 18 38.1 12.6 42.3 12.0 19.7 10 240 260 533 14 33 2862 110 14 18 18 30 10 45 00 5 04 48 59 16 18 60 12 30 43 55 47.2 55 20 14 00 49 11 42 353 353 356 353 16 17 14 12 24 0 23 5 6 295 289 120 21 39 48 45 20 06 47 34 57 08 43 07 50 48 18 34 08 43.5 59 20 37 01 40 16.5 32 01 45 58.6 12.6 43.6 45 54 53 55 53 48 48 49 55 60 42 37 52 -50 -31 -33 16 21 23 55 24 13 10 54 4l 09 56 58 05 09 25 33 24 47.2 16.4 44.2 46 580 1783 434 580 -116- Station Coordinates Station No. 3001 3002 3003 3004 3005 3006 3007 3008 3009 30X0 3011 3012 3013 3450 3601 3602 3900 4001 4002 4003 4004 4007 4008 4009 4650 4900 5001 5002 5003 5004 5005 Station Perkin Elmer, Norwalk, Conn. Hanscom APB, Mass. Cape Canaveral, A, Fla. Perkin Elmer, Pla. Patuxent N.A.S., Md. Port Monmouth, N. J. Holloman, APB, White Sands, New Mex. Whittenburg College, Ohio Wright-Patterson, APB, Ohio Amarillo APB, Tex. Westover AFB, Mass. Eglin APB, Fla. Edwards APB, Calif. Fort Churchill, Manitoba Woomera Range, Edinburg, Australia Salisbury, Australia Wilkes, Antarctica Stanford Res. Inst. Palo Alto, Calif. Lincbln Labs. , Lexington, Mass. Evans Labs, N. J. Diana Radar, N. J. Cornell Aero. Lab., B, N. Y. Stanford Res. Inst., Calif. Laredo Radar, Tex. Jodrell Bank , Macclesfield, Eng. Grand Bahama, B.W.I. Organ Pass, New Hex, SS El Segundo, Calif. PT Eastman, Rochester, N. Y. PT Good Hope, 111. PT Cleveland, Ohio, PT (cont'd.) Longitude East 0 1 R Latitude 286 35 41 09 288 279 279 283 285 253 44 25 27 36 54 40 42 39 04.32 39 • 42 28 28 38 40 32 n 27 26 02 17 17 25 18 02.36 58.48 39 56 08.1 275 55 11 39 47 22 258 286 273 242 265 35 42 30 34 58 28 15 58.43 01 11 30 43 44 30 56 43.19 45 136 46 46 -31 06 06 138 38 45 110 27 237 47 -34 44 13 -66 28 37 25 288 30 31 42 37 02 285 56 20.4 285 05 42 28l 16 36 40 11 02 40 12 42 55 56 237 49 29 37 24 11 260 29 21 357 41 38 27 31 07 53 30 11 281 253 24l 282 26 32 33 43 39 06.8 26 51.741 50 33 58 269 20 278 20 30 46 30 276 11 02.9 03 19 30 04 55 Height Meters 152 36 34.9 25 24.550 1651 50 03 38 40 38 41 30 -117- Statlon Coordinates (cont'd.) Station No. 5006 5007 5008 5009 5010 5011 5450 5451 5800 5801 6001 6002 6003 6004 6005 6006 6007 6008 6010 6011 6019 6450 6700 6701 6900 6901 Station Ansco, Binghampton, N. Y. PT Albuquerque, Mew Mex.PT Petersburg, Alaska, PT Menlo Park, Calif. , PT Haul Hawaii, SS Ho 11oman AFB, White Sands, New Mex., B Meanook, Alberta Newbrook, Alberta Quito Station, New Hex. College Of A and M Quito Station, B Washington, D. C, R. H. Wilson Washington, D. C, Smithsonian Inst. Milton, Mass., H. Stubbs Weston, Mass., A. Campbell Dover, New Hampshire Cornell Aero. Lab., A Charleston, 3. C. , G. L. Luke Dahlgren, Va., NPG Welcome, Md. , L.T. Johnson Hampton, Va. , HastingsRaydist, Inc. Washington, D. C, H Fitzpatrick College Geophysical Station, Alaska Jockls Meteorlogical Obs. , Finland Helsinki Obs., B Cape Hallett, Antarctica Air Force, Arctic Longitude East H Latitude 284 10 42 07 253 227 237 203 253 35 56 37 20 33 20 00 50 44 23.4 50 26.949 0 1 Height Meters n 00 45 25 42 36 3058 07 56.183 246 39 15.4 247 02 43.7 281 39 54 36 58.6 54 19 28.3 - 0 05 30 281 31 282 59 24 - 0 12 38 50 68 67 282 58 24 38 53 17.3 288 53 42 13 288 43 25 42 23 09 175 289 07 26 281 19 30 280 01 43 23 10 42 57 05 32 55 213 282 57 59-07 282 53 26 38 17 03.19 38 24 29 238 39 03.409 37 00 56.210 282 56 24 38 56 06 212 10 12 64 51 18 23 19 25 02 30 170 18 251 30 60 49 60 12 54 -72 18 81 24 -118Statlon Coordinates Station No. 7000 7001 7002 7003 8001 8002 8003 8004 8005 8006 8007 8008 8009 8010 8011 8012 8013 8014 8015 8016 8017 8018 8020 8021 8022 8023 8024 8025 8026 Station (cont'd.) Longitude East n 149 Canberra, Australia, Lawley House 149 Canberra, Australia, National Univ. Pezinok, Czechoslovakia 17 27'5 Decatur, Georgia 282 Blossom Pt. Md., R. H. Wilson 5 Utrecht B, Netherlands • 802 Hilversum, Netherlands 5 805 Steenwljk, Netherlands - 6 807 239 Sacramento MW, D 283 Washington D. C, L. Holloway 279 Cape Canaveral B, Fla. 241 Pasadena. Calif., (Pasacal) Washington, D.C., MW, C 282 14 Navy 237 Mt. Vaca, Calif., (Sacramento MW) 291 Navy 242 China Lake, Calif. 282 Blossom Pt., Md. L.T. Johnson 284 Univ. of Perm. , B Cape Canaveral, C, Fla. 279 Cape Canaveral, D, Fla. 279 Cape Canaveral, E, Fla. 279 Cape Canaveral, F, Fla. 279 288 Quebec, Canada 5 Weesp, Netherlands 803 Blaricum, Netherlands 5 804 Amsterdam, Netherlands 4 806 6 Emmen, Netherlands 80S Beverwijk, Netherlands 4 809 Latitude • 1 Height Meters V 08 -35 19 570 06 30 -35 16 560 170 323 16 21 42 57 54 48.2 48 17 47 33 47 27 38 25 49.6 05 20 52 05 31 10 00 52 12 20 07 01 52 46 59 08 36 03 38 38 06 38 52 26 21.5 50 38 28 31 29.3 34 06 56 11 47 30 52 53 24 38 45 30 35 51 38 24 30 69 34 42 22 30 55 36 01 12 35 41 38 38 25 31 25 25 26 24 31 02 39 28 28 28 28 46 52 24 05.5 40.4 11.0 38 06 21 59 57 16.3 06 33.8 30 02.2 27 58.3 53 03 18 12 14 53 52 16 15 42 00 52 18 25 54 15 52 46 40 38 56 52 28 58 74 6 6 9 -119- Station Coordinates Station Mo. 8027 8028 8029 8030 8031 8032 8034 8035 8036 8037 8039 8500 8501 8502 8503 8505 8506 8507 8508 8509 8510 9O01 9002 9003 9005 9004 Station (cont'd.) Longitude East a M 1 Bussum, Netherlands 5 810 Sneek, Netherlands 5 811 Netherlands - 812 6 Netherlands - 813 5 Landstraat, Netherlands k 814 282 Washington, D. C, Bald Eagle Hill 287 Mansfield, Conn. 254 Boulder, Radio Armagh Obs. , B 353 264 Univ. of Kansas Cape Canaveral, Fla. 0 279 238 Sacramento, Calif., MW, B 238 Sacramento, Calif., MW, C 242 Spokane, Wash. , MW, B 262 Fort Worth, Tex« MW, B 278 Cleveland, Ohio, MW, B 273 Sylacauga, Ala., MW, B Near Adelaide, 138 Australia 238 Sunnyvale, Calif. , MW, B 282 Springfield, Va. Washington D. C. MW), B 286 New York City, MW, B. Organ Pass, New Mex. BN 253 Olifantsfontein, 28 S. Africa BN _ Woomera, Australia, BN 136 Tokyo, Japan, BN 139 Cadiz, Spain, BN 353 353 Latitude 0 n 09 18 52 16 52 39 52 53 02 25 08 28 03 14 44 59 52 19 51 52 39 50 52 37 39 59 31 38 49 13 48 42 21 45 24 59 4l 40 54 38 28 38 40 12 38 38.4 14 58.8 42 37 10 44 35 30 51 18 39.8 48 49 05 21 37 16 41 4l 20 12 31 18 19.8 11 411 38 33 05.4 47 32 40 33 -34 45 42 25 10 55 00 42 30 20.3 39 01 48 37 12 56 48 38 54 12 40 44 23 04 10 26 51 0 741 32 25 24.5 -26 11 42 08 25.5 25-5 48 32 30 47 42 Height Meters -31 08 35 40 21.4 35 36 27 42.0 1707 59 30 -120- 6. Acknowledgements We wish to emphasise that the observational data stem from the efforts of thousands of persons who, In the true spirit of the International Geophysical Year, have given freely of their tine and work. It is a privilege for us to acknowledge these contributions which have made possible the tracking of artificial earth satellites. At the Smithsonian Astrophysical Observatory, the task of obtaining, screening, and processing the raw data has been the obligation of the Optical Satellite Tracking Pro gram under Dr. J. Allen Hynek, associate director of the observatory, and K. H. Drummond, executive officer of the tracking program. It fell principally upon the staff of the Computations and Analysis Section of this program to cope with the large volume of data and to present the mar terlal in a useful form. For the manuscript preparation of the report, we wish to thank Thelma Bourne, Lillian Christ mas, Janet Clarke, Connie Cowhig, Jane Henderson, Bringfriede Jensen, and Rlnda Rogers. We wish especially to express our appreciation to Dr. 0. F. Schilling for his devoted interest, encouragement, and guidance in the compilation and Mrs. Lyle Boyd for her editorial assistance. 0 IGY Satellite Report Series Number 2 IGY WORLD DATA CENTER A ROCKETS AND SATELLITES NATIONAL ACADEMY OF SCIENCES STATUS REPORTS ON OPTICAL OBSERVATIONS OF SATELLITES 1958 ALPHA AND 1958 BETA (Special Report No. 11 of the Smithsonian Astrophysical Observatory) NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, D. C. IGY World Data Center A fa-rj Rockets and Satellites . National Academy of Sciences Washington, D. C. Report 1IGY Satellite -SeriesNumber 2 April 30, 1958 STATUS REPORTS ON OPTICAL OBSERVATIONS OF SATELLITES 1958 ALPH A AND 1958 BETA EDITED BY G. F. Schilling KOMEMY Of " library' MAY 2 3 i558 ^#41 BESEAWH Smithsonian Institution Astrophysical Observatory (Special Report No. 11) Project Director: Fred L. Whipple Associate Director: J, Allen Hynek Cambridge, Massachusetts ! : :" Preface The original intent of this collection of short reports was the presentation of preliminary data, to the U. S. National Committee for the International Geophysical Year, obtained by the Optical Satellite Tracking Program of the Smithsonian Astrophysical Ob servatory with regard to the first artificial earth satellite launched by the United States on January 31, 1958. At the present time, however, three more objects have been successfully launched into satellite orbits from Cape Canaveral, Florida. The collection has there fore been expanded to include such additional orbital information and results of data analyses as could be put into usable form, as well as descriptions of the principal machine computation programs in use. Since we are endeavoring to make these satellite data available as rapidly as possible to all scientists participating in the International Geophysical Year, we have of necessity included information of an ex tremely preliminary nature. Gerhard P. Schilling Cambridge, Massachusetts March 31, 1958 STATUS REPORTS ON OPTICAL OBSERVATIONS OP SATELLITES 1958 ALPHA AND 1958 BETA Table of Contents CHAPTER I: CHAPTER II: Page PRELIMINARY RESULTS FROM OPTICAL TRACKING OP THE tt. S. EARTH SATELLITES by J. Allen Hynek and Fred L. Whipple.. 1 OPTICAL SATELLITE OBSERVATIONS The Network of Precision Photographic Satellite Tracking Stations — by Karl G. Henize 5 Moonwatch Observations of Satellites 1958 Alpha, 1958 Beta and 1958 Gamma — by Leon Campbell, Jr 7 CHAPTER III: SCIENTIFIC RESULTS The Orbit and Variable Acceleration of Satellite 1958 Alpha — by Charles A. Whitney 14 The Density of the Upper Atmosphere — by Theodore E. Sterne 18 Life Expectancy of Satellite 1958 Alpha — by Luigi G. Jacchia 23 CHAPTER IV: USE AND DISTRIBUTION OF SATELLITE PREDICTIONS — by R. M. Adams 24 Program for Determination of Geographic Sub-Satellite Points — by Luigi G. Jacchia 26 Predictions for Crossings of Given Latitude Parallels — APO Ephemeris 5 — by John Gaustad 28 Predictions for Photographic Satellite Tracking Stations — APO Ephemeris 4 — by Charles H. Moore and Don A, Lautman. 30 Table of Contents Page CHAPTER IV (cont'd) : Program of Spot Predictions for Specific Observing Sites — APO Ephemeris 3 — by R. Briggs 33 Charts of Predicted Satellite Positions — by Jean B. Fairman and George Veis 3^ CHAPTER V: HARVARD ANNOUNCEMENT CARDS ^0 CHAPTER I PRELIMINARY RESULTS PROM OPTICAL TRACKING OP U. S. EARTH SATELLITES by J. Allen Hynek* and Fred L. Whipple** In the satellite program of the International Geo physical Year the complex operations performed by the Op tical Satellite Tracking Program of the Smithsonian Astrophysical Observatory are a result of teamwork in the fullest sense of the word. The manifold tasks include the visual acquisition of the artificial earth satellites, the com putation of search ephemerides and predictions, the opera tion of a world-wide network of precision tracking cameras capable of photographing small objects at distances of hun dreds of miles and timing these photographs to better than a thousandth of a second, the screening, reduction, and analysis of incoming data, and last but not least, the dis semination of the reduced data to the scientific community. Remembering that since October 4, 1957, there has been a total of eight objects projected into satellite orbits, we hardly need to point out that the efforts expended by thousands of persons, including the volunteer Moonwatch team members, in the Optical Tracking . Program alone are outstanding. With great scientific enthusiasm and satisfaction, our staff members have participated in this undertaking, often well beyond the normal call of duty. We have not noted similar dedication save in times of national emergency. The cooperation of the U. S. Naval Research Laboratory in furnishing us with critical prediction data for satellites with live radio*-: has been of major importance. Also, the computation of ephemerides and orbital data would have been virtually impossible without the generous cooperation of the International Business Machines Corporation and the Compu tations Laboratory at the Massachusetts Institute of Tech nology in Cambridge. * Associate Director, Smithsonian Astrophysical Observatory, in charge of the Optical Satellite Tracking Program ** Director, Smithsonian Astrophysical Observatory 2 The subsequent sections of this collection have been prepared individually by members of the Smithsonian Astrophysical Observatory who are actively working in this particular field and therefore best able to present a factual and informative account of the respective aspects of the program. In this initial chapter, we wish to summarize as well as outline from an overall point of view the orbital data and results which we have been able to obtain with regard to Satellites 1958 Alpha, 1958 Beta One, and 1958 Gamma. The mainstay of the long-range optical tracking pro gram is the worldwide network of precision photographic stations, employing at each observing station a 3-&xis, 20-inch aperture, f/1 camera designed especially for the photographic tracking of artificial earth satellites. The optics for these cameras were designed by Dr. James Q. Baker, and constructed by the Perkin-Elmer Corporation. They employ a unique 3-corrector lens system having 4 aspherical surfaces, in combination with a 31-inch con ventional spherical mirror, providing a useable field of 30°. The motor *-driven mechanical drive provides se quential tracking of a satellite and of star background on the same 250 x 55 mm. film frame, in cyclical succession so that many individual photographs can be obtained during a given satellite passage. The unique mechanical system was designed by Mr. Joseph Nunn and fabricated by Boiler and Chivens, Inc., all of South Pasadena, California. The urgency imposed upon the optical tracking program by the launching of the Russian satellites made It de sirable to expedite the construction of the stations and to obtain the use of auxiliary cameras to go into operation before the arrival of the Baker-Nunn cameras . Through the excellent cooperation of the Ballistic Research Laboratory we have obtained the use of two S M T (Small Missiles Telecamera) instruments. In addition, several phototheodolites have been furnished through the courtesy of the U. S. Air Force, thus making possible the completion at any earlier date than otherwise possible an effective tracking network. As discussed by Karl G. Henize in his report, the full complement of Baker-Nunn cameras is ex pected to be in operation by mid June. - 3 - For an artificial satellite tq be tracked most* effective ly for scientific purposes, the tracking accuracy must be of the order of seconds of arc and of 0.001 seconds of time. A crystal clock of extreme precision has been built by the Ernst Norrman Laboratories, Williams Bay, Wisconsin-, for each of the twelve observing., stations.. *The time presentation within each camera Is photographed on each frame. It can be stated that the scientific value of a satellite for many geophysical . purposes rises greatly with its longevity. Precision observations » of non-aspherical,* close artificial satellites are of little value in solving major geodetic problems because of the variable motion introduced by vary ing orientation and the* consequent irregular drag. Pence the present schedule iriI* establishing the -precision' camera programs has occasloned. ltlttle scientific loss. This more leisurely program has more than offset this loss, in terms of improved optical and*mechanical performance. The successful photographs of the first two American satellites by several Of the network stations is a grati fying signal of the routine, tracking soon to be effected. The establishment of- the photographic network- would not have been possible without* the cooperation of several 1 foreign governments . Particular note must be taken of the great assistance received through the respective I'lG.Y. committees from the governments of Argentina, Australia, India. Iran, Japan, Netherlands Antilles, Peru and the Unipn of South Africa. Their sympathetic appreciation of the urgency of the total program has been 4-nMspensible, and ou^r work in those several countries has been carried out in a thoroughly cooperative manner appropriate to the spirit of the Inter national Geophysical Year. An integral part of the optical tracking program, complementary to the precision program, is the far-flung visual observing project termed M00NWATCH. Conceived primarily as an acquisition and reconnaissance mission to cover periods immediately after launching and shortly be fore demise, in final stages of the existence of a satellite, M00NWATCH teams have served continuously" ' as Interim tracking stations during the period of final preparation of the photographic tracking stations . The exemplary work of the several thousands of persons involved in this program stands out as a significant contribution to the satellite program, and an outstanding example of lay participation in an international scientific venture. - 4 - Largely through the use of MOONWATCH observations, the computations and analysis division -of Smithsonian Astrophysical Observatory has been able to derive signifi cant, even through preliminary, scientific results. These are treated in Chapter III and include the orbit deter mination of 1958a and an evaluation of the variable acceleration of this satellite and of its life expectancy With respect to 1958p2> tne perigee distance is so relatively high that little can be said of its life expectancy save that in all probability It must be counted in decades. Its rocket carrier, 19583, will probably have a significantly shorter lifetime, but still perhaps a decade or more. Various computational programs have been devised, and others are in process, for the utilization of satellite observations for prediction purposes as contrasted to their use for results of geophysical interest. Ephemerides for general use as well as for specific use at given geographical points have been programed; an example of the latter is the program Which prints out actual Baker-Nunn camera settings which can be cabled directly to the network stations. Implicit in the prediction program is the objective to disseminate not only specific predictions but general satellite information of an astronomical character to the public through the several mass media. This we have recognized and met by concise statements to the press and by the preparation of charts illustrating visible passages of satellites over the United States. - 5 - CHAPTER II OPTICAL SATELLITE OBSERVATIONS The Network of Precision Photographic Satellite Tracking Stations by Karl Q. Henize* 1. Station Operation On the date of this report, nine photographic satellitetracking stations of the planned twelve-station network are in operation. These stations are listed below in Table One together with their dates of first useful operation and with the Instrument now installed at each station. TABLE ONE Stations in Operation Station No. 9001 9002 9003 9004 9005 9009 9010 9011 5012 Location Date New Mexico 5 Nov. '57 South Africa 20 Feb. •58 Australia 12 Mar. '58 Spain 17 Mar. ♦27 Mar. '58 JaDan partial Curacao 12 Mar. 1 58 Florida 18 Mar. 1 58 Argentina **25 Mar. '58 est. . r c7 Hawaii 21 Instrument Bake r-Nunn Baker-Nunn Baker-Nunn Baker-Nunn Baker-Nunn SMT SMT Super Schmidt Super Schmidt Japan reports partial operation only, and we may anticipate full operation within two to three days. ** * A cable from Argentina 21 March estimated this 25 March operation date. Senior Astronomer, in charge of photographic tracking stations, Optical Satellite Tracking Program, Smith sonian Astrophysical Observatory - 6 - At four of the stations listed above, Super Schmidt meteor cameras or Small Missile Telecameras have been in stalled on an interim basis. As shown in Table Two, these instruments will eventually be replaced by Baker-Nunn ca meras, thus resulting in a twelve-station network equipped with identical instruments of superior precision and accuracy. The dates in Table One are dates of actual accomplishment. The dates listed below in Table Two represent our present schedule for the remaining Baker-Nunn cameras. TABLE TWO Scheduled Operational Dates of Additional Baker Nunn Cameras Station No. 9006 9007 9006 9009 9010 9011 9012 2. Location Shipping Date India Peru Iran Curacao Florida Argentina Hawaii 29 8 18 28 8 18 28 Mar. Apr. Apr. Apr. May May May •58 •58 ■58 '58 •58 '58 Date in Operation 15 28 8 8 18 7 12 May Apr. May May May June June 58 58 58 58 58 58 58 Photographic Reduction Photographs of American satellites 1958 a and 1958 were first obtained during the visibility period around March 18, 1958, at our photographic tracking stations. Suc cessful photography continues and the films showing satellites, after immediate field reading, are being reduced for precise data evaluation. The image quality is such that we may be able, with further efforts, to obtain also precise photographs of Satellite 1958 P2. This program for precise data reduction at Cambridge is under the supervision of Dr. George Van Biesbroeck, Consultant. Special precision measuring engines for film reading and search are used, resulting in highly accurate position information. It is expected that a catalogue of pre cision data from the tracking cameras can be issued soon in a nature similar to the catalogues of M00NWATCH data. 3. Reduction of PHOT0TRACK Observations A considerable number of photographs of the Soviet sa tellites have been received from PHOTOTRACK stations and ama teur photographers and are being reduced in an analogous man ner. No such photographs have as yet been received here of the U. S. satellites. - 7 - Moonwatch Observations of Satellites 1958 Alpha, 1958 Beta One, 1958 Beta Two, and 1958 Gamma By Leon Campbell, Jr.* Since the launchings of the U.S. artificial earth satellites, 13 MOONWATCH stations participating in the Smithsonian Astrophysical Observatory's visual observing program have reported a total of 59 observations. These were made between February 3 and March 24 of 1958a and between March 19 and March 26 of 1958BI. In addition, the first sighting of 1958p2 was made on March 20, 1958 and the first sighting of 19587 was reported on March 27, 1958. All observations listed in the following Catalogue were used in the Smithsonian Observatory's computer pro gram for determining subsatellite points. Some very few other observations are not listed here because the timing of the observations was not to the second or the position to one degree of arc. However, these unlisted observations were useful since, having been made during very early orbiting of the satellites, they served as checks on pre liminary orbital elements. It will be understood that at this time, only days after the 1958p and 19587 launchings, the observations reported of satellites 1958B2 and 19587 are preliminary values and not yet confirmed by our Computations and Analysis Section. It may easily develop that some of these sightings must be discarded later. The catalogued observations were reported (by tele phone and cable) from MOONWATCH stations, in the United States, Australia, Union of South Africa, and Japan. The faintness of the objects and the small inclination of their orbits to the equator account for the fact that only 13 stations have made observations to date (March 27, 1958). There are, as of March 27, a total of 230 stations associated in the Smithsonian Observatory's MOONWATCH network, with 126 of these located In the United States and its terri tories, and 104 in other countries. These observations of * In Charge MOONWATCH Project - 8 - the U.S. satellites were made during a period in which many of the 230 stations were engaged in observing 1957^1 as well0 Two MOONWATCH teams reported unique observing experi ences o Alamogordo station 102 on March 19 observed 1957Pi* 1958a and 1958Pi; the latter two objects were about 13m 30s apart. Albuquerque station 103 on March 20 observed 1958f3i, 1958p2 and 1958a in that order. The Catalogue lists the observations by object, and in chronological order. The Key to MOONWATCH Station Code Numbers gives the geographical coordinates of the stations listed in the Catalogue. It will be noted that the position of the satellites is given either in right ascension and declination or in azimuth and altitude. Azimuth is measured clockwise from north through 36O0. The Catalogue and Key to Station Code Numbers follow: 3k lk s 06 29 56 S 26 s 10 55 39°09 !k5" N 38 32 N 25.2 35 39 N 52 2k. 32 3 N 18.3 57 34 N 15 k 00. S 33 55.3 11].. 30 7 N k2 39 03 N 36 35 00 N 19.5 22 02 Ik N Station Longitude Name Latitude Number Code MCODE STATION TO KEY NUMBERS O NWATCH wwwwVw E £E E E E E 6 37.9 35. k 01. 01.9 29.2 30 ik '51" 09 00 5k hh k6.8 '281 20 22 39 57 36 23 33 39 1328 Ok 36 96C 96 97 117 105 106 139 132 136 26 18 28 138 Albuquerque, Japan Mexico New Higashimatsuyama, JoS. Africa han esburg, S. Africa Bloemfontein, S. AAdelaide, ustralia CChina Lake, alifornia New Alamogordo, Mexico S. Town, Cape Africa Kansas Manhattan, Texas Worth, Port Japan Yokkaichi, Texas Bryan, Kure, Japan 027 065 069 098 102 103 210 226 258 kOl 600 lj.02 k03 o <D -p u o H O o I ri bO-O a -p cd s CO + °? + + in m ^VO C0.C0. op mm t^COVOCO + + -h flOr CO o H > Cd W CO C O •H 43 O rH CD > a m tH O .1 C •H -P rH < <M O W o En I o o o o mo -3- o CM ro o o oooj mo o\ o\^t ow cm m f-co^t-co >->vO C--C0UD CD 3 P O -P <D cd P C § I COi-HVO o t--=1m ■=* % •H -P m rH O f-Q P c bO o <H CO cc: <c CO CM m o o o 00 ? -3- o mo o vo o r-cooo CO rH -3" V£> ■5t CM o - rH m in m o o i 1 i o o o cm o^t co o o CM CM CM CM CM CM CM CM CM CM CM O O O ro O00C0 O O CM COO CO O O O O O CM CO OHHOOfOOOfO O O O O O t-rH o o o w o o oo CM it o o\ ■=* co o- - m -3ro rH ocvJcvi^-^wt^OLnocosocvit^ cmoococmcmcm iH^ocorocOr-tcMCMcocOr-iroo mm ooinnHCUH vo^t- cm t-^t-voco moootnH^o t---^- mmo oaco om^cm cm mmmm-=t oooocMcomrHCMmmmcMom COCMrHOACMCTNC^CMCOCMCM OOCOCO CMOOrHCMCMCMCOt-OOOOOOOOOOOOrHrHO-HOOOOHrH mv£> t^co cococoohcj wmm irwo sonen mvo oo OOOOOOOHHHHHHHHHOJWWOJCJCl Eh < • <H S -H H S5 ctf O O A) •a 00 m o^ cd x: a* r-l < CO m rH o H CD u a g CD o •H -P Cd -P CO S • O S S • C C • << • • < • Cd < rH S5 cd • • ca CQ • CQ P, • cd Pi cd co o co co d . cd CO B 00 5 CD *-3 C *-» Cd n ">.(U O 2. 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Whitney* 1. The Orbital Parameters There is no need at present to alter significantly the orbital elements of satellite 1958 Alpha as published in the Harvard Announcement Card 1404, reproduced in Chapter V. It should be noted that the value of^Lis empirical andujis derived from it using the theoretical ratio. 2. The Variable Acceleration During launching, the final stages of 1958 Alpha were given a spin about the body axis. This spin has been expected to stabilize the body axis parallel to the velocity of the rocket at burnout. However, such an orientation was soon discovered to be inconsistent with Smithsonian data on the variations of acceleration of the rocket. Dr. Charles Lundquist of the Army Ballistic Missile Agency informed the writer that radio-signal strength measurements of the Jet Propulsion Laboratory , California Institute of Technology, indicate tumbling ,with a period of about 7 seconds. This period is consistent with the suggestion that a slight dissipation of energy and near-conservation of angular momentum very rapidly led to a reorientation of the body axis into a plane per pendicular to the axis of rotation. The rocket now rotates about the axis of greatest moment of inertia, its angular momentum having been essentially unaltered. ♦ Physicist, Smithsonian Astrophysical Observatory - 15 - In an effort to test this suggestion, the periodchanges of 1958 Alpha have been re-examined. Table I lists normal points for the perigee times as a function of revolution number, counting from the first passage through perigee and computed for the perigee given on H.A.C. 1404. Times are given in 1958 year days and decimals taking January 1.0 = 366. 0. TABLE I Perigee Times of 1958 Alpha Normal Points N T (o-c) N T 0 397.1619(8) +.00009 350 425.07758 - . 00013 50 401.15290 - . 00007 400 429.06215 . 00000 100 405.14304 +.00004 450 433.04572 +.00007 150 409.13187 . 00000 500 437 • 02806 - . 00001 200 413.11963 +.00001 550 441.00932 +.00001 250 417-10645 -.00001 600 444.98940 - . 00002 300 421.09246 +.00002 . . . Changes of anomalistic period are derived by double differentiation of this table. To facilitate the differentia tion and to smooth the data, the following representation of the time of perigee has been derived: T = 397.16189 + 0.07982705N - 1.91 x 10"7N2 + 0.0003fsin (0.0153N) - 0.000062 sin (0.0112N). - 16 - This expression replaces that given on H. A. C. 1404. Differences (O-C) between the normal points and this expression are given in Table I, and the fit is within the uncertainties. The acceleration is then = -3.82 x 10"' - 0.87 10"' sin (.0153N) + 0.078 10" sin (.0119N) Table II lists values of this acceleration. TABLE II Acceleration of 1958 Alpha x 10 7 in days/Rev2) N N Obs. Theo. • Obs. Theo. 350 -3.2 -5-78 -4.09 400 -3.8 -4.95 -4.6 -4.77 450 -4.4 -5.58 150 -4.4 -4.70 500 -4.7 -5.31 200 -3.8 -3.95 550 -4.6 -4.40 250 -3.25 -3.17 600 -3.7 -3.50 300 -3.0 -3.06 0 -3.8 50 -4.4 100 Lundquist has kindly made available a numerical inte gration of the equations of motion— drag included— starting with initial conditions specified by the writer. A value of acceleration some 5.8 tines the observed value was obtained > through choice of parameters. By adjusting the mean value to the observed mean, the column of theoretical accelerations in Table II is obtained. - 17 - The agreement is adequate to confirm the suggested rocket attitude. It is easily shown that the observed accelerations are not compatible with the body axis and the spin axis parallel. Such a direct scaling of the theoretical accelerations is not strictly legitimate because long-period variations are improperly manipulated. However, these latter appear smaller than the air-drag term so the comparison is probably not mis leading. Further, it should be noted that the perigee drops too fast in the integration, accounting for the increase in the mean of the theoretical acceleration. - 18 - The Density of the Upper Atmosphere* By Theodore E. 1. Sterne** Introduction I shall present a formula for the inference of air density from the orbital motion and physical characteristics of artificial earth satellites, and then I shall apply it to orbital data, for the American earth satellite 1958 Alpha, kindly provided me by Dr. Charles A. Whitney. 2. A Formula for Inferring Atmospheric Density from the Motion of Artificial Earth Satellites In a paper in press1 the author has made a basic theoretical study of the effects of air resistance upon the motion of close earth satellites. The first equation of Section 2 of that paper is 4 (1+e c°S E) /g 1° (l-e cos E)1/2 «* • a) where a and e_ are the mean distance of the satellite orbit and its eccentricity, respectively; where^is an operator denoting the increase in one revolution of the quantity upon which it operates, where a is the earth's equatorial radius, where P(r) is the atmospheric density at geocentric distance r, and where E is the eccentric anomaly. In equation (l) c/ is the The formula and conclusions about atmospheric density, article, have been communicated to Science. in this #* Associate Director, Smithsonian Astrophysical Observatory, and Professor of Astrophysics, Harvard University. 1 T. E. Sterne, "An Atmospheric Model, and some Remarks on the Inference of Density from the Orbit of a Close Earth Satellite", Astronomical Journal (in press). - 19 - dimensionless quantity C^A Po ae/m, where A Is the satellite's cross-sectional area, m its mass, Cp the dimensionless aerodynamic drag coefficient that is believed on theoretical grounds to be approximately 2, and P is the atmospheric density at sea level. 1 0 Now a, the time derivative of a, is clearly £a/P where P is the orbital periods Moreover, Kepler's second law states t;hat P varies like a/'2. Therefore P/P = (3/2)a/a, and therefore P = 3Aa/2a. The only important contributions to the integral in (l) come from portions of the orbit near perigee because of the rapid decrease of density with increasing height. If the density P(r) is approximated, through a region near perigee and above it, by r - /v *-KZ where fLls the density at perigee, z is the altitude above perigee, and K is the logarithmic gradient of density near perigee K = -2.3026 (d/dz) log10 p, (2) then the integral can be shown to be given approximately but closely by 7T X I^c) where c = Kae, and where I purely imaginary argument. P= - 37T^DP ae"c7 m 'TT ^ 1 and I, are Bessel functions of It follow that (l+etc.) In(c) + (2e+etc.) In(c) ° x J with rather high accuracy under all conditions. The Bessel functibns can be expanded asymptotically in descending powers of c_, and if this is done equation (3) becomes * - " 3C» 4*. fir ItJ VS" f (°'e) (4) - 20 - where f(c,e) = l+2e + (3e2/2) + l^S=^£ 8c + ^30e+85.5e2 (5) 1280^ correctly to a few percent when e lies between 0. 02 and 0.20 and K exceeds 0.01. Outside these limits, equation (3) is still valid, and may always be used. If a is measured in units of a , 6378 kilometers, results Trom (4) the practical formSla there l/.2 /? - - 4.826 x 10-15 P -BL- -1_ — gm/cm3, (6) '7T A CD a f (c,e) • where P is the rate of change of period in seconds per day, m is the mass of the satellite in grams, A is the satellite's area in square centimeters projected on a plane normal to the direction of motion, Cp is the dimensionless aerodynamic drag coefficient, believed to be approximately 2; a is the mean distance expressed in earth radii of 637o kilometers; c is 6378 Kae if z, in (2), is in kilometers; and f(c,e) is given by (5). An average value of the A of a non-spherical satellite should be used in (2), and for a convex satellite of which all orientations occur with equal frequency the average A is one fourth of its total superficial area. The value of K, somewhat dependent on perigee height, can be approximated by applying equation (l) somewhat above perigee to a model atmosphere like the ARDC. Alternatively, K may be determined without reference to assumed models by applying equation (5)> or (3)* to two or more satellites with different perigee heights and adjusting K until it is consistent with the resulting perigee densities. I am indebted to Dr. G. P. Schilling for urging me to develop some simple, approximate, formula. R. A. Minzner and W. S. Ripley, "The ARDC Model Atmosphere, 1956". Air Force Surveys in Geophysics, No. 86, Geophysics Research Directorate, APCRC, ARDC, December 1956. - 21 - 3. Density inferred from 1958 Alpha Dr. Charles A. Whitney provided orbital data for the American artificial satellite 1958 Alpha, as of February 1, 1958. The data, 3 which he obtained from an analysis of "Moonwatch" (visual) and "Minitrack" (radio) observations, were: eccentricity 0.139, Inclination 33° • 2, argument of perigee 120°. 0, anomalis tic period 0d. 0798274, rate of decrease of period 3.9 x 10-7 days per period or about 0s. 42 per day. From these data I have inferred a mean distance of 1.22757 earth radii, corresponding to a perigee height above the international ellipsoid of 368 kilometers. The satellite is^ a cylinder 6 inches in diameter and 80 inches long, with a mass of about 14 kilograms. The area A of such an object, relevant to its air resistance, is its area projected on a plane normal to its direction of motion. The average over all possible orientations for random tumbling is l/4 of the total superficial area, or 2520 cm2. The same value is obtained if it is considered that the cylinder spins about a transverse axis, randomly oriented with respect to the orbital plane, and gradual orbital changes influence the orientation of the spin axis near perigee from passage to passage. Averaged over a spin period, over orientations of the spin axis with respect to the orbit plane, and over the motion of perigee the same average value is obtained as for random tumbling, 2520 cm2; this value has been employed as A in equation (6). The aerodynamic drag coefficient has been taken to be 2. The density has been inferred by the method described in Section 2 of this article from this value, the mass, the average area, the eccentricity, the mean distance, the rate of decrease of period, and the logarithmic derivative of density near perigee given by the ARDC model atmosphere. -l4 / "3 The density thus found, about 1.5 x 10 gm/cm-' at a geometric altitude of 368 kilometers (348 geopotential) is about 14 times that predicted at such an altitude by the 3 See also Harvard College Observatory, Announcement Card 1404 (1958). 4 Harvard College Observatory, Announcement Card 1390 (1958). - 22 - ARDC model. It falls nearly on the middle curve, No. 2, in a study5 that tentatively suggested a modification of the ARDC atmospheric model to satisfy a density of 4.5 x 10-13gm/cm3 at 220 kilometers (213 geopotential) that had been inferred" from observations of the USSR satellite 1957 Alpha 2. This value was about 9 times the ARDC density. The values 4.5 x lO"1^ gm/cm^ and 1.5 x 10-1* gm/cm3 depend somewhat, although not strongly, upon the gradients of density of the ARDC model employed in the reductions. It seems better to adjust the model so as to render it consistent with the perigee densities that result from the K's of the adjusted model. A formal least- squares adjustment has not yet seemed warranted but a non- least- squares adjustment, allowing for the effect of the adjustment upon K, has indicated densities of about 4.0 x 10-13 gm/cm3 at 220 kilometers (geometric) and about 1.4 x 10-14 gm/cm3 at 368 kilometers (geometric). These values do not agree well with the densities predicted by Harris and Jastrow7 as extrapolations from altitudes of about 220 kilometers and below. They appear to be in unexpectedly good agreement with curve -No. 2 of reference 5, do not involve any very implausible temperature gradients, and I prefer them. 4. Adjustment of the ARDC Atmosphere The preferred values at 220 and 368 kilometers can be represented by an additive correction to the common logarithm of the density of the ARDC model, of roughly 0.89 + 0.0016 (z - 220) where z is the geometric altitude in kilometers above sealevel. 5 T. E. Sterne, G. F. Schilling, and B. M. Polkart, Special Report No. 7, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge (1957)* Figure 2. 6 T. E. Sterne and G. F. Schilling, Special Report No. 3, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge (1957). I. Harris and R. Jastrow, Science 127, 451 (1958). - 23 - Life Expectanpy^f Satellite 1958 Alpha Luig<xJ&. Jacchia* Dr. D. G. King-Hele of the Royal Aircraft Establishments, Farnborough, England, has kindly transmitted to us a useful formula developed by Dr. D. C. M. Leslie for computing the lifetime of a satellite. #At a given time t let P be the period of the satellite, P the rate of change of the period, and e the orbital eccentricity. The life expectancy of the satellite at time t can then be expressed as T = ^ e [l + O (ejj j (T°(e) = errors of order ej This equation gives excellent results when applied to satellites 1957 <xl, 1957 o2 and 1957 (3. According to Dr. Charles A. Whitney,1 on February 1, we had for satellite 1958 a: P = o?crT983; P - -4?78 x lOVday; 1958 e - 0.139- From these data Leslie's formula yields a life expectancy of 1740 days, or 4 years and 9 months; the satellite should then fall toward the end of 1962. Before the value of P became accurately known from observations, a rough calculation of the drag to be expected on the basis of the physical characteristics of the rocket satellite and of the Smithsonian Interim Atmosphere^ densities had given a predicted value of -5d7 x 10^/day for P, from which a life expectancy of 3 to 5 years was "deduced. Physicist, Smithsonian Astrophysical Observatory Harvard Announcement Card No. 1404; March 17, 1958. T,UE. Sterne, B. M. Folkart, and G. F. Schilling: "An Interim Model Atmosphere Fitted to Preliminary Densities Inferred from USSR Satellites". Special Report No. 7, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, December 31 > 1957. - 24 CHAPTER IV USE AND DISTRIBUTION OF SATELLITE PREDICTIONS by R. M. Adams* r The individual sections of this Chapter discuss in detail the various ephemerides, or computer programs, used by the Smithsonian Astrophysical Observatory for the ana lysis of incoming observational data. The sub-satellite program, developed by Dr. L. Q. Jacchia, is a computer program used internally to rapidly analyze incoming observations and to derive the basic information for the computation of search ephemerides. The program was devised by Dr. Jacchia and originally programed for the IBM type 650 computer by R. E. Briggs. It was later trans lated for use with an IBM type 704 Calculator by C. T. Apple. Ephemeris 5, described by John Gaustad, produces sa tellite predictions of a nature which are useful for Moohwatch and other observing teams and, in addition, are also of interest to the general public. These predictions are easily obtained and can be distributed readily. Normal operating procedure consists of mailing these predictions to Moonwatch teams, astronomical observatories, and other groups of interested observers on a regular basis. The predictions are normally accompanied by the orbital elements used in making the predictions. These predictions are also used for constructing the charts described by Pairman and Veis. Ephemeris 4, discussed by Charles Moore and Don Lautraan, is designed to produce precise predictions for the twelve photographic tracking stations established throughout the world by the Smithsonian Astrophysical Observatory. These predictions are sent in coded form by telecommunication channels on a day by day basis. Ephemeris 3, discussed by R. Briggs, is designed to produce a sequence of predictions for particular stations in the nature of time, azimuth, altitude, height, and dis tance for the latitude crossing, and time, altitude, and distance for the meridian crossing. Although it was ori- * Chief, Computations and Analysis Section, Optical Sa tellite Tracking Program, Smithsonian Astrophysical Observatory - 25 - ginally felt that predictions of this nature would be neces sary for the individual observing stations, this has not proved to be the case. Due to the comparatively large amount of machine time required for these predictions, it is now felt that they will be made only in particular applications when the situation warrants. The charts of predicted satellite positions, described by Jean 6. Fairman and George Veis, were originally intended for internal use and, incidentally, for presenting predictions to interested news agencies in a form convenient for public use. However, the use of these charts has been extended. They now provide information which is broadcast over the Civil Air Patrol Communications Network, thus enabling rapid dissemination of predictions. Arrangements have been made whereby observing teams are contacted daily by CAP units providing the most recent predictions of satellite passages. To a great extent, this arrangement alleviates the problem encountered in distributing predictions by mail. This is particularly true, of course, in those instances in which it is impossible to make accurate predictions for more than 3 or 4 days in advance due to fluctuations in the rate of a satel lite's acceleration. - 26 - Program for Determination of Geographic Sub-Satellite Points by Luigi Q. Jacchia* The sub-satellite-point routine was devised for the double purpose of rapidly analyzing incoming observations and of obtaining from them the basic results necessary to compute a search ephemeris. Osculating equatorial elements are assumed for a time tQ (either an ascending node or a perigee crossing) and instantaneous elements are derived from them for any time t, using empirical equations to account for secular perturbations and drag. The elements are given in the following form: t^ (or t^ ) - tQ + G-jn + c2n2 + c^n^ cj = dQ + dxt + d2t2 + d^t^ i = constant q = constant Here Uis the time of ascending -node crossings, the time of""perigee crossings , co the argument of perigee, i the orbital inclination, q the perigee distance, and n the number of revolutions elapsed since t0; c^, Co , c3 ' dn>dl< d2> d3 are constants. The right ascension of the ascending node, aj^, is given only in crude form ( QL.X= ao + OLt), since it is required only to know whether the observation was made on the ascending or the descending half of the orbit. Every observation consist of two spherical co-ordinates (right ascension and declination, or azimuth and altitude) referred to a time t and to a set of station co-ordinates, which are fed into the machine program as input data. First the machine computes the value of n at the node or perigee crossing immediately preceding t, then computes the nodal or anomalistic period for that value of n by differentiation of t^o* tjj. t proceeds to compute from It the ♦Physicist, Smithsonian Astrophysical Observatory. - 27 - instantaneous major axis a and the eccentricity e. The height above the sea level at the time of observation is obtained by an iterative process - first it is computed for an orbital point at the latitude of the observing station; using this height, an approximate sub-satellite point is computed, for which in turn a new height is ob tained using its latitude; this gives a new approximation to the sub-satellite point, and so on. Once the sub-satellite point is stabilized, instantan eous values of o^and t^ are computed from it using the orbital elements; residuals are taken for both quantities from empirical equations to facilitate the task of plotting their values on large-scale diagrams . The program gives somewhat uncertain results when the observations are made near the orbital apex (the point of highest or lowest latitude). In those cases, if a» is well known from other observations, the iteration for the sub-satellite point can be made to start from 0% instead of #'(0% = right ascension of station, f3' = geo centric latitude of station) . The times t0 and tT will still be useable, although no independent value of a can thus be obtained. °^ - 28 - Predictions for Crossings of Given Latitude Parallels — APO- Ephemeris 5 by John Gaustad* Ephemeris 5 is a general satellite prediction program written for the IBM 704 computer. It is designed to pre pare a concise summary of predictions in a form easily usa ble by observing teams and other interested parties and yet general enough for quick production and distribution. It is not intended to have the specific applicability of Ephemerides 3 and 4 to individual M00NWATCH or camera tracking stations, but because of its generality it takes relatively little computer time. The program produces as its primary output a list of all crossings of a parallel of latitude in a specified period of time. It lists for both the south-north and the north-south crpsaings the time of crossing, the longitude, and the height of the satellite above the earth's surface. The angle at the point of crossing between the meridian and the trace of the satellite path on the earth's aurface is also computed. The program is general enough so that it can be used for any satellite and any parallel of latitude . For the Russian satellites, 1957 Alpha and 1957 Beta, the most useful information was the crossings of the 40th parallel, this being about the middle of the United States . For the American satellites, because of their lower inclination, 30th parallel crossings are the most generally used. The program can also be used in making predictions for the southern hemisphere. The format of the predictions can be varied by the use of code numbers on the input cards . Times may be com puted and printed in either Universal Time (UT) or Eastern Standard Time (EST) , longitudes in degrees west or east of Greenwich^ and heights in either miles or kilometers. ♦Physical Science Aide, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. - 29 - In addition the results may be rounded to the nearest minute, tenth of a degree, and mile, or one hundredth of a minute, one thousandth of a degree, and one hun dredth of a mile, for time, longitude, and height, respectively . The elements necessary as input data for the pro gram are as follows : an equation either for the time of crossing the ascending node or of passage through perigee as a function of the number of revolutions, quadratic equations in time for the argument of perigee and the right ascension of the ascending node; the in clination; and the perigee distance. The perigee dis tance is assumed to be constant over the range of pre diction. Prom these elements the predictions are made using the standard equations for an elliptic orbit. Secular and long period perturbations causing changes in the argument of perigee and right ascension of the node are accounted for in the quadratic equations for these elements. Atmospheric drag is accounted for empirically in the equation for time of nodal crossing or perigee passage. Short period perturbations are not included. The semi-major axis is computed directly from Kepler's Third Law, using either the nodal or anomalistic period, depending on the form of the time equation. This leads to some error in the heights, but for the present satellites, this does not exceed one mile. A secondary part of the program is concerned with producing a "situation" report which gives the most pertinent facts about a satellite's orbit. Computed for any day are the period, rate of change of period, latitude of perigee, rate of change of latitude of peri gee, height of perigee, height of apogee, rate of change of height of apogee, and height over a specific parallel of latitude (4oth for 1957 Alpha and 1957 Beta, 30th for 1958 Alpha and 1958 Beta) for both the south-north and north-south crossings . The program is in operating condition and has been used successfully for the past several weeks in making predictions for the U. S. satellites. Changes are con templated in the future to incorporate a more accurate method of determining the heights . Tests will be made to insure that the program works properly for special cases such as inclinations greater than ninety degrees (retrograde satellites) . - 30 - Predictions for Photographic Satellite Tracking Stations — APO Ephemeris 4 by Charles H. Moore* and Don A. Lautman** Ephemeris 4 is the computer program for predicting satellite positions for the Baker-Nunn camera stations. The present formulation utilizes the currently best set of elements available, accounting for the drag by means of a polynomial in the mean motion, and including only secular perturbations. The prediction subroutine is a numerical integration which includes the effects of oblateness and drag exactly. In the case of satellites which are high enough so that drag can be neglected, a complete first-order perturbation theory including periodic per turbations can be used. The basic requirements demanded of predictions in tended for camera stations are: (1) predictions must be limited to observable passes and (2) predictions must be made for the point of culmination. The optimum approach would be to integrate the equation of motion for the sa tellite, obtaining these predictions, as well as other data, directly. However, a quicker, though less accurate, method is discussed here, which has been developed in an attempt to obtain predictions as soon as possible. This program for the IBM EDPM 704 employs the orbital elements of the satellite and transforms them by graphical (trigonometric) means into specific predictions. The ac curacy of the predictions is well within the accuracy of the orbital elements employed, and is probably the best that can be gotten without employing more sophisticated methods, and is fitted to the requirements of the Baker-Nunn tracking cameras . The input to the computer consists basically of the coordinates of the stations (latitude, longitude and height above sea level) and the orbital elements. The latter in clude the time at which the satellite is at the ascending * Physical Science Aide, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory ** Mathematician, Optical Satellite Tracking Program, Smith sonian Astrophysical Observatory - 31 - node (or at perigee) , the right ascension of the ascending node, the argument of perigee, the inclination of the orbit to the equatorial plane, the value of perigee, and the ec centricity of the orbit. Time is given as a polynomial in the number of revolutions, from which the period can be determined; position of the ascending node and perigee are polynomials in time; the other elements are instantaneous values at an arbitrary, specified time. Additional input data includes positions of the vernal equinox and the sun for January 0 of the current year, and the dates for which predictions are desired. The program follows the general outline listed below: (1) (2) (3) (4) Reduces the station coordinates to more con venient form. Updates the instantaneous values of the orbital elements. This is done each revolution. Computes the point of entry into and exit from the earth's shadow. This data may be printed out if desired. It is useful for general pre dictions where great accuracy is not expected. Computes the position of culmination for each station, determines whether the conditions for visibility from the stations are fulfilled, and if so prints that information. There are three distinct portions of the output. First, the latitude, longitude and time of entry into or exit from the earth's shadow. Second, the altitude, azimuth, range, angular velocity, and time of culmination of visible passes for each station. The conditions for visibility employed require that the satellite be visible at least 15° above the horizon and be illuminated by the sun, while the station is inside the earth's shadow. No restriction is placed upon the photographic magnitude of the satellite. Hence, the range is printed to be taken into consideration when using the pre dictions. Angular velocity is useful for tracking purposes. The third portion of the output is essentially the sta tion prediction described above, however, it is put into a code suitable for teletype transmission, which may be sent directly without further reworking. Thus, the program computes predictions over a specified interval of time and supplies the following information at each visible passage of a station: (1) Altitude and azimuth of the point of closest approach . - 32 - (2) (3) (4) (5) 16) (7) Time of closest approach. Apparent angular velocity. Angle between point of closest approach and passage into or out of the earth's shadow. Time of intersection with the earth's shadow. Distance of the satellite. Zenith angle of the sun. The advantages of the program are an expected minimum of computation time, and the elimination of superfluous data, namely non-observable predictions. With such a program, predictions can be made to the necessary accuracy as soon as orbital elements are available. The disadvantage of the pro gram is its dependence upon the independently determined or bital elements. - 33 - Program of Spot Predictions for Specific Observing Sites — APO Ephemeris 5 by R. Briggs* This program computes for a given observing station a sequence of satellite positions in altitude -azimuth and corresponding times. This sequence comprises all the ob servable (visual or otherwise) latitude and meridian crossings which will occur within a specified interval of time. Ac curacy is limited at the present to the use of first and second derivatives' of the nodal period, to the use of first derivatives in the Motions of perigee and the node, and to the assumption of constant perigee distance. When the ef fects of air drag are included under these restrictions, experience has shown that over two weeks the positions may be in error by at most four degrees and the times in error by a few seconds. As yet, Ephemeris 3 has not been used for the American satellites. It is planned to make minor revisions in the program so that the anomalistic period of the satellite can be used in place of the nodal period. Further, derivatives of the anomalistic period will include trigonometric and/or exponential terms. These changes are presently being deve loped and the program will see use when the operational si tuation warrants the comparatively large amount of machine time required. * Mathematician, Smithsonian Astrophysical Observatory - 34 - Charts of Predicted Satellite Positions by Jean B. Fairman* and George Vels** In an effort to provide more information in forms immediately useful, without considerable computation, for observers in the U.S. and readily understandable to the general public, we have made our prediction data avail able in several forms other than the formal Ephemerides, the primary prediction material sent by mail. 1. Visibility Maps The first of these additional distribution operations was our production for the newspapers, wire services, and networks of daily maps of the northern hemiphere showing the visible passes of the satellites. The aim of this distribution has been to encourage the publishing of these maps and/or satellite predictions on a daily basis by the papers both for the specific information of our many observers and for the interest of the general read er, as a supplement to the sometimes delayed mail deliver ies. To date, they have been regularly picked up by the Associated Press and sent to New York for distribution, although their correspondent reports a general lack of interest among subscribing papers. A sample of these maps is shown. following this section. Each map contains all visible passages of the satellite for the morning or evening twilight period of a given day, and shows in an easy to grasp fashion the time, location and direction of the pass relative to the observer, who can locate himself easily on the map. The maps are designed to appear as simple as possible, with a legend briefly explaining the meaning of the outlines (omitted in the samples). ♦Computer, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. ♦♦Consultant, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. - 35 The visible portion of each passage is shown as a solid line, and its dashed extension represents the nonvisible interval of the orbit which lies within the area of general visibility. Each of the cross bars on the satellite path represents a minute of travel, so that the time of the satellite's passage over any point can easily be determined. The dot separating the solid and dashed orbit locates the point at which the satellite enters or leaves the earth's shadow, and the line which interrupts the opposite end of the visible orbit represents the 6° twilight (Civil Twilight) boundary. The closed dotted or dashed form encloses the complete area within which the satellite may be seen above 15° altitude. In addition to the twilight boundary, the other sides of the area show the distance from which the satellite may be seen, as a function of its height. In spite of the relative simplicity of the diagram, Its construction incorporates corrections for the following factors, which give it a reasonably good de gree of accuracy: (1) Inclination of the orbit. (2) Period or speed of the satellite — this affects the time markings on the satellite path. (3) Eccentricity and true anomaly. Corrections for these factors further refine the time Intervals. (4) Height of the satellite. Distances of visibility and location of the earth's shadow depend on this factor. (5) Rotation of the earth. This affects the longi tude of the sub-satellite points . (6) Regression of the ascending node. This correction further locates the points over which the satellite will pass (7) Changes in the coordinates of perigee. Correction for this adds to the accuracy of the height and period adjustments. (8) Changes in the declination of the sun. This revision updates the twilight time limits and position of the earth's shadow. - 36 - (9) Changes in the Greenwich Hour Angle of the sun. This correction refines the time designations around the earth. The production of these maps was begun for Satellite 1958 Alpha on February 26, in anticipation of the visibility period which lasted from about February 27 to March 27. The maps have been produced and distributed regularly throughout the period, including a total of 30 daily projections of visible passages of 1958 Alpha. 2. Modified Maps In a further effort to encourage the regular publishing of satellite data, we have cooperated with various publica tions in drawing up modifications of the standard, individual maps. The most successful venture of this sort to date have been the modified maps carried by the New York Times from March 19, when visibility of all the satellites was at its peak, through March 22, when visibility from the U. S. was diminishing. These particular modified maps combined in one illustration the visible paths of all the satellites, showing the time intervals of visibility for each passage, but ^omitting for simplicity the areas of visibility. In this map, Satellite 1958 Alpha is represented by the heavier orbital paths, the lighter paths describing Satellite 1957 Beta one. Those visible passages which terminate in an arrow actually move out of visibility beyond the margins of the page. The particular map included here, for comparison with the first, was sent to the Times before Satellite 1958 Beta was launched and so does not include it, although it was added by the paper before publication. We hope to establish this sort of regular publication even more firmly during the next visibility period. 3* Broadcast Releases Realizing that even if a large percentage of news papers published the maps, that some observers would still not be reached, we have arranged through the efforts of the U. S. National Committee for the International Geo physical Year and the cooperation and facilities of the Civil Air Patrol, to get our predictions to the observing teams and the public through the Civil Air Patrol 1 s scheduled shortwave broadcasts. This program operates - 37 hand-in-hand with the "Relative Position Grid" kit issued by the U.S. National Committee of the I.G.Y. to all observing teams, which allows these observers with the addition of our specially tailored prediction messages, to produce for themselves "maps" giving the same sort of information which our regular maps would otherwise supply. In addition to the channels of communication supplied by the Civil Air Patrol, we have been aided in getting these predictions onto the air by the American Radio Relay League . When the last visibility period began on February 27 , we started -sending these special predictions to the National Academy of Sciences for relay to the Civil Air Patrol broadcast stations, and are now sending the predictions directly to four Civil Air Patrol Stations, across the country. These predictions were issued regularly for Satellite 1958 Alpha throughout the last visibility period until March 27. During the subsequent period of no visibility, a statement is substituted for the regular messages to that effect. These three areas of activity, then, are the means by which we have to date attempted to supplement the mailings of standard 30th Parallel Crossings in order to get the needed information to observing teams in this country in an easy to use form, which can readily be revised and corrected without time lapse to provide the very latest information, on time. We have had an encouraging measure of success in this area, and anticipate further benefits from these efforts. CO Id CO Id Z P - 40 - CHAPTER V HARVARD ANNOUNCEMENT CARDS Announcement Card 1390 Satellite 1958*. — The U.S.A. National Committee for the International Geophysical Year has announced that an instrumented earth satellite was placed in orbit on Feb ruary 1, 3fi55m058 U.T. at a point approximately 25°. 84 N and 73°. 61 W. It was launched by a U.S. Army Jupiter C rocket on February 1, 3n48m U.T. from Cape Canaveral, Florida at 28°. 5 N and 80°. 6 W. Including the empty rocket casing of the last stage, the satellite weighs about 30 lbs, is cylindrical in shape with a length of 80 inches and a diameter of 6 inches. It contains two radio transmitters; amplitude modulated trans mission at 108.03 mc with power level of 50 milliwatts; phase modulated transmission at 108.0 mc with power level of 10 milliwatts; telemetry of data by both transmitters. The surface of the visible with binoculars fic experiments include impact, and temperature February 1, satellite is white and may be under optimum conditions. Scienti cosmic ray observations, meteoric measurements. 1958 Fred L. Whipple Announcement Card 1393 Satellite 1958a. Dr. Paul Herget and Dr. Raynor L. Dun combe of the Naval Research Laboratory in Washington, D.C. have obtained the following preliminary orbital elements for Satellite 1958& from analysis of Minitrack observations extending over the first 32 revolutions, for 3h58m U.T. on February 1, 1958: Minimum Height Maximum Height Period Eccentricity Inclination Longitude of Ascending Node Argument of Perigee Mean Anomaly at Epoch Semi-major Axis 219 miles 1587 miles 114.95 minutes 0.14052 33°. 58 342°. 95 (motion -4.26 per day) 120°. 76 (motion +6.31 per day) 14°. 68 1.2278 earth radii - 41 - The following optical observations of Satellite 1958*x have been received from Moonwatch teams: Date February Time Ü.T. Position R.A. Dec. Type of Obs. 2 Alamogordo, New Mexico , (Lat. 32°. 52' 24fl N Long. 105° 57' 02" W) 2h45m54s 4h54m ±5m +33°06» vis. +8 mag. 3 Manhattan, Kansas AL»t. 39°109'.75 N Long. 96° 28'. 85 W) ln44m168 5*37* -1°40' vis. +5 mag. 3 Alamogordo, New Mexico (Lat. 32° 52' 24" N Long. 105° 57' 02" W) 3h^&a10s 5h23m +14°54' vis. +8 mag. China Lake, (Lat. 35°. 657 N 2h24m42sAz. N 177°. 25 E 6 February 5, California Long. 117°. 663 W) Alt. 71° vis. 1958 Fred L. Whipple Announcement Card 1404 Satellite 1958a. — Dr. Charles A. Whitney of the Smithsonian Astrophysical Observatory has obtained the following orbital elements for Satellite 1958a from an analysis of MOONWATCH and Minitrack observations through March 3, 1958: Epoch and Time at Perigee e = .139 q = 1.0566 1958 Feb. Q = 1.3985 ld 3h 52m 53s (apogee distance) i = 33°. 19 .a-3430. 4 cj=120°.0 Times at Perigee 1.16182+ 0.798274 N x 10'7N2 Feb. + 0.00025 sin. .0177 - 1.910 (N - 20) Motion of Perigee and Ascending Node (deg/day) cj= 6.334 £h = -4.237 March 17, 40.00084 (T - 0.00059 1958 - Feb. 1.0) (T - Feb. 1.0) Fred L. Whipple IGY Satellite Report Series Number 3 IGY WORLD DATA CENTER A ROCKETS AND SATELLITES NATIONAL ACADEMY OF SCIENCES SOME IN PRELIMINARY REPORTS OF EXPERIMENTS SATELLITES 1958 ALPHA AND 1958 GAMMA NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, D. C. IGY World Data Center A_ frV) G&ockets and Satellites. National Academy of Sciences Washington, D.C. [iGY Satellite BTtCT Number 3 May 1, 1950 SOME PRELIMINARY REPORTS OF EXPERIMENTS IN SATELLITES 1958 ALPHA and 1958 GAMMA Contents 1. 2. 3. Status Reports On Optical Observations of Satellites 1950 Alpha and 1953 Deta, edited by G. F. Schilling (Excerpted from IGY Satellite Series, Number 2, IGY World Data Center A, Rockets and Satellites.) The Determination of the Orbit of 1958 Alpha . at the Vanguard Computing Center, (Joseph W. Slry, Naval Research Laboratory) Satellite Micrometeorite Measurements (E. Manring and M. Dubin, Geophysics Research Directorate, Air Force Cambridge Research Center) 1 17 25 4. Satellite Temperature Measurements for 1958 Alpha (External Publication No. 481, Jet Propulsion Laboratory, California Institute of Technology; E. P. Duwalda and A. R. Hibbs) .... 31 5. The Observation of High Intensity Radiation by Satellites 1958 Alpha and Gamma (J. A. Van Allen, G. H. Ludwig, E. C. Ray, and C. E. Mcllwain, State University of Iowa) 73 KCAGEMr OF LIBRARY MAY 2 7 This report is issued in accord with inter national arrangements on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies available at cost to scientists upon their request. These data and/or report contents are re produced as received from the experimenter. Recipients of these reports are advised to communicate with the authors prior to utiliza tion of experimental data for further pub lication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites 1. STATUS REPORTS ON OPTICAL OBSERVATIONS OF SATELLITES 195C ALPHA AND 1958 BETA Edited by: G. F. Schilling I. III. preliminary Results from Optical Tracking of U.S. Earth Satellites, J. Allen Hynek and Fred L. Whipple Scientific Results: The Orbit and Variable Acceleration of Satellite 1958 Alpha, Charles A. Whitney Excerpts from IGY Satellite Series No. 2, IGY World Data Center A, Rockets and Satellites (Original Source: Special Report No. 11, Smithsonian Institution Astrophysical Observatory, Cambridge, Massachusetts). CHAPTER I PRELIMINARY RESULTS PROM OPTICAL TRACKING OP U. S. EARTH SATELLITES by J. Allen Hynek* and Fred L. Whipple** In the satellite program of the International Geo physical Year the complex operations performed by the Op tical Satellite Tracking Program of the Smithsonian Astrophysical Observatory are a result of teamwork in the fullest sense of the word. The manifold tasks include the visual acquisition of the artificial earth satellites, the com putation of search ephemerides and predictions, the opera tion of a world-wide network of precision tracking cameras capable of photographing small objects at distances of hun dreds of miles and timing these photographs to better than a thousandth of a second, the screening, reduction, and analysis of incoming data, and last but not least, the dis semination of the reduced data to the scientific community. Remembering that since October 4, 1957, there has been a total of eight objects projected into satellite orbits, we hardly need to point out that the efforts expended by thousands of persons, including the volunteer Moonwatch team members, in the Optical Tracking . Program alone are outstanding. With great scientific enthusiasm and satisfaction, our staff members have participated in this undertaking, ofton well beyond the normal call of duty. We have not not«£ eimilar dedication save in times of national emergency. The cooperation of the U. S. Naval Research Laboratory in furnishing us with critical prediction data for satellites with live radio*- has been of major importance. Also, the computation of ephemerides and orbital data would have been virtually impossible without the generous cooperation of the International Business Machines Corporation and the Compu tations Laboratory at the Massachusetts Institute of Tech nology in Cambridge. * Associate Director, Smithsonian Astrophysical Observatory, in charge of the Optical Satellite Tracking Program ** Director, Smithsonian Astrophysical Observatory 2 3 The subsequent sections of this collection have been prepared Individually by members of the Smithsonian Astrophysical Observatory who are actively working in this particular field and therefore best able to present a factual and informative account of the respective aspects of the program. In this initial chapter, we wish to summarize as well as outline from an overall point of view the orbital data and results which we have been able to obtain with regard to Satellites 1958 Alpha, 1958 Beta One, and 195° Gamma. The mainstay of the long-range optical tracking pro gram Is the worldwide network of precision photographic stations, employing at each observing station a 3-axis, 20-inch aperture, f/1 camera designed especially for the photographic tracking of artificial earth satellites. The optics for these cameras were designed by Dr. James 0. Baker, and constructed by the Perkln-Elmer Corporation. They employ a unique 3-corrector lens system having 4 aspherical surfaces, in combination with a 31-inch con ventional spherical mirror, providing a useable field of 30°. The motor —driven mechanical drive provides se quential tracking of a satellite and of star background on the same 250 x 55 mm. film frame, in cyclical succession so that many individual photographs can be obtained during a given satellite passage. The unique mechanical system was designed by Mr. Joseph Nunn and fabricated by Boiler and Chlvens, Inc., all of South Pasadena, California. The urgency Imposed upon the optical tracking program by the launching of the Russian satellites made it de sirable to expedite the construction of the stations and to obtain the use of auxiliary cameras to go Into operation before the arrival of the Baker-Nunn cameras. Through the excellent cooperation of the Ballistic Research Laboratory we have obtained the use of two S M T (Small Missiles Telecamera) instruments. In addition, several phototheodolites have been furnished through the courtesy of the U. S. Air Force, thus making possible the completion at any earlier date than otherwise possible an effective tracking network. As discussed by Karl G. Henize in his report, the full complement of Baker-Nunn cameras is ex pected to be in operation by mid June. 4 For an artificial satellite tp be tracked most-effectively for scientific purposes, the tracking accuracy must be of the order of seconds of arc and of 0.001 seconds of time. A crystal clock of extreme precision has been built by the Ernst Norrman Laboratories, Williams Bay, Wisconsin-, for each of the twelve observing- stations . (The time presentation within each camera is photographed on each frame. It can be stated that the scientific value of a satellite for many geophysical . purposes rises greatly with its longevity. Precision observations » of non-aspherical,« close artificial satellites are of little value in solving major geodetic problems because of the variable motion introduced by vary ing orientation and the- consequent irregular drag. Pence the present schedule in • establishing the precision- camera programs has occasioned, little scientific loss. This more leisurely program has more than offset this loss, in terms of improved optical and -mechanical performance. The successful photographs of the first two American satellites by several Of the network stat'ions is a grati fying signal of the routine, tracking soon to be effected. ' The establishment of- the photographic network would not have been possible without* the cooperation of several foreign governments. Particular note must be taken of the great assistance received through the respective I-iG.Y. committees from the governments of Argentina, Australia, India... Iran, Japan, Netherlands Antilles, Peru and the Union of South Africa. Their sympathetic appreciation of the urgency of the total program has been indispensible, and our work in those several countries has been carried out in a thoroughly cooperative manner appropriate to the spirit of the Inter national Geophysical year. An integral part of the optical tracking program, complementary to the precision program, is the far-flung visual observing project termed MOONWATCH. Conceived primarily as an acquisition and reconnaissance mission to cover periods immediately after launching and shortly be fore demise, in final stages of the existence of a satellite, MOONWATCH teams have served continuously" • as interim tracking stations during the period of final preparation of the photographic tracking stations . The exemplary work of the several thousands of persons involved in this program stands out as a significant contribution to the satellite program, and an outstanding example of lay participation in an international scientific venture. Largely through the use of MOONWATCH observations, the computations and analysis division *of Smithsonian, Astrophyslcal Observatory has been able to derive signifi cant, even through preliminary, scientific results. These are treated In Chapter III and Include the orbit deter mination of 1958a and an evaluation of the variable acceleration of this satellite and of Its life expectancy With respect to 1958f32> perigee distance is so relatively high that little can be said of Its life expectancy save that In all probability It must be counted In decades. Its rocket carrier, 19583^ will probably have a significantly shorter lifetime"!" but still perhaps a decade or more. Various computational programs have been devised, and others are in process,, for the utilization of satellite observations for prediction purposes as contrasted to their use for results of geophysical interest. Ephemerides for general use as well as for specific use at given geographical points have been programed; an example of the latter is the program which prints out actual Baker-Nunn camera settings which ban be cabled directly to the network stations . Implicit in the prediction program is the objective to disseminate not only specific predictions but general satellite Information of an astronomical character to the public through the several mass media. This we have recognized and met by concise statements to the press and by the preparation of charts illustrating visible passages of satellites over the United States. 6 CHAPTER III SCIENTIFIC RESULTS The Orbit and Variable Acceleration of Satellite 1958 Alpha By Charles A. Whitney* 1. The Orbital Parameters There is no need at present to alter significantly the orbital elements of satellite 1958 Alpha as published in the Harvard Announcement Card 1404, reproduced in Chapter V. It should be noted that the value of^/iis empirical andujis derived from it using the theoretical ratio. 2. The Variable Acceleration During launching, the final stages of 1958 Alpha were given a spin about the body axis. This spin has been expected to stabilize the body axis parallel to the velocity of the rocket at burnout. However, such an orientation was soon discovered to be inconsistent with Smithsonian data on the variations of acceleration of the rocket. Dr. Charles Lundquist of the Army Ballistic Missile Agency informed the writer that radio-signal strength measurements of the Jet Propulsion Laboratory, California Institute of Technology, indicate tumbling ,with a period of about 7 seconds. This period is consistent with the suggestion that a slight dissipation of energy and near-conservation of angular momentum very rapidly led to a reorientation of the body axis into a plane per pendicular to the axis of rotation. The rocket now rotates about the axis of greatest moment of inertia, its angular momentum having been essentially unaltered. Physicist, Smithsonian Astrophysical Observatory 7 In an effort to test this suggestion, the periodchanges of 1958 Alpha have been re-examined. Table I lists normal points for the perigee times as a function of revolution number, counting from the first passage through perigee and computed for the perigee given on H.A.C. l404. Times are given in 1958 year days and decimals taking January 1.0 = 366. 0. TABLE I Perigee Times of 1958 Alpha Normal Points N T (o-c) N T 0 397.1619(8) +.00009 350 425.07758 - . 00013 50 401.15290 - . 00007 400 429.06215 . 00000 100 405-14304 +.00004 450 433.04572 +.00007 150 409.13187 . 00000 500 437.02806 - . 00001 200 413.11963 +.00001 550 441.00932 +.00001 250 417.10645 -.00001 600 444.98940 - . 00002 300 421.09246 +.00002 Changes of anomalistic period are derived by double differentiation of this table. To facilitate the differentia tion and to smooth the data, the following representation of the time of perigee has been derived: T = 397.16189 + 0.07982705N - 1.91 x 10" 7N2 + 0.00037 sin (0.0153N) - 0.000062 sin (0.0112N). 8 This expression replaces that given on H. A. C. 1404. Differences (O-C) between the normal points and this expression are given in Table I, and the fit is within the uncertainties. The acceleration is then || = -3.82 x 10"7 - 0.87 10"7 sin (.0153N) + 0.078 10"7 sin (.0119N) Table II lists values of this acceleration. TABLE II Acceleration of 1958 Alpha (4| x 10 7 In days/Rev2) N Obs. Theo. N Obs. Theo. 350 -3.2 -3-78 -4.09 400 -3.8 -4.95 -4.6 -4.77 450 -4.4 -5.58 150 -4.4 -4.70 500 -4.7 -5.31 200 -3.8 -3.95 550 -4.6 -4.40 250 -3.25 -3.17 600 -3.7 -3.50 300 -3.0 -3.06 0 -3.8 50 -4.4 100 Lundquist has kindly made available a numerical inte gration of the equations df motion— drag included— starting with initial conditions specified by the writer. A value of acceleration some 5.8 times the observed value was obtained, through choice of parameters. By adjusting the mean value to the observed mean, the column of theoretical accelerations in Table II is obtained. The agreement is adequate to confirm the suggested rocket attitude. It is easily shown that the observed accelerations are not compatible with the body axis and the spin axis parallel. Such a direct scaling of the theoretical accelerations is not strictly legitimate because long-period variations are improperly manipulated. However, these latter appear smaller than the air-drag term so the comparison is probably not mis leading. Further, it should be noted that the perigee drops too fast in the integration, accounting for the increase in the mean of the theoretical acceleration. 10 The Density of the Upper Atmosphere* By Theodore E. 1. Sterne** Introduction I shall present a formula for the Inference of air density from the orbital motion and physical characteristics of artificial earth satellites, and then I shall apply it to orbital data, for the American earth satellite 1958 Alpha, kindly provided me by Dr. Charles A. Whitney. 2. A Formula for Inferring Atmospheric Density from the Motion of Artificial Earth Satellites' In a paper in press'1 the author has made a basic theoretical study of the effects of air resistance upon the motion of close earth satellites. The first equation of Section 2 of that paper is (1) 0 where a and e are the mean distance of the satellite orbit and its eccentricity, respectively; where^ is an operator denoting the increase in one revolution of the quantity upon which it operates, where a is the earth's equatorial radius, where p(r) is the atmospheric density at geocentric distance r, and where E is the eccentric anomaly. In equation (l) <s* is the * The formula and conclusions about atmospheric density, article, have been communicated to Science. in this * Associate Director, Smithsonian Astrophysical Observatory, and Professor of Astrophysics, Harvard University. 1 T. E. Sterne, "An Atmospheric Model, and some Remarks on the Inference of Density from the Orbit of a Close Earth Satellite , Astronomical Journal (in press). 11 dimensionless quantity C«A ^ ae/m, where A Is the satellite's cross-sectional area, m its mass, CD the dimensionless aerodynamic drag coefficient that is believed on theoretical grounds to be approximately 2, and P is the atmospheric density at sea level. 1 0 Now a, the time derivative of a, is clearly Aa/P where P is the orbital period y Moreover, Kepler's second law states that P varies like a3'2. Therefore P/P = (3/2)a/a, and therefore P - 3Aa/2a. The only important contributions to the integral in (l) come from portions of the orbit near perigee because of the rapid decrease of density with increasing height. If the density P(r) is approximated, through a region near perigee and above it, by C - tr e"Kz where fLis the density at perigee, z is the altitude above perigee^ and K is the logarithmic gradient of density near perigee K = -2.3026 (d/dz) log1Q^, (2) then the integral can be shown to be given approximately but closely by where c = Kae, and where I purely imaginary argument. P= - 37T^(j!rae-c<| and I, are Bessel functions of It follow that (1+etc.) IQ(c) + (2e+etc.) I^cv) with rather high accuracy under all conditions. The Bessel functibns can be expanded asymptotically in descending powers of c_, and if this is done equation (3) becomes (3) 12 where f(c,e) - l+2e + (3e2/2) + l-6e-10.5e2 8c + _2t30e+8|^e2 (g) 1280^ correctly to a few percent when e lies between 0.02 and 0.20 and K exceeds 0.01. Outside these limits, equation (3) is still valid, and may always be used. If a is measured in units of a , 6378 kilometers, results Trom (4) the practical formSla there l/2 ft « - 4.826 x 10-15 P -2— gm/cm3, (6) *TT A CD a f (c,e) » where P is the rate of change of period in seconds per day, m is the mass of the satellite in grams, A is the satellite's area in square centimeters projected on a plane normal to the direction of motion, C-r, is the dimensionless aerodynamic drag coefficient, believed to be approximately 2; a is the mean distance expressed in earth radii of 6378 kilometers; c is 6378 Kae if z, in (2), is in kilometers; and f(c,e) is given by (5). An average value of the A of a non- spherical satellite should be used in (2), and for a convex satellite of which all orientations occur with equal frequency the average A is one fourth of its total superficial area. The value of K, somewhat dependent on perigee height, can be approximated by applying equation (l) somewhat above perigee to a model atmosphere like the ARDC2. Alternatively, K may be determined without reference to assumed models by applying equation (5), or (3)> to two or more satellites with different perigee heights and adjusting K until it is consistent with the resulting perigee densities. I am indebted to Dr. G. P. Schilling for urging me to develop some simple, approximate, formula. R. A. Minzner and W. S. Ripley, "The ARDC Model Atmosphere, 1956". Air Force Surveys in Geophysics, No. 86, Geophysics Research Directorate, AFCRC, ARDC, December 1956. 13 \ 3. Density inferred from 1958 Alpha Dr. Charles A. Whitney provided orbital data for the American artificial satellite 1958 Alpha, as of February 1, 1958. The data, 3 which he obtained from an analysis of "Moonwatch" (visual) and "Minitrack" (radio) observations, were: eccentricity 0.139, inclination 33°. 2, argument of perigee 120°. 0, anomalis tic period 0d. 0798274, rate of decrease of period 3.9 x 10- ' days per period, or about 0s. 42 per day. From these data I have inferred a mean' distance of 1.22757 earth radii, corresponding to a perigee height above the international ellipsoid of 368 kilometers. The satellite is2* a cylinder 6 inches in diameter and 80 inches long, with a mass of about 14 kilograms. The area A of such an object, relevant to its air resistance, is its area projected on a plane normal to its direction of motion. The average over all possible orientations for random tumbling is 1/4 of the total superficial area, or 2520 cm2. The same value is obtained if it is considered that the cylinder spins about a transverse axis, randomly oriented with respect to the orbital plane, and gradual orbital changes influence the orientation of the spin axis near perigee from passage to passage. Averaged over a spin period, over orientations of the spin axis with respect to the orbit plane, and over the motion of perigee the same average value is obtained as for random tumbling, 2520 cm2; this value has been employed as A in equation (6). The aerodynamic drag coefficient has been taken to be 2. The density has been inferred by the method described in Section 2 of this article from this value, the mass, the average area, the eccentricity, the mean distance, the rate of decrease of period, and the logarithmic derivative of density near perigee given by the ARDC model atmosphere. The density thus found, about 1.5 x lO-1^ gm/cm^ at a geometric altitude of 368 kilometers (348 geopotential) is about 14 times that predicted at such an altitude by the 3 See also Harvard College Observatory, Announcement Card 1404 (1958). ^Harvard College Observatory, Announcement Card 1390 (1958). 14 ARDC model. It falls nearly on the middle curve, No. 2, In a study5 that tentatively suggested a modification of the ARDC atmospheric model to satisfy a density of 4.5 x 10-13gm/cm at 220 kilometers (213 geopotential) that had been inferred6 from observations of the USSR satellite 1957 Alpha 2. This value was about 9 times the ARDC density* The values 4.5 x lO"1^ gm/cm3 and 1,5 x 1C--12* gm/cm3 depend somewhat, although not strongly, upon the gradients of density of the ARDC model employed in the reductions. It seems better to adjust the model so as to render it consistent with the perigee densities that result from the K's of the adjusted model. A formal least- squares adjustment has not yet seemed warranted but a non-least-squares adjustment, allowing for the effect of the adjustment upon K, has indicated densities of about 4.0 x 10-13 gm/cm3 at 220 kilometers (geometric) and about 1.4 x 10" 14 gm/Cm3 at 368 kilometers (geometric). These values do not agree well with the densities predicted by Harris and Jastrow? as extrapolations from altitudes of about 220 kilometers and below. They appear to be in unexpectedly good agreement with curve No . 2 of reference 5* do not involve any very implausible temperature gradients, and I prefer them. 4. Adjustment of the ARDC Atmosphere The preferred values at 220 and 368 kilometers can be represented by an additive correction to the common logarithm of the density of the ARDC model, of roughly 0.89 + 0.0016 (z - 220) where z_ is the geometric altitude in kilometers above sealevel. 5 T. E. Sterne, G. F. Schilling, and B. M. Polkart, Special Report No. 7, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge (1957), Figure 2. 6 T. E. Sterne and G. F. Schilling, Special Report No. 3, IGY Project Noo 30.10, Smithsonian Astrophysical Observatory, Cambridge (1957). I. Harris and R. Jastrow, Science 127, 451 (1958). 15 Life Expectanc < Lu .J. > ' Satellite 19 58 Alpha Jacchia* _/ Dr. D. G. King-Hele of. the Royal Aircraft Establishments, Farnborough, England, has kindly transmitted to us a useful formula developed by Dr. D. 2. M. Leslie for computing the lifetime of a satellite. oAt a given time t let P be the period of the satellite, P the rate of change of the period, and e the orbital eccentricity. The life expectancy of the satellite at time t can then be expressed as This equation gives excellent results when applied to satellites 1957 al, 1957 a2 and 1957 P. According to Dr. Charles A. Whitney,1 on February 1, we had for satellite 1958 a: P = 0?crr983; ? - -4^78 x 10"6/day; 1958 e = 0.139- From these data Leslie's formula yields a life expectancy of 1740 days, or 4 years and 9 months; the satellite should then fall toward the end of 1962. Before the value of P became accurately known from observations, a rough calculation of the drag to be expected on the basis of the physical characteristics of the rocket satellite and of the Smithsonian Interim Atmosphere^ densities had given a predicted value of -5d7 x 10"^ /day for P, from which a life expectancy of 3 to 5 years was "deduced. if Physicist, Smithsonian Astrophysical Observatory 1 Harvard Announcement Card No. 1404; March 17, 1958. 2 T.-.E. Sterne, B. H. Folkart, and G. F. Schilling: "An Interim Model Atmosphere Fitted bo Preliminary Densities Inferred from USSR Satellites". Special Report No. 1, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, December 31 > 1957. 2. THE DETERMINATION OF THE ORDIT OF 1958 ALPHA AT THE VANGUARD COMPUTING CENTER by Joseph U. Siry Naval Research Laboratory Washington, D.C. THE DETERMINATION OF THE ORBIT QP 1956-4 AT THE VANGUARD COMPUTING CENTER By Joseph W. 81x7 The VANGUARD orbit determination facilities hare been used to determine the orbit of 1958-a, known as EXPLORER-I. This system is described in the following paragraphs. The objective of the VANGUARD orbit determination program is to determine and predict the orbits of the IGY satellites on the basis of the available observational data. Tne VANGUARD Computing Center, a network of Mini track radio tracking stations, and a high-speed coa-iw'lcations nyetcm Joining them hsve been established in order to achieve this objective. The VAlfGUARD Computing Center facility has been established at 615 Pennsylvania Avenue, N. W., Washington, D. C. by the International Business Machines Corporation under a contract with the Office of Naval Research. In tne following discussion the tern VANGUARD Computing Center will refer to the portions of this facility and the personnel which are associated with tin laval Research Laboratory's Project VANGUARD. The system of Minitraik radio tracking stations has been established by the Naval Reaearcn laboratory. TSe Army is playing an important role in connection with tne establishment of many of the Minitrack sites and the r'igh-speed cournunication facilities. Operation of the Minitrack system 1b controlled su)r directed from tr,c. VANGUARD Control Center at the Neval Research Laboratory. Observational n*P «»«J qotu^T«TR vmojvna 0% »q^ dHTODBWi I««*noo ao^HOO ^o oq^ t*a«b vjoaoooos jCzoq.iuoq7i poo aouaqq. ^ ©TO dgvDQi'fA 2hiT%AdH03 joqnoo q.* {19 *T**AT£aTraoj 'otuxoay °g 'woqScnpqaa/i °a rMpnpoj voT^ooxpp jo ©qq. qavx*T*TK oppaz JBuppax* i»q.e£a pn» »qq dHVTlDffVA fc-fVuiBJOO annoo «T poam«l— Xq V>»fa*<£ OTWIMVA jo aq* t»a»i qojo»»»a •Xxoqoloqai Ixmy^ aowuTiaj <zoj »q* nw«T»*5» J* *TO 191 ••*TTIW»» >t poa«x< «odh «Tq* wsnarfa qoTV* aoa?jdaJDa *q* qaaaqprni poode-q»Tq win u -f mum '••nrnMo »qq asmupfA io*q.a©o ,jn»o p*» »qq asmoiYA »m»«»o »£Ot«»0 ji on qo«qT«TK rpw»T« ojoa 'pa*T»©*x m «T*»«*g» PT^o* %JT1* o% Oupoq TwsfA «or^T«Tn»a« •rporn-snj! eqj ojpu Jtoq.*-pww«* «T »q* HSHOTaXZ «T oxqT*»*»o qVF* aq% qaw*p»Tlt 'ma%uJia *i avq poquode .xoj « poTaod jo ©*q »qs i«ve jo aq* —MOl ■nTIW*" TTT* arrar*«o» oq. oq powpKoqop pwt po^oipoaC »« •TV OSTQCfrTA t«TfMtaoo jov»0 vae*«naxqa oq* q**x*prnt OTP** •ovt^ojtt a*aajpcoftf*Y •orenowfdo *» povrapaaaBTP -zoj aqq. tljovoq jo ■j«xz»«qo **oq»fcoaq* «H *TV« awowoTpoad poqapraj *q (HWHWYA »«TV*«"«Q MW3 «• »q* >T««q J« »q* qa*xrp(TM ««»?i«/ucaoqo aj* p«m tvpncp aq* Xpcoo %Jn*i J» «,o*TTW*» wpwn o* *oa*Tp aqq. nxmo jo aq* x»oT^do 9«Tqouq. mnni qofqA oxa 3**aq poq»TTq**«» jfq oq^. no«q^p«B cptf TWTsXqdoj^gy £xoq.«JLxasqo japan aqq. ■•STdtnv jo »<n *n *s iTOOTCDji Qfj»p— jcqj aqq. '101 oqj Anmr-Kl TWftrr *m J© »TO (MVUDfiVA BttTVuft»o *»V»q 'uoq* «vq uooq o* aapiiDO XDI>*R» o*ttiov»« sq^q-Jo «o rFeoq J© oq* jp>*xq.TTrnt Various mathematical methods are ^ : ".able for use at the VAHGHAKD Computing Center for the purpose of de arsdning the orbits of the ICfJf satellites on the basis of the Minitr&sk and optical observations . can be categorised In various ways. Those For example, there are methods and programs for determining the principal features of the orbit, and methods and programs for determining the orbit precisely. The former will be referred to as the elliptic or circular erblt programs, and the latter as precise orbit programs, There are two principal types of elliptic or circular orbit programs, one designed for observations which are neighboring In a Taylor series sense, the other designed to use observations, one or more of which are vilely separated from the ether in this same sense. Two types of precise orbit programs are used at the VAJKWARD Computing Center. They use the method of numerical integration, and the method of general pertur bations, respectively. The elliptic orbit programs can serve three purposes. First, they furnish the initial estimates of the key parameters of the approximate elliptic orbits such as, for example, the classical set of elements ft, 1, u, a, e, and T, or an eesiivalent set, riich is perhaps in this context, consisting of ft, 1, u, 4, s, and T. the perigee and apogee distances, respectively. more appropriate Here f and s refer to A second purpose of the elliptic orbit programs is the furnishing of Initial conditions for the numerical integration. Finally, the elliptic orbit programs may also provide checks of the more precise orbit determination pro grems . 21 The method of the numerical integration prorides a means for determining the precise erbit relatively early is the acquisition process, and for providing the very important measurement of the air density in the neighborhood of perigee on the basis of the orbital decay. The method of general perturbations developed by Berget and Nusen provides the means for computing the orbit over longer periods of time „ This method is superior to the method of numerical integration since it is not so subject to the building up of errors with the passage of The first sets of observations of the object come from the Minitrack station at Antigua., and possibly also from the Minitrack station at Grand Turk. data are transmitted three times and the computer applies checks whether transmission errors have occurred. The to determine These observations may extend over a tenth of a radian or more of the initial orbital arc as viewed at the earth's center » The data are smoothed parabolically and calibrations are applied. The result is three or four smoothed observations spanning the observed arc. A variant of the Gaussian method is applied to these observations to furnish the initial estimates of the elements of the ofulvalent elliptic orbit. The corresponding position and velocity vectors associated vlth one of these first smoothed observations also provide the first set of Initial conditions for the The observations can then also be regarded as a redundant set. appropriately weighted equations By forming of condition and solving the equations, differential corrections to the six initial I. Ionospheric refraction corrections are applied in connection with I Her get, f., and Musan, F. , "General theory of Ob lateness Perturbations" Proceedings of the Symposium on Orbit Theory, American Mathematical Society. April 1957. 22 . J Since the air density Is not accurately- known at satellite altitudes, It Is Important to regard one or two atmospheric parameters as unknown to be determined through the solution of the enlarged set of normal equations . The next observations were those from the Mlnltrack station at San Diego, California. The corresponding equations of condition are then used to differ entially correct the numerically Integrated orbit based on the Antigua observations. When this method does not go through, the observations obtained at Antigua and San Diego are smoothed to yield two observations of appropriate weight, and the corresponding equivalent circular orbit is determined. The initial conditions which it implies is used to restart the numerical integration, and the least squares, differential correction technique is again applied. The orbital arc determined by repeated applications of tee numerical integration, least squares, differential correction method is extended forward by means of numerical Integration. Once the orbit obtained by these methods has settled down sufficiently, the use of the method of general perturbations is begun. The basic predictions consist of the minute vectors, i.e., the latitude, longitude and height of the satellite at each minute of time. Convenient condensed versions are also issued. For example, the orbit is specified by giving latitudes, longitudes and heights at four-minute Intervals for one orbit, as well as the period and the motion of the node in an earth-fixed coordinate system. These data permit the observer to determine the portions of the orbit which are of interest to him. 23 These capsule ephemerides axe reissued as often as the changing orbital elements require. More detailed predictions of simulated Mini track observations and azimuths, elevations and ranges are also provided for certain official observers , The effect of atmospheric drag upon the orbit of this satellite has been considerable and somewhat difficult to predict at times, due to the fact that the drag force depends so strongly upon the angle of attack in the case of a cylindrical satellite of large fineness ratio such as EXPLORER-!. The orient ation of this satellite as a function of time has been difficult to predict at times. This has made the task of predicting the orbit correspondingly difficult. Preliminary estimates Indicate that the lifetime of the satellite EXPLOREF-I will be about five to ten years and that the atmospheric density in the neighborhood of perigee at about 370 kilometers is approximately lO"1^ gms/cu c This is an order of magnitude greater than the value predicted for this altitude by the ABDC model. The orbit computation methods are established by the Working Group on Orbits whose members are Dr. 0. K. Clemence, Dr. R. Duncombe, Mr. J. J. Fleming, Dr. P. Herget, and the author who serves as chairman. The detailed formulation of the orbit computation methods was largely developed by Dr. Herget. The members of the Working Group also participate in the direction of the orbit computation operations at the VABOUARD Computing Center. Detailed analyses of the orbital data for the purpose of extracting geo physical information will be continued. 3. SATELLITE MICROMETEORITE MEASUREMENTS by E. Kanring an.l M. Dubin Geophysics Research Directorate Air Force Cambridge Research Center Air Research and Development Command L. G. Hanscom Field Bedford, Massachusetts 26 SATELLITE MICROMETEORITE MEASUREMENTS The existence of dust and material particles in interplanetary space has been known for many years. One of the more dramatic evidences of such material is the visual meteor trail which appears when the material enters the earth's atmosphere. The zodiacal light observable during clear moonless twilights, especially at lower latitudes, is another evidence of interplanetary particles. This phenomena, when associated with the morning twilight, is often referred, to by desert dwellers as the false dawn in that it becomes visible an hour or so before the beginning of morning twilight. An intense ionization along a meteor trail entering the atmosphere reflects radio waves. This is an effect which can be detected by short wave listeners and more precisely by radar type gear designed specifically for this purpose. Finally, both dust collections at high altitudes and ocean sediments yield particles which, from their content and shape, are identified as being of extra-terrestial origin. Systematic studies of these effects have been made in recent years by many groups. Notable among these studies are the photographic work of Harvard and the radio echo work of Stanford and Jodrell Bank, England. Visual, photographic, and radar echo techniques give a direct measure of the number of particles entering the earth's influence. Their velocities may be determined from the measurements and, by theoretical considerations, the mass..and dimensions of the particles may be inferred. However these two methods of observation can detect only particles of 10"4 gm. or larger. It is observed that the smaller particles are much more numerous. The results of these direct observations may be extrapolated to obtain an estimate of particle density for the smaller sizes (micrometeorites). Studies of zodiacal light, dust and sediment also give a measure of micrometeorite densities. These studies however, are necessarily uncertain because of difficult experimental methods and uncertain theoretical interpretations. Estimates determined from the various methods differ greatly. Measurements of micrometeorite densities are very necessary to verify or reject existing theory, to expand it, or to formulate new theory. Densities and size distribution, composition, velocities, inhomogeneitie s and space distribution are all important factor s in obtaining complete know ledge of the planetary system and its formation. Aside from the scientific interest, it is important from an engineering standpoint to evaluate the meteor hazard to space flight. These hazards include (a) structural damage due to impact of large meteors, (b) penetrating impacts which may allow vital gas to escape or to damage 27 electronic components, and (c) surface sandblasting due to impact with tiny cosmic dust particles. Meteor particles large enough to do structural damage can be detected as they enter the earth's atmosphere. Hence their density in the vicinity of the earth is fately well known. It can be -stated that the probability of such damage is extremely small. The probability of damage by tiny but penetrating particles is also small if skin thicknesses of one hundredth inch of metal or greater are used. However, very long flights (such as are ^^oct^d expected of high-altitude satellites) may experience one or. more.etKihi.impacts during their life. The sand-blast effect due to micrometeorites could measurably effect the vehicle's surface. Long-lived vehicles will probably depend upon solar batteries which may be sensitive to surface effects. Sur faces, however, can be coated with metal oxides to radiate thermal energy more effectively into space in order to provide cooling. Reflecting coatings may be desirable in other cases. It is quite important to evaluate all possible surface effects. Numerous meteorite and micrometeorite detectors were devised for the Vanguard satellites. Working within very tight weight and power limitations a devise consisting of twelve gauges was developed by the Geophysics Research Directorate of Air Force Cambridge Research Center. These gauges present a total of about two square inches of sensitive area and each of the twelve is sensitive to the impact of a single micrometeorite of 5 to 10 microns in diameter. The individual gauges are 1 square centimeter in area and wound with enamelled wire 17 microns in diameter in two layers. This insures that the entire area is covered and is sensitive to impacts. An impact upon one of the gauges destroys its electrical continuity and this is r reported back by telemetry. When it was decided to launch the Vanguard II experiments on a Jupiter-C vehicle, the -.micrometeorite gauges were adapted to the new vehicle by means of a slight modification of the holder used to attach them to the skin. The gauges were connected to a sub-carrier generator which modulated the low power transmitter. It became possible also to mount a microphone detector on 1958 Alpha. This unit detects the acoustical energy generated by particles which impact the skin, and change the frequency of a sub-carrier generator. A schematic wiring diagram is attached. 28 The gauge detectors without holder weigh about two (2) ounces and utilize about three (3) milliwatts electrical power for the sub- carrier generator. The microphone amplifier combination weighs in the vicinity of ei ght (8) ounces and requires about five (5) milliwatts of power. Since very little information was available in designing the units for an expected micrometeorite density, they were planned to cover as large a density range as possible. If the range had been better known ahead of time, it would have been possible to make somewhat more precise measurements. However, it was considered of greater importance to obtain meaningful and reliable .. measurements even though they might be limited. The two units complemen ted each other. The microphone transmits data each time the satellite is over one of the more numerous 108.83 Mc/sec receivers. The gauges, on the other hand store their information and report it via the longer-life 108. 0 Mc/sec transmitter. With about 10% of the microphone data and perhaps 50% of the gauge data available, it is possible to provide the following information: 1. Seven hits have been detected by the microphone. 2. After 32 days not more than one gauge has registered an impact. Due to the relatively low precision with which the telemetered record can be read, the possibility exists that no gauges have been hit. The data indicates influx values which will be subject to some modification as additional data becomes available. However, the gauges give a reliable indication that the average influx of particles 10 microns in diameter or greater in the vicinity of the earth during the period of 32 days was no greater than 10~3 per square meter per second. The microphone indicates that an average influx of about 10" ' per square meter per second of particles four microns or larger was measured during the interval. Some uncertainty exists in the case of the microphone response. This is being studied at present with an identical microphone mounted in a fourth stage mock up. There is some indication that the sub- carrier generator was not in perfect balance. These effects should be understood better when all the data has been analyzed. The two values given above are in fair agreement 29 since the ratio of 3 to 10. micron to micron particles is expected to be from It is important to note that 1958 Alpha will not yield data during the intense meteor showers which occur in August and November. It is also important to emphasize that the amount of data gathered can not be con sidered statistically significant. However, the data is reliable and yields an excellent measure ment of micrometcorite influx rates. Much more work must be done to determine influxes under other conditions. The present experiments have provided all the information which could have been expected of them. They will prove of great value in understanding micrometcorite s, and in providing ... design information for the construction of more sophisticated measuring equipment. GENERATOR CARRIER SUB- tr UJ cr UJ H H CO X o ■—i ■—i a: UJ l—i «—1 1 1 i *—i 1 1 Q_ O eg o < tr i- 4. SATELLITE TEMPERATURE MEASUREMENTS FOR 1958 ALPHA- EXPLORER I by E. P. Duwalda and A. R. Hibbs External Publication No. 481 * Jet Propulsion Laboratory California Institute of Technology Pasadena 3, California Abstract A review of the analysis of the temperature problem for the Explorer is given, together with a comparison between the results of the analysis and the temperatures actually measured during the first 2 months in the life of Explorer I. The comparison is limited to the internal meas urements, although the data on both internal and external measurements are presented. On the basis of the results, it is concluded that the completely passive technique used, requiring only a fairly simple surface preparation, is adequate for the temperature control of an artificial satellite - at least, for the protection of electronic equipment. 33 I. INTRODUCTION The control of the temperature of a satellite is, in principle, a very simple problem. Its temperature is determined only by the amount of radiative heat which the satellite receives from the earth and sun, and by that heat which the satellite re-radiates or reflects to the empty space around it. The satellite is not in contact with any other body from which it must be insulated, nor is it immersed in an atmosphere of any appreciable density. Thus, in principle, it would be possible to achieve almost any temperature in a satellite and to hold it at an almost exactly constant value, without recourse to refrigerating or heating devices. All that would be required are simple mechanisms to adjust a system of reflecting or absorbing screens on the outer surface. However, in a minimum-weight satellite, such as the Explorer, even such simple mechanisms as these are too costly - in terms of weight - to permit their use. It is necessary to use a completely passive technique to achieve the necessary temperature control. For the Explorer, the temperature restrictions are imposed by the electronic equipment carried in the instrument section. At temperatures below about -5°C, the batteries cease to operate properly. However, if the temperature were to fall below this limit, no permanent damage would be done. The equipment would function properly if it were warmed up again. At temperatures above +45°C, the electronic equipment does not operate properly. However, it does not suffer permanent damage until the temperature exceeds +80°C. Therefore, the aim of the temperature-control technique for the Explorer was to try to hold the temperature of the electronic equipment between the limits of -5°C and +45°C; but, in any case, the temperature was never to exceed +80°C. The only completely passive technique available is to cover the outer surface with materials which have the proper radiative characteristics. Even when the surface is prepared in the best possible way, some temperature variation is inevitable. As the satellite moves in its orbit, it passes alternately between sunlight and shadow. The period of this cycle is of course the period of one revolution around the earth, or about l'a to 2 hours. Only if a high inclination of the orbit to the "equator" were attained, so that the satellite were in sunlight continuously, could this wide variation be avoided. Fortunately, the equipment within the satellite need not experience the same degree of variation as the shell. Tests on a prototype model showed that the electronic equipment could be so well insulated from the shell that its temperature varied only a few degrees, while the fluctuations in shell temperature exceeded 100°C between extremes. In this case, the temperature of the electronic equipment stays near the average temperature of the shell, averaged over one cycle. However, as the orbit regresses around the earth, as the line of apsides precesses about the orbit, and as the earth turns about the sun, this average temperature varies. Furthermore, the attitude 3* of the satellite with respect to the sun is also important, since the Explorer is roughly cylindrical in shape. Thus it is necessary to: 1. Find surface materials which will maintain the average temperature of the shell within the prescribed boundaries, keeping in mind the long-term variations caused by the motion of the plane of the orbit, the line of apsides, and the earth. 2. Launch at the right time of day to achieve the proper attitude of the satellite with respect to the sun. 3. Insulate the electronic equipment from the shell. The present paper outlines the mathematical development of the heat-flux equation for the shell. The result shows how the temperature of the shell depends on surface characteristics, position of the orbital plane, and attitude of the satellite. This outline is followed by a discussion of the surface characteristics problem, and a description of the materials used on the surface of the Explorer. Next is given a comparison of the predicted and observed temperatures of the electronic equipment, and a presentation of all of the temperature data received from Explorer I — 1958 alpha. 35 II. SHELL TEMPERATURE ANALYSIS Mathematical Development The rate of change of the temperature of the shell of a satellite is (1) dt mc where Tp = the temperature of the shell; lg = the radiative power absorbed from sunlight; lg = the power received from thermal radiation of the earth; A' = the power radiated from the shell; t - time; and mc = the total heat capacity of the shell. The use of the total heat capacity of the shell implies that the assumption has been made that all parts of the shell are in good thermal contact with each other; that is, it is assumed that the rate of heat transfer by conduction from one part of the shell to another is much greater than the rate of heat transfer by radiation between the surface of the shell and the surrounding environment. It also implies a second assumption; namely, that the electronic equipment on the interior is so well insulated from the shell that it can have no effect on the temperature of the shell over the time periods of importance. The first assumption is valid, but the second is somewhat questionable. Actually, the temperature of the internal equipment did vary several degrees in the period of one orbit; hence it did have an effect on the shell temperature. However, the effect on the average shell temperature is not great; consequently, for the present problem, it is probably not worth the added complexity to introduce this effect. Solar radiation is received by the satellite in two ways. First, radiation is received directly from the sun at the rate lSl = ASalS where A<* = the projected area of the satellite as seen from the direction of the sun; a j = the coefficient of absorptivity of the shell for solar radiation; and S = the solar constant - 1.94 cal/cm /min (2) 36 The projected area of the satellite for the receipt of direct solar radiation is, naturally, a function of the shape of the satellite. In the present analysis it has been assumed that the portion of the satellite body which is important for temperature control has the following characteristics: (1) It has a conical nose. (2) The base of this cone is attached to a cylindrical section of the same radius. (3) The combined surface of the cone and cylinder is exposed to radiative heat transfer with the surrounding environment. (4) The base of the cylinder is thermally insulated from the remainder of the payload and acts as a radiation shield for this base area. A sketch of this configuration is shown in Fig. 1. The projected area of the satellite for the receipt of radiation is a function of the angle of orientation t) shown in Fig. 1. In order to determine this angle for the receipt of radiation from any particular source (e.g., the sun), it is necessary to make some assumptions about the motion of the satellite. Explorer I was launched into orbit spinning about its longitudinal axis. If it were a rigid body, it would maintain this spin orientation for a considerable period of time, since no appreciable external torques are acting perpendicular to the angular momentum vector. However, Explorer I is not a rigid body. Extending from its sides are four wire antennas (aircraft control cables). The flexing of these wires introduces appreciable internal damping. Since no external torques are applied by this flexing, the angular momentum must stay fixed in both direction and magnitude. The only way that energy can be dissipated is for the mode of spinning to change, eventually reaching a minimum energy mode for constant angular momentum. This is what happened. Within a day after launch, Explorer I was rotating end over end about a transverse axis, with the angular momentum vector still pointing in the original direction. Since the angular momentum vector maintains a fixed direction in Newtonian space, it is convenient to define the orientation of the satellite with respect to this direction. Since the spin around this vector takes place within a period much shorter than any thermal time constants important for this problem, the area of the satellite is averaged over the angles ij traversed in one spin cycle. Let f] j be the angle between the angular momentum vector and the direction of a source of radiation. Let <f be the angle between the longitudinal axis of 'the satellite and the plane defined by the angular momentum vector and a line from the satellite to the radiation source. Then for a motion consisting of spin about a transverse axis, the average area is where r] is defined by cos r] = cos £ sin and the function Airj) for the conical section configuration of the Explorer is shown in Fig. 2, where its ratio with the total surface area A j is plotted as a function of rj. For the cylindrical section, this function is simply 2r/s sin 17. If the source of radiation is the sun, then 77 ] =VS' 37 The satellite will also receive solar radiation which is reflected from the earth. The radiative power received by the satellite through reflection from an element dS of the earth's surface area is dl<. = (P. A.) a}i (a) cos acos P. dI (3) where P. A. - projected area of the satellite seen from the surface area dS; i(a) - the radiative power reflected at an angle a to the normal of the surface element with primary radiation normal to the element; /3 = the angle between the direction of the sun and the normal to the surface element dS; an ! p - the distance between the surface element and the satellite. The geometry of the earth-to-satellite radiation process is shown in Fig. 3. Since the satellite shape under consideration has cylindrical symmetry only, each surface element of the earth will see a different projected area of the satellite. Thus, the angle of orientation Jjj will be a variable in the subsequent integration of dlg^. Let dS cos a be the surface element of a sphere of radius p. Then dS cos a = p 2 sin 77 j d 77 j d\jj where 77 j and ii are spherical polar coordinates about the center of the satellite with the polar axis coinciding with the direction of the angular momentum vector of the body. Rewriting Eq, (3) in terms of r/j and 6 gives dl g = As — cij i cos y sin 77 j</ rj j d u Ay where y is defined as the angle between the direction of the sun and the normal to the surface element p2 sin 77 j df) j d\fi . With the help of Fig. 4 it can be seen that cos y ~ cos 0S [ cos (rjQ - ^j) - sin (i70 - 77 ^) ctn r/^] + cos r)g sin (tJq - rjj) esc r/n where 3& 0$ = the angle between the radius vector from the center of the earth to the satellite and the direction of the sun; r)$ = the angle between the direction of the angular momentum vector of the satellite and the direction of the sun; and t}q - the angle between the direction of the angular momentum vector of the satellite and a radius vector from the center of the earth to the satellite. The assumption has been made that » is independent of a.; that is, that the reflection from the earth is perfectly diffuse. The total power received by the satellite through reflection may now be written as n 1 AS ls = 2 a j sin 77 j {cos 0s[cos (rjQ - 77 j) - sin {t)q - 77 j) ctn rjQ] 2 0 0 AT (4) + cos 77 s sin (?70 - rjj) esc j}q } d^^dxjj where the limits of integration over 0 depend on 77 j and r/Q cos ip j = - ctn r/Q ctn rjj 0, = 77 Integration with respect to for rj1 < for 77 j > 5 - tjq t?0 is immediate; however, the mathematical form of the ratio A§/ A j as a function of 77 1 is too complex to permit analytical integration. Therefore, the integration with respect to 77 j must be carried out numerically. In the above integration it has been assumed that the earth is flat; hence the earth as seen from the satellite covers half of the sky. In an earlier study by Dr. A. R. Hibbs of the Jet Propulsion Laboratory (Ref. 1) the total power received by a spherical satellite through reflection was found to be /§2 = 2772a2 a, v 2y) cos 6S . through the first order in y , where 7 = h/rQ; h = height of the satellite above the earth's surface; and Tq = radius of the earth. 3S The factor (1 - ^2y) cuts down the fraction of the sky filled by the earth, and can be thought of as the altitude effect. Assuming that the altitude effect is independent of the shape of the satellite, the results of the integration of Eq. (4) are corrected by the factor (1 - /2y). If the integral over the term with the coefficient cos 6g is called Af (1 - /2y)~* , and of the integral over the term with the coefficient cos t}§ is called Af^ (1 - /2y) , then the result for the power received from sunlight is 2 =a-iirr[Ar cos 6$ + Af cos 775] 12 (5) Referring to Figs. 3 and 5, it can be seen that cos Bo = cos 6 cos cos tjg = cos <j> cos (r/Q - 6) where Q = the polar angle of the satellite in its orbit measured from noon transit; and <f> = the angle between a radius vector from the center of the earth to the sun and the plane of the satellite orbit. Substituting these relationships in Eq. (5) gives Is 2 = a j t 7rcos 0 [ Ar cos 6 + AT sin 6] 3 4 (6) where \ = Afl+ Ar2COB7,0'> **d The function t (a), appearing in Eq. (3), is defined for the sun vertically above a particular surface element. With this definition the total power radiated from a particular surface element into a hemisphere can be obtained with a simple integration. The result is rr i = E If the coefficient for diffuse reflection from the earth is 77 i = Srg , then the equation becomes Actually is not a constant for all surface elements on the earth. For this study an average value over the earth's surface, which is approximately 0.4 (Cf. Ref. 2), is used. The total power contribution from solar radiation may now be written as lg = a j S [ + T£ cos <f> (Af cos 6 + Ar sin 6)] (7) Thermal radiation from the earth is received by the satellite at the rate /£ . This term may be evaluated in the same manner as that employed in determining the power contributed from reflected solar radiation. It is not necessary to consider the position of the sun; therefore, the angles dg and rjg do not appear in the result of the integration. Use of the Stefan-Boltzmann law yields the following result: £ = AE a2oT% (8) wh ere Ag «= the total projected area of the body for receipt of thermal radiation from the earth [based on an integral similar to that of Eq. (4)]; a = the Stefan-Boltzmann constant; Tg = the effective temperature of the earth = 250°K (Ref. 3); and a2 = the coefficient of absorptivity of the body for receipt of thermal radiation at 250°K. The thermal radiation from the satellite may be written as R = A j 6j °" T where = the total surface area of the body; and = the coefficient of emission for thermal radiation from the satellite. For a particular wave length of radiation Kerchoff's law states e = a We expect the satellite to be at approximately the same temperature as the earth. Therefore, the important wave length region of its radiation should be approximately the same as that of the thermal radiation from the earth, so that to a good .approximation (9) Hi We may now rewrite the equation for the rate of change of the temperature of the satellite shell in the following manner and the meaning of the superscripts is as follows: Term (1) is the direct solar radiation term and is to be included only when the satellite is in the sun. That is, the term is to be included only when 6 lies between the angles (2n - %) 77- 02 and (2n + lA) 77 + 02 where do - sin [(sin e^cos <f>)] for $ < (n/2 - flj); 62 = 77/2 for <f> > (77/2 - dj ); and 6^ = cos'1 [(r0/r0 + A)] It has already been noted that the calculation of the reflected sunlight contribution was made for a flat earth as seen from the satellite to less than half of the sky. However, one additional effect of the earth's curvature earth as sun from the satellite to less than half of the sky. However, one additional effect of the earth's curvature still remains. It has been assumed that all of the earth seen by the satellite is illuminated. Actually, as the satellite approaches the twilight zone, this is not the case. Fortunately, the resulting error is small, and can be easily taken care of, at least to a very good approximation. The reflected sunlight term, with the superscript (2), is to be included only where 6 lies between the angles (2n -Vi)v and (2n + 77. Thus the reflected sunlight term is cut off as the satellite passes over the terminator. Inclusion of the complete term on the sunlit side of the terminator implies too much reflected light. Dropping the term completely on the other side implies too little reflected light. The two errors nearly cancel out. B. Effect of Surface Characteristics If the satellite were always in the shadow of the earth, its temperature would approach the equilibrium value Tp = Tg (Ag/Aj*)^ , independent of the surface characteristics. But, since the satellite spends over half of its life in the sun, this lower limit is never reached. The action of the sunlight raises the temperature. The effectiveness of sunlight in raising the average temperature can be evaluated in the following way. Suppose the factor a2 is divided out of the right-hand side of Eq. (10). The two large factors on this side are competing forcing functions. The first, now with the coefficient (aj/a2) S, is positive, but acts only part of the time. The second, now with only a as a coefficient, is negative and is always present. The result is a cyclic fluctuation of temperature, whose details can be controlled only by controlling the ratio a.j/a2, once the shape of the satellite has been determined. The correct choice of this ratio for the satellite surface is critical for temperature control. Actually, since the satellite is spinning with a period much shorter than any of the important thermal time constants, only the average value of (Xj/aj over the surface is important. For this reason, it is not necessary to find a single material with the correct ratio ai/*2 f°r whole surface. If two materials can be found whose ratios of ai/ao bracket the desired value, then the surface may be coated with a pattern of these two materials. Selection of the proper fraction of the surface to be covered by each will then permit the correct average ratio to be achieved. Two surface materials have been considered, steel (since the satellite shell is made of steel) and Rokide , a ceramic material, (since the satellite is exposed to aerodynamic heating during the launch phase). A steel surface accepts a relatively large amount of power from solar radiation (high value of Cti/a*), whereas a Rokide-coated surface accepts a relatively small amount of such power (low value of dj/dj). The value of a\/a2 f°r the surface materials to be used must be carefully measured if accurate temperature predictions are required. Such measurements have been made for steel and Rokide surfaces for the Jet Propulsion Laboratory by the Mechanical Engineering Department of the University of California at Berkeley. A discussion of these measurements may be found in Ref. 4. Briefly, the ratio of &,/a, for Rokide was found to be 0.437. Two types of steel were used with two different surface preparations. For the steel used on the cylinder a\/a2 »■ 1-92, whereas for the steel used in the nose cone the ratio is 4. 12. Rokide A, aluminum oxide applied by a patented process of the Norton Co., Worcester, Mass. III. AVERAGE TEMPERATURES OF THE SATELLITE SHELL The average temperature of the satellite shell may be determined by numerical integration of Kq. (10). It is necessary to specify the time of launch, the angle between the plane of the orbit and the direction of the sun, the characteristics of the orbit, the surface characteristics of the satellite, and the total heat capacity of the satellite payload. A number of such integrations have been carried out to illustrate the effect of the various parameters upon the temperature of the satellite shell. Examples of the average temperatures obtained from these integrations are displayed in Figs. 5 and 6, where h - the altitude of the circular orbit in miles; <f> = the angle between the plane of the orbit and the direction of the sun; and S = the angle around the circular orbit measured from the launching point. Explorer I is approximately 80 inches long and 6 inches in diameter (see Fig. 9) and is composed of three sections: the nose cone, the cylindrical section to which the nose cone is attached, and the empty fourthstage motor case. Each of the three sections is thermally insulated from the others so that the temperature of each section may be considered independently. Control of the temperature is necessary only for the first two sections since they contain the electronic equipment. For this study it was assumed that the thickness of the satellite nose cone shell was 3 mm at the tip and 0.8 mm over the rest of the body. The total heat capacity of the nose cone shell was determined from the weight of this section of the shell (352.2 grams) and the specific heat capacity of steel (0.127 cal/gm '°C) (Cf. Ref. 5) to be 44.73 cal/°C. The total surface area A j for the configuration shown in Fig. 1 was found to be 136.097 in.^. Both of these values were used in the numerical integrations performed. A second set of average temperatures was obtained for the cylindrical section of the shell, with the dimensions shown in Fig. 9. Both ends of the cylinder were assumed to be insulated from the remainder of the payload and to act as radiation shields. Sample average temperature curves for this configuration are shown in n Figs. 7 and 8. This cylindrical configuration has a total surface area of 376.991 in. and a total heat capacity of 140.6 cal/°C. On the basis of these calculations, a ratio of 25% Rokide was selected for the cylindrical section, giving an average a j/dg of 1.37; and a ratio of 30% Rokide was chosen for the nose cone, giving an average a j/a^ of 1.61. IV. TEMPERATURE PREDICTIONS It is essential to provide the proper temperature environment for the radio equipment carried by the satellite for at least the lifetime of the batteries powering this radio equipment. It is possible to choose the initial temperature of the satellite shell, averaged over the first few orbits, within the proper bounds. This temperature will vary with time due to the precession of the satellite orbit caused by the oblateness of the earth and also due to the change in orientation of the satellite with respect to the sun. The precession of the orbit may be regarded as a change in the angle between the direction of the sun and the plane of the orbit (0). Changes in the satellite's orientation with respect to the sun may be accounted for by varying the orientation angle rj g. Since the temperature of interest is that inside the satellite, only the mean value of the shell temperature over a cycle is considered. 7958 Alpha was injected into orbit at 3 hours 55 minutes 5 seconds Greenwich Mean Time on February 1, 1958. The average altitude of the orbit is approximately 900 statute miles, and the angle of inclination of the orbit to the earth's equator is 33.34 degrees. This set of launching conditions gives initial values of r)g = 107 degrees and 0 = 0 degrees. As pointed out in part II, the original attitude of the axis of symmetry was not maintained. Within a short period of time the satellite had precessed through 90 degrees and was tumbling about its original spin axis with a period of approximately 7 seconds. Thus, the expected temperature-time history for 1958 Alpha must utilize a projected area averaged over the tumbling period. The assumption will be made that the precession of the satellite's axis of symmetry occurred in approximately one day. Thus, on February 2 the satellite is tumbling in a plane approximately 16 degrees away from the direction of the sun and the effective projected area for the receipt of solar radiation corresponds to an average angle of orientation of 116 degrees. Predicted internal temperatures for this geometrical situation have been prepared for the nose cone and the cylinder. These predicted internal temperatures are plotted with the observed temperature data in a later section of this report. 95 V. TEMPERATURE FOR 7958 ALPHA Four direct temperature measurements are made using resistance thermometers. These resistance thermometers are placed as follows: 1. The stagnation point temperature measured at the top of the nose cone and capable of covering a range of ->0°C to t-450°C. The approximate accuracy of this measurement is +20°C. 2. The nose cone skin temperature measured just forward of the antenna gap and capable of covering a range of -50°C to +220°C. At 50°C the accuracy of this measurement is ±16°C. At 0°C the accuracy is ±18°C. 3. The cylinder skin temperature measured aft on the cylinder and capable of covering a range of -50°C to +110°C. Over the range of -10°C to +80°C the accuracy of this temperature data is ±4°C. 4. The internal temperature of the cylinder measured in the high-powered transmitter and capable of covering a range of -60°C to +110°C. The accuracy of this measurement ranges from ±2°C at T = 0 to 30°C to ±20°C at T = 90°C. In addition to these direct temperature measurements, indirect measures of internal temperature are available. The internal temperature of the nose cone may be inferred by observing the frequency level of the cosmic ray measurement channel. Calibrations of the subcarrier oscillator indicate that the internal temperature of the nose cone is known to ±12°C for T = 0 to 25°C and to ±6°C for T = 25 to 50°C. There is continuous transmission of all telemetry data. The stagnation point temperature and the nose cone skin temperature measurements are transmitted by the low-powered transmitter. The internal and skin temperatures of the cylinder are transmitted by the high-powered transmitter. The data are recorded at the following locations: Patrick Air Force Base 28° N. Latitude Earthquake Valley 33° N. Latitude San Gabriel 34° N. Latitude Nigeria 10° N. Latitude Singapore 2° N. Latitude Patrick Air Force Base, Earthquake Valley, and San Gabriel receive approximately four passes a day; Nigeria and Singapore receive about seven passes a day. Data from the low-powered transmitter are received at all stations. Information from the high-powered transmitter is received at Patrick Air Force Base and San Gabriel only. The telemetry data from some five hundred and eighty-eight passes has been reduced and plotted against time. The time period covered is from February 1, 1958, to April 1, 1958. Individual figures have been prepared V6 for each of the temperature measurements. The predicted internal temperature for the nose cone and for the cylinder has been added to the plots of these quantities. These data are shown in Figs. 10 through 26. Both the measured internal temperature in the cylinder and the indirect measure of internal temperature in the nose cone show a range of 35°C. This range is traversed semi-periodically with an apparent period of approximately 2% days. However, it is very probable that this temperature range is experienced during each orbit. It should be remembered that the maximum fraction of an orbit over which data is recorded is approximately 25%. The records show an internal fluctuation from 0°C to 35°C inside the cylinder and from 5°C to 40°C inside the nose cone. In completing the temperature predictions some allowance was made for the remaining uncertainties, such as unpredicted variations in attitude and altitude. In making this allowance, a conservative approach was used consistently based on the requirement that in no case was the temperature to exceed +80°C, the value at which the electronic equipment suffers permanent damage. It was estimated that this allowance might contribute as much as 15°C to the simpler prediction. It is this conservative prediction which is shown in the Figures of this report. Thus, before the firing, it was estimated that the actual temperatures might run as much as 15° below the conservative predictions. The data show that the temperatures were generally about 10° below this conservative prediction. Shell temperatures ranging from -25°C to 75°C have been observed. An inspection of Figs. 5 through 8 indicates that a temperature variation of 80 to 90°C during one orbit would be expected. VI. CONCLUSIONS Actually, almost no geophysical unknowns entered into the problem of temperature control; hence little if any basic scientific information can be gained by an analysis of the temperature records. At the best, it might be possible to improve the estimate of the earth's albedo. But this would require not only an extremely careful analysis of the problem (including the effect of the internal equipment on the shell temperature, omitted from the present analysis), but also more detailed information on the attitude of the satellite, which so far appears unobtainable. The reason for carrying out the experiment and analyzing the results is the same as the reason for testfiring a guided missile. Its purpose is to answer a very simple question: "Will the scheme work or won't it? Has anything been overlooked?" In the present case, the results show that the scheme did work. There were some unknowns which did enter into the problem. For example, the temperature is somewhat dependent on the altitude of the orbit. This altitude cannot be exactly predicted, at least with the current satellite launching vehicles. It was hoped that sufficient allowance had been made in the calculations for this altitude uncertainty. As it turned out, this hope was justified. Another question was whether or not the satellite would maintain its predicted attitude with respect to the sun. This attitude is very important in the temperature problem. As it turned out, the predicted attitude was not maintained. Fortunately, however, the actual attitude finally achieved was such that the temperature was not changed greatly from that predicted. Of course, precautions were taken to guard against any serious effect of an unpredicted attitude change. The chosen surface character istics were such that under no circumstances could the internal temperature exceed the value of 80°C at which temperature the electronic equipment woujd be permanently damaged. However, there was the possibility that such attitudes could be reached that the equipment would be rendered temporarily inoperative. Such attitudes have not been reached. Thus the conclusions of the temperature experiments on 1958 Alpha are the following: It is possible to use a completely passive technique for the control of the temperature in an artificial satellite. The control attainable by such a technique is adequate for the successful operation of electronic equipment. The engineering requirements for such control are simple in both concept and practice, and well within the current state of the art. ^3 =20 INCHES Fig. 1. Dimensions and Orientation of Pay load 200 •»?. deg Fig. 2. The Ratio of Ag/Af for the Conical Section of the Payload H 9 SATELLITE •{' \ / SUN \es ~7 Fig. 3. Geometry of Earth-to-Satellite Radiation Process DIRECTION OF ANGULAR MOMENTUM VICTOR Fig. 4. Relationship Between >jj, 0 Coordinate System and Direction of the Sun so 450 400 CURVE NUMBER deg 1 2 3 4 5 6 7 60 50 40 30 20 10 0 * 350 UJ IT cr Q. LU 300 250 200 120 160 200 240 280 360 400 S, ANGLE AROUND ORBIT, deg Fig. 5. Average Temperature of Conical Section of the Payload Shell vs Angle Around Orbit for Launch 20° Before Noon Transit, h = 1000 miles, <f> = 0°, 10°, 20°, 30°, 40°, 50°, 60° 5-1 CURVE NUMBER deg 1 60 2 50 3 40 4 30 5 20 6 10 7 0 80 120 8, ANGLE Fig. 6. 160 200 AROUND 240 ORBIT, 280 400 deg Average Temperature of Conical Section of the Payload Shell vs Angle Around Orbit for Launch 50° After Noon Transit, h = 1000 miles, <f> = 0° 10°, 20°, 30°, 40°, 50°, 60° Fig. 7.- Average Temperature of Cylindrical Payload Shell vs Angle Around Orbit for Launch at Noon Transit, h = 1000 miles, <f> = 0°, 10°, 20°, 30°, 40°, 50°, 60° 175 150 I25L 40 Fig. 8. 80 120 160 200 240 280 8, ANGLE AROUND ORBIT, deg 320 360 400 Average Temperature of Cylindrical Payload Shell vs Angle Around Orbit for Launch 90° Before Noon Transit, A = 1000 miles, <f> = 0°, 10°, 20°, 30°, 40°, 50°, 53° UJ UJ UJ ICO UJ CO I- -I UJ ~ x £ f> -I UJ x OT o < Q. <r X x X UJ < UJ iE o UJ UJ z o X Q_ o cr o 2 DC o 2 UJ CE ^ h- o — , ± N CO O) O CO ^ — CT UJ O if cr 3 CO z g CO o tr — UJ X o < UJ cvj UJ cr 3 cc UJ Dl ro Q Z < >- o < °UI I- UJ cr CO o a < Z CC UJ H X UJ UJ o C5 O o Q_ 3 < UJ CO $ CO O o z — CM rO UJ CD o ' CO UJ CO tr UJ cr r o uj > z tr O 3 <.JS z cm tr UJ X QJ S 3 < UJ 1 ♦ z CO CO CO UJ z _l cr < z UJ a. cr CM CO UJ d or UJ Z CM 2 _ cr CM o ~ ui CO CO CD < ? UJ 2 Q= z O UJ 3 tr 99 < J 5 — UJ o 3 < CO O Qj CT o y < i z Nil s < o o 3© o a of CM ro CO w I § UJ < 3 X in CD *~ =01 tr ^ mi S5 -o- e©_ G e—to o GO Q-e 8 -0 00 o—e _qo_ OD -GO e© GO GO GO 00 o 00 e© GO GO <» o-e oin 0. '3«niVH3dW31 2/102/112/122/42/52/62/72/82/92/22/32/1 J 8o t Fig. PMfor anil Cylinder FTime Alpha, TIt11. 1958 12. re1 nhrough abmtdsprevsiurcantertdlyure e TEMPERATURE o- PREDrICTED 8C r MEASUREM NT OF DAYS 0 o i, O — Ac t 8 0 0o o 8 o o \\ \ \\ \\ \\ i 8 o 8 o ST TEMPERATURE , °C 9-fo © G—K> U 0 cH-e o -e-o- e 6 8 _Q_ o o 9- 01c m2 "8" -O 5—0 G-e G—0 G-O g—e 6 8 O o o DO ax} o CD2/24 2/23 T I CC0 2/22 Kehruary Alpha, through F Shell Cone for Time TM1958 7958 13 24, iemapsvseg. 13. uraetdure 6 |6 o| © (jo o 2/21 "Cr cf lCfixr) 2/18 2/17 2/19 2/20 dj o DAYSOF MEASUREM NT o coco? o CO O333l0 © O GO 6 od 2/16 EEBJO nrar oinjO-ilj- o 2/15 6 o r O 0 2/14 Qi2> 00 CD 2/13 GEO 50 -25 IT r> (r UJ s UJ s ? TEMPERATURE, °C o O-0 0 0 8 e-0 11 8 G 8 3 o o o ©- J-l* 0-4-0 0—0 0—^0 0 o 6o O o ° o G O G c OGGO 0 o ri ■ft so _=l_ a Ub o o o ° c o § e—o B o Q G-© § D Ul , 2 a: CO o o e—e D D fa > O o o D 3 a Vc cV S- G o-e o D « IIc O u o o c a(0 ° o C in <? D D o G iZ O ° 8 G O o s « 3a ' 31*11VM3dW31 a 6/ TEMPERATURE, *C g-8 o o G-O 4* -0 8 G-© 8-SUT 48 3 -OJ oo 2/12 eo_o- r 2/102/11 OCCO SMFig. for Time Alpha, T1958 Point tFebruary 1 12, e17. hrough mapgsvsenurateiduorne 2/9 to 2/8 GOO AO OF DAYS MEASUREM NT 2/72/52/6 0 9 (IE) -O-O- <L-p— to 1 2/3 3pp mi 1 2/2 d< o 2/1 50h 25r -2Sl_ UJ 2/132/192/202/212/222/152/162/172/182/232/242/14 Stagnation Alpha, MFig. February Tthrough Point for Time 1958 18. 13 24, eampsvseuraetdure MDAYSEASUREM NT OF o o OCD o 1 o Fig. February Alpha, TSMthrough for Time March Point 7958 1958 8, 19. 25 etmapsgvseunraetdiuroen o o o o o o CD o o oo o r o o o o OOCD 11 o o o CO MDAYS OFEASUREM NT o o o 3/53/63/73/83/33/42/252/262/272/283/1V2 o o o O o o Q O o © o > < J ap o a o o 6 CD o o o 0 u ) < o i 501 IS < o o o o o o Alpha, Stagnation for tMarch T20, Point Time 7958 9 1958 ehrough mpvseratures o o o a o ou MDAYS OFEASUREM NT Ig o I o o kn o o o 0 Measured n o o o o o Fig. 20. -o as 4/1 o o o 3/31 o o SMFig. T7958 Point for Time March Alpha, April through 21. 21 1958 1, etampsgvseunraetdiuroen 3/30 o > a o o 3/29 I c ) < 1 3/28 > < CO I MDAYS OFEASUREM NT 3/253/263/27 o II oo col O 1 33/23/24 O o GO 3/22 CO 5/21 oo © 2/12/22/32/42/52/62/72/82/92/102/112/12 j *5 TEMPERATURE J 8 Fig. and February Alpha, IPMtT1958 Cone for Time 22. 1 12, renhrough atmdspevsiurcntaetdlure PREDIr-CTED o -8 8 MEASUREM NT OF DAYS I 8 c i> ti — O o 8o 8 1 o N ~T*\~ i DO through Alpha, TP24, Cone for February MFig. Iand Time 13 1958 7958 23. renmtadpesvsirucntaetdlure > o( ) O < ) ( OFMEASUREMNT DAYS TEMPERATURE -PREDICTED 0 l *8 it 88 I PMFig. Tand Cone for Time February Alpha, March I1958 through 24. 25 8, renmatdpsevsiurcntaetdlure © Q-O OFMEASUREMNT DAYS TEMPERATURE PREDICTED / ? I z I o o °o CD o o o »o Fig. PTIM20, and Cone for Time March tAlpha, 7958 9 1958 r25. enhrough matdpsevsiurcntaetdlure o <%> o o GO o. 3/93/10VII3/123/133/143/15VI63/173/183/19 3 o o O MEASUREM NT OF DAYS II ) J I ol RATURE 1 O TEMPE ICTED PRED / ( b 1 1 O O IPFig. Cone Mthrough Tand for Time Alpha, March April 21 26. 1958 r1, nemtadpesvsirucnrtaetdlure GO GO o oo GO O o MEASUREM NT OF DAYS o o rEMPERATURE % ^PREDICTED O O 3/23V243/31 4/13/253/263/273/213/223/283/293/30 o oo 99sOP O 4 1* REFERENCES 1. Hibbs, A. R., The Temperature of an Orbiting Missile, Progress Report No. 20-294. Pasadena (Calif.): Jet Propulsion Laboratory, March 28, 1956. 2. Goody, R. M., Physics of the Stratosphere. New York: Cambridge University Press, 1954. 3. Handbook of Chemistry and Physics. Cleveland: Chemical Rubber Publishing Company, 1955. 4. Shipley, W. S., Evaluation of the Absorptivity of Surface Materials to Solar and Terrestrial Radiation, with Plots of the Reflectances fat Wavelengths of 0.4 to 25 fi ), for Ten Sample Materials, Including Two Types of Fibrous-Glass-Reinforced Plastic, Progress Report No. 20-319. Pasadena (Calif.): Jet Propulsion Laboratory, April 11, 1957. 5. Mechanical Engineers Handbook. New York: McGraw-Hill Book Company, Inc., 1941. 6.' Randolph, L. W. and Choate, R. L., Calibration Record for the IGY Earth Satellite 1958 Alpha, Publication No. 130. Pasadena (Calif.): Jet Propulsion Laboratory, February 5, 1958. OBSERVATION OF HIGH INTENSITY RADIATION BY SATELLITES 195Q ALPHA AND GAMMA by . A. Van Allen, G. H. Ludwig, E. C. Ray and C. E. Mcllwain Department of Physics State University of Iowa Iowa City, Iowa THE OBSERVATION OF HIGH INTENSITY RADIATION BY SATELLITES 1958 ALPHA AND GAMMA By J. A. Van Allen, G. H. Ludwig, E. Lntroduction and Summary. C. Ray, and C. E. Mcllwain This Is a preliminary report of re sults obtained concerning radiation intensities measured with a single geiger tube carried by the artificial earth satellites 1 1958 a and 1958 y. 1. These satellites are sometimes called Explorer I and Explorer respectively. The counting rate of the counter in 1958 a was transmitted continuously and the data were recorded only when the satellite was quite near one of the 16 receiving stations distributed over the earth. The data collected by 1958 y were also telemetered continu ously. In addition, a small magnetic tape recorder stored the data obtained during each entire orbit. Then, as the satellite passed near one of the receiving stations, a radio command from the ground caused these data to be read out. A preliminary study of the data obtained from 1958 a and several interrogations of 1958 7 has been carried out, with the following results. Reasonable cosmic ray counting rates have been obtained for altitudes below about 1000 km. In particular, we have obtained a plot of omnidirectional intensity vs. height in the vicinity of California for the first two weeks in Feb ruary, This curve, extrapolated down to altitudes previously reached by rockets, agrees with earlier data. At altitudes greater than about 1100 km? very high count ing rates were obtained. This conclusion is the result of a somewhat lengthy analysis. Geiger tube output rat en up to about 140/sec have actually been observed. In addition, periods have been found during !?hich the Geiger tube put out less than 128 pulses in 15 minutes. of 128). (We have a scaling factor The considerations detailed in section 3, b ;lo>*, cause us to conclude that this is net due to equipment mal function, but Is caused by a blanking of the geiger tube by an intense radiation field. We estimate that if the geiger tube had had zero dead time, it would on these occasions have been producing at least 35,000 counts/sec. We surmise that the radiation v?r» have found is closely related to the soft radiation previously detected during 2 rocket flights in the auroral zone. 2. Meredith.- Gottlieb, and Tan Allenr Phys. Rev. 97* 201 (1955). □ o The radiation intensity necessary just to blank the geiger tube is equivalent to 60 mr/hr. In this connection the recommenced permissable dose for human beings is 00 r/week. 3- The present radiation is 0.3 r in 5 hrs or less. S. Kinsman, "Radiological Health Handbook" , page 292 (U.S. Dept. of Health, Education,and Welfare, 1955). Several geophysical effects of this radiation seem possible. It is very likely closely related to aurorae and geomagnetic storms. In addition, a rough calculation suggests that the radiation may be sufficiently intense to contribute important heating to the upper atmosphere. It will be important to investigate the amount of atmospheric ionization, light, and radio noise which would be produced under various assumptions as to the nature of the radiation. 1, Instrumentation for 1958 ja and 1958 y. The instrumentation for 1958 a consisted essentially of a single Geiger Mueller tube, a scaling circuit for reducing the number of pulses to be worked with, and telemetry systems for transmitting the scaler output to the ground receiving stations. The system contained In 1958 y was identical, with the addition of a miniature tape recorder for storing the data for the duration of each orbit, and a command system to cause the telemetry of the stored information over a ground receiving station (Fig. 1). 77 Identical G. M. counters, scaler input circuits, and scaling circuitry were used in the two cases. The G. M. counters were Anton halogen quenched counters having approx imately 0.050 inch thick stainless steel walls. In addition, the counters were surrounded by the stainless steel cases of the payload, which were 0.023 inch thick. Thus the total -2 absorption was approximately 1.5 gm cm of stainless steel (approx. 75 7. iron, 25 % chromium). The G. M. tubes had essentially infinite lives, small variation in counting ef ficiency over the range -55°C to 175°C, approximately 85 7. counting efficiency for cosmic rays, and about 0.3 % counting efficiency for photons of energy 660 kev. The "dead time" of the counters was approximately 100 microseconds . The length of the counter wire is 4" the inside diameter of the counter is 0.781". Following the counters were current amplifiers, which directly fed the first scaler stages. The scalers were bi stable transistor multivibrators, which operated over a wide range of supply voltage, and over a temperature range of -15°C to 85°C. batteries. This limitation was caused by the supply The scaler resolving time was 250 microseconds. If input pulses at higher rates than 4000 per second periodic were received, the scaler simply indicated a constant rate of 78 4000 per second. That is to say3 the scaler would not go out of operation If this rate was exceeded . It did, however, have an input pulse amplitude discrimination level, so that counter pulses of amplitude less than approximately one eighth normal were not counted. In each of the satellites, the output of a scale of thirty-two was telemetered directly by the low power trans mitter. In addition, it was transmitted by the high power transmitter in 1958 a. In all cases, the shift of state of the output scaler stages caused a discontinuous shift in the frequency of the sub-carrier oscillators^ which outputs were transmitted by the appropriate transmitters. The data telemetered in this manner have been readable when the rates of input pulses to the scalers were between 0.14 pulses per second (16 pulses or one change of state per two minute pass) and 80 pulses per second (limited by the bandwidth of the receiving and data reduction systems). In 1958 Y additional scaling circuits were included to provide a total scaling factor of 128 for the data to be stored r It was also necessary to include a time base-, in order that a proper correlation could be established between the data and the satellite position. These two information bits were combined in such a way that they could both be stored and telemetered on a single channel. Figure P. Indicates the manner In which an Inhibitor circuit effected this combination. The time base input was a train of pulses at the rate of one each second. These pulses appeared at the output of the inhibitor, and were recorded, unless one was proceeded by an output from the scale of 128 # in which case it was suppressed. The tape recorder was advanced in a discontinuous manner at the rate of one step per second. As the tape advanced, it wound a spring for the eventual return of the tape to the starting point. Upon receipt of a properly coded interrogation signal by the command receiver in the satellite, a relay system was activated which caused the high power transmitter to be turned on, and the tape to be released 90 that the spring was free to return it to zero. The return tape speed was controlled by an eddy current damping system so that the playback time was approximately five seconds. As the tape returned, the informa tion was read off the tape, telemetered 4 and the tape was erased. Upon completion of the cycle, the relays were reset, the trans mitter turned off, and the next recording begun. The information thus telemetered to the ground was the train of pulses emanating from the inhibitor circuit, except that it was much compressed in time. It can be seen then that (ZD C_ scaler input pulse rates between 0 per second and 128 per second were properly passed on, and that all rates above 128 per second appeared a3 a rate of 128 per second, that is, all pulses missings 2. Summary of preliminary observations. Table I is a list of the stations receiving data and reporting them to us. The stations labelled "JPL" are operated under the auspices of the Jet Propulsion Laboratory at Pasadena, California. Those labelled "NRL" are operated by the Naval Research Laboratory in Washington, D. C. Data were obtained from 1958 a only when it was reasonably- near one of these stations, up data for a later readout. since it had no provision for storing We have already analyzed most of the data from the JPL stations, and some of that from the NRL stations as well. This work is continuing. A small magnetic tape recorder in 1958 y stored the cosmic ray information for an entire orbit, and then played it into a transmitter on command from the ground. Data from nine of these orbits have been reduced in a preliminary way. We already have on hand many more of these passes, and are reducing the data from them in a routine way. It is evident from the above summary that the present report is a very preliminary one. The nine cases from 1958 J occur during the last four days of March, and we expect ultimately to have data obtained during several weeks after those days. In addition, we have so far reduced the data from 1958 y only in *J 81 rather rough vra^ as explained in the following paragraphs. Fin?»llyf we do not yet have highly accurate data on the satel lites orbits. We do have the position of 1958 o as a func tion of time tabulated .in one minute intervals as supplied by the Vaaguard computing center for the month of February. These data seem to be in error by several minutes in time, but apparently are sufficiently accurate for the purposes of the present report. For 1958 yf we so far have only a set of orbital elements for 26 March and position versus time for one orbit on 1 April., together with estimates of the various perturbations. This information., supplied to us by the Vanguard Computing Center^, has made it possible for us to estimate the orbit during the last days of March with reasonable accuracies. In particular 5 we estimate that our error in determining the tiir.e of passage through perigee is not more than about 5 minutes on 51 March, and is less on earlier dates. Our errors in esti mating latitude and longitude may amount to 10° in some cases. Accurate orbital data will ultimately be supplied to us by the Vanguard Computing Center. We discuss first the data obtained from 1958 a, Figure 5 is a plot of height against counting rate near the California coast. All of the passes recorded by J?L stations in California are included in this graph. There is some variation in latitude.* which presumably accounts for some of the scatter of the points. In addition, as explained above, the orbital data are not yet known with good accuracy,, and this presumably contributes significantly to the scatter. A linear extrapolation down to a height of 100 km yields a 2 —1 value of omnidirectional intensity of 1.22 (cm -sec)" , in adequate agreement with from rocket flights, ation. values we have previously obtained considering the crudity of the extrapol The data shown in this figure were nearly all taken before 11 February. The data obtained by the NRL stations in South America during the first two weeks of February are altogether different from those just discussed. The passes fall into two classes. In the first case, one obtains a counting rate of about JO/sec, a roughly reasonable value. In the second case, the telemetered signal fails to show a single scaler output pulse during the approximately rwo minutes of clean signal. This represents an input rate to the scaler Of less than about 0.1 /sec. There are, in addition, a few cases showing a strong change in count ing rate during the pass. For reasons discussed in section 3, below, we believe that the extremely low output rate of the scaler is caused by very intense radiation which "jams" the geiger tube so that it (...) n puts out pulses of such small height that they are below the threshold of the counting circuits. Laboratory tests show that this first' happens for the present equipment when the radiation reaches such an intensity that a counter of the same effective dimensions and efficiency as the present geiger counter but with a zevo deal time would produce 35,000 counts/ sec. Figure 4 is a plot of height versus geographic latitude in the vicinity of 75°W longitude. The positions of 1958 <* during reception of its telemetering signal by various of the NKL stations are marked. information received. A code designates the kind of It is at once evident that the extremely low observed counting rates all occur at a high altitude, while the more or lens normal rates occur at a low altitude. Transi tional cas*ss occur at intermediate altitudes. Quite similar behavior is observed near Singapore, and probably also load an. In these two cases no thorough study has been made, mostly because of the lack of trajectory data for the dates on which extremely low telemetered counting rates occur. In the one case at Singapore where such a rate occurred on a date for which orbital data were available, the extremely low observed counting rate occurred at an altitude of about 2000 km. Figure 5 is a plot of geographic latitude vs. geographic longitude for various orbits. are plotted on this figure. Only the high altitude cases The fact that the segments of data do not correspond to positions of closest approach to the Interrogating stations is due to our so far inaccurate knowledge of the trajectory. These data already suggest a picture of the geophysical phenomenon being measured. more explicit. The data from 1958 y are much Figure 6 is a plot of the scaler output as a function of time as given by the tape recorder readout for the pass ending near San Diego on 28 March 1748 UT. Since the tape recorder can only record one scaler output pulse each second (see section l) the maximum indication on the tape recorder output corresponds to 128 counts/sec for the geiger tube output rate. case). (Our scaling factor is 128 in this It is evident from the figure that reasonable count ing rates occur near the two ends of the pass. These ends correspond to the most northern latitudes and the lowest heights above the earth. The section where the counting rate indication is zero corresponds to a portion of the mag netic tape where no tuning fork pulses were missing, and hence no scaler output pulses occurred. minutes, This condition lasts 15 and 128 pulses were fed to the scaler during this time. This is an average counting rate for the interval of 0.14 /sec. to be compared with the usual cosmic ray rate for a geiger tube of this sort of about 50/sec. The counter goes through the transition from putting out essentially no counts to put ting out a great many very quickly,, and we presume that most of the 128 counts observed during this 15 minute interval oc curred near the ends of the interval. There is, of course, no real evidence for this. As discussed in detail in the next section, we believe tha* if we had had a detector with zero dead time, and a storage mechanism of unlimited capacity, figure 6 would begin where it does now, and at about 15 minutes would have begun rising rapidly to a peak near 25 minutes at which point the counting rate would have been greater than 55,000 counts/sec. After this time, the rate would gradually have subsided, returning finally to about the value actually recorded near the end of the pass. Figure 7 is a plot of geographic latitude versus geo graphic longitude for the orbits the tape recorder readout data of which has so far been analyzed. We have simply Iden tified the transition points between portions of the record where no tuning fork pulses are missing, all tuning fork pulses are missing, or some tuning, form pulses are missing. These three different kinds of region are Identified on the graph as > 15,000 /sec, 128 to 15,000, and ^. 128, respectively. Thft dashed portions of the various curves represent regions where the identification as to counting rate range is uncertain. Since these passes all occurred during the dates 28 March through yi March, the orbit did not have time to precess appreciably. Since perigee was near the most northern latitude, a given latitude corresponds closely to a given altitude. It is evident that at high altitudes and low latitudes mostly in a certain range of longitude the counting rate is very high. Near perigee the counting rate is low. counting rates occur. Elsewhere intermediate Passible interpretations of this result will be discussed in section J>, 5. Interpretation of Observed Bata. We now propose to justify our claim that when essentially no scaler output pulses occur, the apparatus is in fact exposed to very intense radiation. Three possibilities are immediately evident. atus may have some simple malfunction. The appar This possibility can immediately be rejected except for the scalers, geiger tubes, and geiger tube voltage supplies, since the subsequent treat ment of the information is completely different in the 1958 a and 1958 y. Some effect of temperature seems the only reason able possibility here. The temperature of the geiger tube was 1 « 1 ] * ■) i 87 \ I measured in 1958 y, and telemetered cn the continuously oper ating transmitter. The observed temperatures range from 0°C to about 15°C. As discussed in section 1, the operating range cf the circuitry is -15°C to 85°C. In addition, the frequency of the continuously telemetering channels which carried the cosmic ray information are significantly temper ature sensitive. These showed that no extreme temperatures occurred at the location of the corresponding suhcarrier generators. Another possibility might be that the satellite passed through regions to which very few cosmic rays could reach. This is extremely unlikely. A magnetic field of the order of one gauss extending over thousands of kilometers and remaining unbelievably free of local irregularities would be required to exclude a sufficient fraction of the cosmic radiation , The possibility that we firmly believe is correct is that the geiger tube encountered such intense radiation that dead time effects reduced the counting rate essentially to 75v-.ro. In order to explore this possibility, we have carried out the following experiments. A spare flight unit for 1958 a was placed in an X-ray beam which was hardened by a 3/8 inch thick brass absorber. The voltage on the X-ray tube was varied between 50 and 90 kilovolts to vary the flux over a wide range. The counting ywhich rate was measured with and without lead shields'permitted only part of the beam to reach the Geiger tube. In this manner the counting rates with and without the dead time effects were determined. As shown in figure 8 the dead time effects are negligible up to highest rates which can be handled by the telemetering systems. At high fluxes few of the pulses from the Geiger tube have sufficient amplitude to operate the scaling circuit and the counting rate returns to the range which can be telemetered. At very high fluxes no pulses have sufficient amplitude and the counting rate is zero. An ion chamber placed in the position of the satellite apparatus measured an intensity of 60 milli roentgens per hour at the minimum flux required to reduce the counting rate to zero. The ionization produced by different energy X-rays or by charged particles producing this effect would of course be different from this measurement. The X-rays used for this measurement had energies in the range 50-90 kev. We have little concrete evidence concerning the nature of this radiation. netic. Apparently, however, it is not electromag It makes its effects felt through the 1.5 g/cm2 of absorber which constitute the hull of the satellite and the walls of the counter. Photons with such energy should then be seen down to the lowest altitudes our equipment reaches. The radiation c an • presumably be either protons or electrons. If it is electrons, we then are probably detecting bremsstralung formed in the satellite shell. 4. Implications. Any reasonable identification of this radi- ation strongly suggests several geophysical consequences. It is unlikely that the particles have several Bev of energy each. Then, in order to reach such small heights through the geomagnetic field, they must at least initially be asso ciated with plasmas which seriously perturb the magnetic field at an earth radius or so. We presume that this plasma is closely related to geomagnetic storms and aurorae. Secondly, at heights only a little above 1000 km, there is still some atmosphere. Crude quantitative estimates suggest that 'the energy loss in this residual atmosphere of the radiation we detect may contribute significantly if not dominantly to the heating of the high atmosphere. In addition to considering this heating effect, it will be important to cal culate, on various assumptions as to the nature of the radiation^ the amount of visible lightc radio noise, and ionization produced. Finally, these results. there are obvious biological implications of As discussed in section 3, if photons are being detected directly by the geiger tube, and if these photons 90 are in the energy range 50-90 kev, then the radiation .field inside the satellite corresponds to about 0.06 roentgen s/nr. The maximum permissible dose for human beings is 0.5 roentgens/ week. Other assumptions as to the nature of the radiation would obviously lead to different results. ^2^CZ^^^^^X^J Ws owe a -!-arSe debt of gratitude to many individuals and agencies. We are indebted to the Jet Propulsion Laboratory at Pasadena* California for the high speed rocket cluster and for assembly of the satellite payload. The /tony Ballistic Missile Agency at Huntsville, Alabama supplied the booster stage and conducted the launching. Project Vanguard of the Naval Research Laboratory assisted in the early design phases of the instrumentation. They also set up and operated the minitrack tracking and telemetering stations, xlth cooperation and assistance from the countries in which the stations are lofiatad. They supplied us with orbital information for both satellites. The Jet Fropulsion Laboratory set up the micro lock stations for telemetry '.reception and operated all of them except at Ibadan and Singapore. These last two were operated by students at University College, Ibadan* and the University of Maylaya* Singapore, as a part of the British IGY effort. ! Table I - Receiving Stations Blossom Point, Maryland NRL Fort Stewart, Georgia NRL Antigua, British West Indies NRL Havana, NRL Cuba San Diego, California NRL Quito, Ecuador NRL Lima, Peru NRL Antofagasta, Santiago, Chile Chile NRL NRL Woomera, Australia NRL Patrick Air Force Base, Florida JPL Earthquake Valley, California JPL Singapore JPL road an, Nigeria JPL Temple City, California JPL Pasadena, JPL California 92 Captions for Figures Fig. 1 K'.ook diagram cf 1958 y instrumentation. Fig. Illustration of the function of the inhibitor circuit. 2 Fig. 3 Counting rate versus height near California for Fig. 4 Position?; in altitude versus latitude for telemetry of n.ata from 1958 a over South America. Fig, Z* Positions in latitude versus longitude for teller.:-1;* of data from 1958 a ever South America. Fig. 6 A parrple cf the results of a tape recorder rear'.ou,; near San EHepo on 28 March 1748" U™. Tig. A plot of variout orbits of 1958 y showing the range sf counting rates as a function of position. 7 g, 8 C/hs-rved counting rate of a counter like that in lc58 n s^d y versus the counting rate of a similar counter but y-ith z;ero dead tine. SUB CARRIER OSCILLATORS CENTER FREQ. TEMPERATURE INPUT 560 CPS CENTER FREQ. TEMPERATURE INPUT 730 CPS LOW POWER TRANSMITTER CENTER FREQ. MICROMETEORITE RATE INPUT-H 960 CPS G.M. SCALE CENTER FREQ. COUNTER OF 32 1300 CPS I HV POWER SCALE SUPPLY OF 4 10 MILLIWATTS 108.00 MCS PHASE MOD. LINEAR. POLARIZED TAPE RECORDER 512 CPS SCALE INHIBITOR RECORD RECORD TUNING FORK OF 512 CIRCUIT AMP HEAD PULSE POWER ADVANCE GENERATOR AMP SOLENOID COMMAND RECEIVER LATCHING RELEASE RECEIVER RELAY RELAYS SOLENOID BAND PASS £ HIGH POWER PLAYBACK PLAYBACK FILTER TRANSMITTER AMP HEAD ~~3 I 60 MILLIWATTS ^ 108.03 MCS AMPLITUDE MOD. LINEAR. POLARIZED COUNTING RATE (SEC)"1 HEIGHT (km) — NO — COUNTS OCCUR 90 80 100 COUNTS GEOGRAPHIC OCCUR I 70 LONGITUDE 60 (°W) 140 1 1 1 1 1 — 120 1958 r SAN DIEGO 28 — MARCH 100 1748 UT — _ "L 80 sa — £ 60 cr o | 40 — o 20 1 1 1 i 40 60 80 100 0 TIME 0 20 FROM PREVIOUS INTERROGATION (MINUTES) 120 0 (o) aaruuvn IGY Satellite Report Series Number 4 July 15, 1958 IGY WORLD DATA CENTER A Rockets and Satellites NATIONAL ACADEMY OF SCIENCES OBSERVATIONAL INFORMATION ON ARTIFICIAL EARTH SATELLITES (Excerpts from Special Reports Nos. 12 and 13 of the Smithsonian Astrophysical Observatory) NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, P. C. INTERNATIONAL GEOPHYSICAL YEAR WORLt) DATA CENTER A National Academy of Sciences 2101 Constitution Avenue, N.W. • Washington 25, D. C, U.S.A. World Data Center A consists Airglow and Ionosphere: IGY World Data Center A: Airglow and Ionosphere Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado, U.S.A. the following eleven archives: Glaciology: IGY World Data Center A: Glaciology American Geographical Society Broadway at 156th Street New York 32, New York, U.S.A. Longitude and Latitude: Aurora (Instrumental): IGY World Data Center A: Aurora (Instrumental) Geophysical Institute University of Alaska College, Alaska Aurora (Visual): IGY World Data Center A: Aurora (Visual) Rockefeller Hall Cornell University Ithaca, New York, U.S.A. Cosmic Rays: IGY World Data Center A: Cosmic Rays School of Physics University of Minnesota Minneapolis 14, Minnesota, U.S.A. IGY World Data Center A: Longitude & Latitude U. S. Naval Observatory Washington 25, D. C, U.S.A. Meteorology and Nuclear Radiation: IGY World Data Center A: Meteorology and Nuclear Radiation National Weather Records Center Asheville, North Carolina, U.S.A. Oceanography: IGY World Data Center A: Oceanography Department of Oceanography and Meteorology Agricultural & Mechanical College of Texas College Station, Texas, U.S.A. Rockets and Satellites: IGY World Data Center A: Rockets and Satellites National Academy of Sciences 2101 Constitution Avenue, N.W. Washington 25, D. C, U.S.A. Geomagnetism, Gravity, and Seismology: IGY World Data Center A: Geomagnetism, Gravity & Seismology Geophysics Division U. S. Coast and Geodetic Survey Washington 25, D. C, U.S.A. Solar Activity: IGY World Data Center A: Solar Activity High Altitude Observatory Boulder, Colorado, U.S.A. Note: (1) Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: Director, World Data Center A, National Academy of Sciences, 2101 Constitution Avenue, N.W., Wash ington 25, D. C, U.S.A.; (ii) Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate archive listed above. 1 IGY Satellite Report Series Number 4 July 15, 1958 irIGY World Data Center A ' ^Rockets and Satellites National Academy of Sciences Washington 25, D. C. OBSERVATIONAL INFORMATION ON ARTIFICIAL EARTH SATELLITES ' Edited by J. A. Hynek and G. F. Schilling Smithsonian Astrophysical Observatory (Excerpts from Special Reports Nos. 12 and 13) Project Director: Fred L. Whipple Associate Director: J. Allen Hynek Cambridge, Massachusetts Note 1. This report is issued in accord with international arrange ments on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies avail able at cost to scientists upon their request. 2. These data and/or report contents are reproduced as received from the experimenter. 3. Recipients of these reports are advised to communicate with the authors prior to utilization of experimental data for further publication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites OBSERVATIONAL INFORMATION ON ARTIFICIAL EARTH SATELLITES Table of Contents 1. The USSR Satellites Page A precision Measurement of the Brightness of Satellite 1957 Alpha One, G. S. Hawkins 1 Note on the Mass-Area Ratios of the USSR Satellites, G. F. Schilling and J. S. Rinehart 5 Orbital Results for Satellite 1957 Beta One, L. G. Jacchia 9 2. The U.S. Satellites Moonwatch Catalogue, E. P. Bullis and L. Campbell, Jr 17 The Acceleration of Satellites 1958 Alpha and 1958 Gamma, C. A. Whitney.... 22 The Secular Perturbations and the Orbital Acceleration of Satellite 1958, Beta Two, L. G. Jacchia 23 Improvements in the Prediction Program for Crossings of Given Latitude Parallels, R. M. Adams 27 3. Satellite Characteristics and Scientific Results Densities of the Upper Atmosphere Derived from Satellite Observations, G. F. Schilling and T. E. Sterne 30 Technical Parameters of the Artificial Satellites, G. F. Schilling 37 1. The USSR Satellites A Precision Measurement of the Brightness of Satellite 1957 Alpha One by 0. S. Hawkins* A photograph taken by members of the Physical Research Laboratories of BoBton University on October 17, 1957, has been used to determine the apparent brightness of the last stage of the carrier rocket of Sputnik I, designated 1957 al. This photograph was obtained during a double-station The following data were sent to the Smithsonian Astrophysical Observatory and Harvard College Observatory and published on Harvard Announcement Card 1383: Satellite 1957 al.- Dr. P. Dow Smith reports simultaneous photographs from two stations obtained by the Physical Research Laboratories of Boston Uni versity in Boston, Massachusetts. The parallactic angle was If 6 and a reduction of the plates yields the following heights and positions for the rocket: October 17, 1957 Subsatellite Point Longitude 9h 53ro 2130 23.0 24.0 Latitude Height Above Sea Level (Statute miles) 74°49'15"W 40°13'281,N 332.7 74 44 55 74 40 22 40 06 48 40 02 10 334.2 ' 333.4 Accuracy: Time +0.1 seconds Height +1.5 miles Longituae +117 Latitude +113 The reduction was made by Drs. Aschenbrenner and Hawkins of Boston University. November 5, 1957 Fred L. Whipple Director, Boston University Observatory and Research Associate, Harvard College Observatory. 2 A visual comparison, using the Sherbom film, was madh between the images of stars trailed at the diurnal rate and the trailed image of 1957 oil. This is a stan dard procedure in meteor photometry and has been des cribed by Whipple and Jacchia (1957) and Hawkins (1957) • Table I gives the data for the stars selected for the measurement. These stars were approximately equi distant from the projection center. The B.D. number is the Identification number of the star In the Bonner Durchmusterung Catalogue, and the H.D. number is that used in the Henry Draper Catalogue (Harvard Annals 91-100) . The photovisual magnitude is obtained from a photograph using a special yellow filter to simulate the response of the eye, and the photographic magnitude is obtained from exposures on standard blue -sensitive emulsion. To check the color characteristics of the emulsion, the magnitude of each star was measured with respect to. 2 of the stars of spectral type A. The color index is the difference between the magnitude estimated from the A stars and photometric magnitude. In Table I, it will be noticed that there are two determinations of color index for each star. It can be seen that there is no systematic change of index with spectral class, from which we may conclude that the emulsion exhibits a visual response curve. The images on the emulsion, therefore, give photometric or visual magnitudes. It will be no ticed that Star F appears to be about 0.7 magnitudes too faint on the film; the reason for this discrepancy is not known and Star F has been retained in the comparison sequence . First the satellite trail was compared with star trails on a copied negative film. Secondly, the satellite was compared with star trails that were cut from the same film. Comparisons were made in each series. The results are given in Table II. c at £ X <D •O C H .U O H O O ro rH a} 3 *° «H oi CO K at U oj ■P PJ o >J ft CM CM H H CO H tn p + H O l p1 p + p 1 O 1 p + p + o + P 1 + CM CM • O I OJ m • o + rH CO• p + vo H • O + CM H • O + CM H • O + CM • p + CM m i o + CM • o + H in • o i CM <? O 1 <? o + o + <? <? O 1 ? o 1 ? <? O fa O in < CM < o o in m «« OJ < in <: on < O fa O to •sio in -=tt-=* o m ro ro cn vo 4^4 ct\ co 4 m cr* 4 h o\ -=!• -st cm cm in 4 inir>44 o t>m CM VO on O VO ■=* in 00 in H in CM CM ro o> m in O ■sf o m CO CM CM in o oo m CM VO 0> t-CM o o H O 1 H O 1 H H « O 1 H ? H O + • o r-M ' 3 P 60 -H o c, £ Ml O at rH o •H <D Pi -O -P 3 <D -P S& P Sfl O aT u a jo ON r-l m VO o7 m vo ro in o CO ** O rH CM H 3 in o> rH CO CM CM O op CM vo ro ■sj- in ro Ot tCM 55 • OJ CP I CMrHincTvCMOOvomcr\vocMm CO CO CM rH rH -=»W (J\ 0\ 4 4 vo vo vo t- t- vo t- vo vo vo vo vo vo in U at p CO in H + in H + H + rH + CO H + W fa H m rH + in rH + CM CM + CM CM + H CM + o H CM + ll TABLE II Star Satellite Magnitude Series 1 4.3 4.5 4.6 4.6 4.9 4.0 5.0 5.1 A B C D E P 0 H J K L M N It 4.4 4.6 5.0 Satellite Magnitude Series 2 4.4 4.8 4.4 ?-8 4.8 5.0 a 4.6 4.8 5.0 The mean values were: Series 1 Series 2 M = 4.63 M = 4.60 Standard deviation +0.34 Standard deviation +0.36 This is the magnitude that the satellite would have shown if it moved across the sky at the diurnal rate of stars at declination + 17°, the mean declination of the comparison stars. As the trail was interrupted at known time intervals, the angular velocity of the satellite was known. We may obtain the actual magnitude of the satellite by correcting for the trailing velocity according to equation (110) of Whipple and Jacchla (1957). The visual magnitude was found to be -1.1. That is to say the satellite 1957 cxl was 1/2 magnitude fainter than Sirius. References 1. Whipple, F. L., and L. 0. Jacchla: Smithsonian Contributions to Astrophysics, 1, 183, 1957. 2. Hawkins, Q. S., Smithsonian Contributions to Astrophysics, 1, 208, 1957. 5 Note on the Mass-Area Ratios of the USSR Satellites by 0. 1. F. Sohilling* and J. S. Rinehart** Introduction In order to make precise predictions for the orbital behaviour of artificial earth satellites in elliptical orbits relatively close to the earth's surface, the effect of atmospheric drag has to be taken into account. In turn, observed changes of the orbital elements may easily be: used in quantitative methods to derive air densities at the perigee altitudes. However, accurate computations require a knowledge of the ballistic drag parameter, that is, the mass-area ratio, the exact shape of the orbiting object, and its orientation as a function of time, including rates of tumbling and spin. In practice, so far, none of these quantities has been known with any desirable degree of ac curacy for the first Soviet satellite, 1957 a2, and only in form of guesses for 1957 al and 1957 In an early report (l) we pointed out these difficulties, as well as the operational reasons that inducedus nevertheless to attempt at least speculative estimates of the size and weight of the Soviet satellites in orbit. These numerical estimates were derived from optical observations of the dif ferent luminous intensities. They were then applied by Sterne, Polkart, and one of us (2,3) to infer some preliminary values of upper atmospheric densities from observed changes in or bital periods. Since then, a number of other investigators have ob tained air densities from observations of 1957 ct2, which seam to agree surprisingly well with those based on our early, rather speculative mass-area ratios for 1957 al and 1957 P. (See CHAPTER III, page 25 of this Report) We felt encouraged, therefore, to reconsider our early estimates and to attempt the reverse approach, i.e., the inference of mass-area ratios of the Soviet satellite rockets from calculations of atmos pheric density. * Executive Assistant to the Director, Smithsonian Astrophysical Observatory ** Assistant Director, Smithsonian Astrophysical Observatory. 6 3. Method of Approach we conducted a mathematical exercise that Inferred weights and areas of the Soviet carrier rockets, which were In orbit as 1957 al and 1957 01, from air density results obtained In relation to 1957 a2, and actually observed lifetimes. In principle, we employed a method which was used to determine mass-area ratios of ablating hypervelocity pellets In ballistic studies (4) . The de tailed derivation as well as the numerical computations will be published elsewhere. It should be emphasized that our computations re sulted in effective mass-area ratios, rather than actual mass-area ratios. For aerodynamic purposes, we are in terested in the effective presentation area which a nonspherical object displays during its flight path. We therefore define the effective mass-area ratio as m/A, where m is the mass of an object in a satellite orbit, and A is the average cross-sectional area of the object projected on a plane normal to the direction of flight. If all orientations occur with equal frequency, A is the total superficial area, a, divided by 4, taking also into account antenna drag effects. It can be proved generally that the value of A, averaged over all orientations of any convex body, is exactly one-fourth of the total superficial area (2) . 3. Conclusions The results of our calculations indicated to us that the Soviet satellites may have had effective mass-area ratios, and possibly maximum weights and presentation areas, very close to those listed in Table I. An effective massarea ratio of about 14.5 g/cm2 was obtained for Satellite 1957 al, the last stage carrier rocket which was launched on 4 October 1957 and remained in orbit until 30 November 1957. For Satellite 1957 01, the instrumented rocket satellite launched on 3 November 1957, an effective mass-are ratio of approximately 17 g/cm2 was deduced. If random orientation during flight is assumed, an average cross-sectional area of the order of 18 m2 is indicated - very tentatively - for both objects. 7 Table I Newly Derived Estimates of "Reasonable" Satellite Parameters (Based on speculative, unconfirmed assumptions) ' Effective m/A Satellite g/cm2 Maximum Mass (*) kg Effective Area (A) m2 t 1957 al 14.5 1957 a2. 24.1 1957 01 17.2 2,690 83.6 3,200 18.6 0.347 18.6 However, we want to draw only one firm conclusion: Estimates of upper atmospheric density based on obser vations of the Soviet Satellite 1957 «2 appear to be reliable and indicate substantially higher densities than previously often assumed. This conclusion has recently received strong confirmation by Sterne (5) through estimates of density based on observations of the U.S.A. Satellite 1958 a. However, density values which have been inferred from observations of 1957 al and 1957 01 are mathematically uncertain by more than 50 percent, and involve so many speculative assumptions that we see no way to use the observational data for density deter minations with real confidence. In other words, we have to wait until the U.S.S.R. announces the basic design values before definite scientific conclusions about upper atmospheric density can be drawn from observations of the Soviet Satellites 1957 al and 1957 01. Since the Sputnik launchings were part of the International Geophysical Year Program, we expect that these rocket parameters will be made available soon. Until they are released, however, we wish to consider the above estimates as "reasonable" results of a mathematical exercise only. 8 4. Acknowle dgeme nt 8 We wish to thank Professor T. E. Sterne for his valued criticisms of our manuscript as well as his contributions with respect to density values inferred from satellite obser vations . 5. References 1. Rinehart, J. S. and G. P. Schilling: "Additional Orbit Information for USSR Satellites 1957 Alpha One and Beta One." Special Report No. 2, IGY Pro ject No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, November 5, 1957. 2. Sterne, T. E. and G. P. Schilling: "Some Preliminary Values of Upper Atmosphere Density from Observations of USSR Satellites." Special Report No. 3, IGY Pro ject No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, November 15, 1957. 3. Sterne, T. E., B. M. Polkart, and Q. P. Schilling: "An Interim Model Atmosphere Pitted to Preliminary Densities Inferred from USSR Satellites." Special Report No. 7, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, December 31* 1957. 4. Allen, W. A., J. S. Rinehart, and W. C. White: "Pheno mena Associated with the Plight of Ultra-Speed Pellets." Journ. Appl. Physics, 23, 132-137, January 1952. 5. Sterne, T. E.: "The Density of the Upper Atmosphere." Chapter III in Special Report No. 11, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. Note A4494 in Proof A recent Soviet release states that "... the values (of density) ob tained were five to ten times greater than the values indicated for these heights (225-228 kilometers perigee) in a number of studies of the atmos phere based on rocket measurements prior to the launching of the satellites." Since these values agree exceedingly well with those derived in Reference 2, we can consider this as corroborative evidence that our speculative mass-area ratios for the Soviet satellites may be quite reasonable, (cf. Chapter I, Page 8 of this Report) 9 Orbital Results for Satellite 1957 Beta One by Luigi Q. Jacchia * Introduction A first set of orbital data for Satellite 1957 Beta One, covering its lifetime up to February 10, 1958, was published in Special Report No. 9 (1). The present report covers the complete lifetime of the satellite. Since all the observations have been reduced anew with improved elements, this report supersedes the aforementioned Report No. 9. Method of Reduction Tables 3 and 4 summarize the results of an analysis of approximately 2800 optical and radio observations, reduced by means of an improved version of the author's subsatellite program ( 2) which contains the following new features: A. Continuously varying perigee distance. The relation q ■ q(a) between perigee distance and major axis is determined by fitting the solution of the differential equation da/da ■ f(q, a) through well -observed points, and then is fed into the machine program in the form of an approximating equation with 10 numerical coefficients. B. A special high-latitude program. Observations at low and middle latitudes yield independent determinations of the right ascension and of the time of the ascending node. For observations made at high latitudes, near the orbital apex, the effect of observational errors is greatly magnified in the independent solutions. If, however, the position.' of the node is accurately known for the time of observation, an accurate time for the equatorial crossing can still be obtained. The new feature in the sub-satellite program provides for an optional switch to the latter type of reduction when the sub-satellite point is within a specified number of degrees of latitude from the apex. For the computation of the sub-satellite points, the following orbital elements were used : Inclination i = 65"; 29 Argument of Perigee CO » 58?0 - V. 3938 (t-T) - 2°50 x 10"4 (t-T)2 - 3° 1 x 10"7 (t-T)3 (T= 1957 Nov. 6.0 U.T.; t in days). The major axis of the orbit was obtained from the nodal period, obtained by differentiation of the interpolating equations H d 6 2 d 0.0017n 1. T^ = 1957 Nov. 4.41000 + 0 .0720825n -1.19 x 10 iT -0.03820(e -1) + 0101700 sin(0,;237n - 128°). (0<n^l800) ♦Astrophysicist, Smithsonian Astrophysical Observatory. 10 2. = 1958 March 9.51267 +0^066453^-1800) -2?56 x 10"6(n-1800)2 -0*00125927 r0.0095(n-18OO).q 3. ( 1800< n^2300) = 1958 April 10. 95583 + 0?062547(n-23O0) -8d78 x 10"6(n-2300)2-8. 316 x 10 _S r-0.097 (n-2300) ^ {n>23QQ) The residuals from these equations never exceed o4o02 and the errors in the computed period and heights are negligible in the computation of sub-satellite points, nodes and equatorial crossings. The relation between the major axis and the perigee distance is given in Table 1. Table 1 a a e 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.03360 1.03333 1.03302 1.03268 1.03230 1.03187 1.03137 1.03079 1.03008 1.02920 1.02805 1.02639 1.02370 1.01869 0.1012 .0936 . 0858 .0780 .0700 .0619 .0538 .0456 .0373 .0291 .0209 .0131 .0061 .0013 a: Semi -major axis of orbit in units of the earth's equatorial radius. qi Perigee distance e: Orbital eccentricity. Values of dq/da were computed from Sterne's equations (3) using the Smithsonian Interim Atmosphere (4) and integrated starting from the normal point q = 1.03302 for a = 1. 13. The integration was performed by Mr. J. Slowey using a special program on the I.B. M. Type 704 Calculator. For the reduction of the high-latitude observations the following equations were used for the position of the ascending node. 11 U = J08S2 - 2°6079 (t-Nov. 6.0) - 1?6S6 x 10~3 (t-Nov. 6.0)2 - £08 x 10"6(t-Nov. 6.0)3. (for dotes before 1958 Mar. 11 J 2. ■ 112U - 3°175(t-Mar. 11.0) - KS x 10"4(t-Mar. 11. 0)3 (for date* after 1958 Mar. 11). ' Results Normal values of are given in Table 2. at 5 -day Intervals, together with the observed precession, Table 2 t(U.T.) Hi 1957 November 6.0 11.0 16.0 21.0 26.0 December 1 .0 6.0 11.0 16.0 21.0 26.0 31.0 1958 January 5.0 10.0 15.0 20.0 25.0 30.0 February 4.0 9.0 14.0 19.0 24.0 March 1.0 6.0 11.0 16.0 21.0 26.0 31.0 April 5.0 10.0 14.0 108? 2 95"; 0 81.7 68.3 54.8 41.5 28.0 14.4 0.7 346,9 333.1 319.1 305.1 291.0 276.7 262. 3 247.9 233.3 218.6 203.9 189.0 174.0 158.8 143.4 127.8 112.1 96.3 80. 2 63.8 47.1 30. 1 12.7 358.2 : Right ascension of the ascending node da^/dt s Nodal precession in degrees per day da^/dt -2»64/day -2.65 -2.66 -2.67 -2.68 -2.70 -2.71 -2.73 -2.74 -2. 76 -2.78 -2.80 -2.82 -2.84 -2.86 -2.88 -2.90 -2.92 -2.94 -2.96 -2.99 -3.02 -3.05 -3.09 -3. 13 -3.16 -3.20 -3. 25 -3.31 -3.37 -3:45 -3.57 c 12 Table 3 gives normal values of T^, the time of the equatorial crossing of the satellite from south to north, at intervals of 25 revolutions. The numbering of the revolutions is the same as in Special Report No. 9 (1); the first crossing in the list (n a 0) was actually the 16th crossing after the launching of the satellite. Also given are the nodal period, P^, , and the orbital acceleration dP/dt, in seconds per day; these quantities were obtained by numerical differentiation of T^ . The last fifty revolutions are tabulated in greater detail (at Intervals of 5 revolutions) in Table 4. A plot of dP/dt against n, covering the first 2100 revolutions, is given in Figure 1. Due to the slow motion of the perigee for the particular inclination of this satellite, there is no difference, within the tabular accuracy, between the accelerations of the nodal and the anomalistic period. A discussion of the observations coveringthe last revolution and the demise of 1957 Beta One will be the object of a separate report. Table 3 n 0 25 50 7S 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800 TjUU.T.) 1957 Nov. 4. 39469 6.19415 7.99206 9.78842 11.58327 Q 3. 37664"] D5.16860J D6-95918J Q8. 74830 Q20.53596J Q22. 322143 C24. 10679J 25.88993 27.67149 29.45146 1957 Dec. 1.22989 3.00673 4.78202 6.55577 8.32796 10.09857 11.86764 13.63516 15.40117 17. 16566 18.92860 20.68992 22.44952 24. 20735 25.96338 27.71753 29.46977 31.22002 to (0*1072009) .071947 .071885 .071824 .071764 _. 0717063 1.0716513 Z. 071 5943 1.0715363 ..071477J 1.0714173 1.0713563 .071294 .071231 .071168 .071105 .071042 .070981 .070919 . 070856 .070794 .070732 .070671 .070610 .070549 .070486 .070419 .070349 .070278 .070204 .070128 .070050 .069970 dP/dt -2?97/day -2.92 C-2.84 3 C-2.71 3 L-2.66 3 L-2.79 J L-2.85J L-2.86J C-2.93 3 IT- 2. 95 3 [-3.05 3 -3.07 -3.04 -3.06 -3.03 -2.99 -3.05 -3.06 -3.03 -3.00 f -2.97 -2.96 -3.04 -3.17 -3.37 -3.48 -3.57 -3.68 -3.78 -3.90 -4.05 13 Continued n 825 850 875 900 925 950 975 1000 1025 1050 1075 1100 U25 1150 1175 1200 1225 1250 1275 1300 1325 1350 1375 1400 1425 1450 1475 1500 1525 1550 1575 1600 1625 1650 1675 1700 1725 1750 1775 1800 1825 1850 1875 1900 1925 1950 1975 2000 2025 2050 2075 Table 3 dP/dt T&U.T.) 1958 Jan. 1.96825 3.71436 5.45850 7 . 20068 8.94090 Do.679lfl D 2. 41520 Q.4.14928J Q5. 88102) 17.61056 19.33801 21.06338 22. 78666 24.50798 26. 22734 27.94476 29.66027 31.37387 2.08553 19S8 Feb. 3.79525 5.50294 7. 20851 8.91190 10.61300 12.31171 14.00809 15.70225 17.39420 19.08389 20.77124 22.45618 [?4. 13870] £25. 81897) p7.4970|] 1958 Mar. T 1.17279J 2. 84608 4.51683 6.18491 7. 85025 9.51273 11.17220 12.82844 14.48130 16.13073 17.77672 19.41925 21.05828 22.69375 24. 32557 25.95362 27.57771 d 0.069887 .069804 .069726 .069648 .069569 C. 0694883 C 0694043 C-069315D £.069225j .069139 .069056 .068973 .068892 .068814 .068735 .068658 .068582 .068505 .068428 . 068349 .068266 .068180 .068091 .067996 .067901 .067810 .067722 .067633 .067541 . 067446 . 067349 C 06722511 Q 0671 60 Q 0670773 r.06698Q .066881 .066777 .066669 .066557 .066440 .066315 .0661183 . 066046 . 065909 .065771 .065631 .065490 .065346 .065198 .065044 .064882 -4! 12/ day -3-96 -3.84 -3.91 -3.97 C-4.083 C-4. 33j C-4.513 £-4.393 -4.20 -4.18 -4.15 -3.98 -3.92 -3.51 -3.84 -3.85 -3.90 -3.94 -4.10 -4.28 -4.42 -4.67 -4.85 -4.75 -4.54 -4.50 -4.61 -4.80 -4.97 -4.94 C-4. 62:1 C-4. 523 C-4. 803 f-5.063 -5. 27 -5.50 -5.69 -5.92 -6. 28 -6.72 -7.05 -7.14 -7.21 -7.28 -7.37 -7.51 -7.71 -8.00 -8.38 -8.82 Continued Table 3 n dP/dt T.) 2100 2125 2150 2175 2200 2225 2250 2275 2300 2325 2350 1958 Mar. 1958 Apr. 29. 19766 30.81321 1 . 42396 3.02941 4.62906 6. 22238 7.80859 9.38686 10.95582 12.51318 14.05088 0^064712 .064529 .064327 .064106 .063863 .063596 .063296 .062957 .062547 .062008 .06050 - 9! 40 /day -10.28 -11.34 -12.48 -13.80 -15.3 -17.3 -20.2 -25.3 -38.2 -430. : Values enclosed in brackets are uncertain because of scarcity of observations, n »> Number of revolutions elapsed. Tj^ ■ Time of ascending -node crossing. « Nodal period in days. dP/dt = Orbital acceleration in seconds per day. Table 4 The Last Fifty Revolutions of Satellite 1957 fll n 2300 2305 2310 2315 2320 2325 2330 2335 2340 2345 2350 TA(U.T.) 1958 Apr. 10.95582 11.26830 11.58032 11.89184 12. 20281 12.51318 12.82285 13.13175 13.43970 13.74637 14.05088 dP/dt 0. 062547 .062543 .062355 .062251 .062136 .062008 .061920 .061692 .061477 .06117 .06050 -25! 3 /day -26-8 -28.0 -30.4 -33.6 -38.2 -43.0 -52.0 -69.0 -120. C -430. : 0 500 2000 1500 1000 n function of 1. Figure change number the Rate period orbital as a (n) (For 3.) rTable of cto time eovna see n ovleurtsio.ns Revolutions of Number References (1) Jocchia, L. G. , "Basic Orbital Data for Satellite 1957 Beta One. " Special Report No. 9, ICY Project No. 30. 10, Smithsonian Astrophysical Observatory, Cambridge, February 21, 1958. (2) Jacchia, L. G. , "Program for Determination of Geographic Sub-Satellite Points. " Chapter IV, Special Report No. 11, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. (3) Sterne, T. E. , "An Atmospheric Model, and Some Remarks on the Inference of Density from the Orbit of a Close Earth Satellite. " Astronomical Journal (in press). (4) Sterne, T. E. , B. M. FolkartandG. F. Schilling, "An Interim Model " Atmosphere Fitted to Preliminary Densities Inferred from USSR Satellites. " Special Report No. 7, IGY Project No. 30. 10, Smithsonian Astrophysical Observatory, Cambridge, December 31, 1957. (Published in Smithsonian Contributions to Astrophysics , Vol. 2, No. 10, pp. 275-279, 1958.) 17 2. The U.S. Satellites Moonwatch Catalogue by E. P, Bullis* and L. Campbell, Jr.»* This catalogue of MOONWATCH observations is from March 25# 1958 to April 30, 1958, continuing from the MOONWATCH Catalogue of ICY Report No. 11, (Campbell, Leon, Jr. : "Moonwatch Observations of Satellites 1958 Alpha, 1958 Beta One, 1958 Beta Two, and 1958 Oarama. Chapter II, p. 7 in Special Report No. 11, Smithsonian ABtrophysical Observatory, Cambridge, March 31# 1958.) Twenty-four MOONWATCH stations have reported a total of 154 observations of Satellites 1958 a, 6, and y. The first three United States satellites have been faint and thus, difficult to observe with the typical 50 mm, 5.5 power telescope used by most MOONWATCH teams. Bloemfontein 401, Cape Town 402, China Lake 098, Alamogordo 103, and Yuma 107, however, are using Ml 7 elbow telescopes modified with 120 mm objectives and of 20 power, as well as the standard M17 of 50 mm objective and of 8 power. The key to the MOONWATCH station, code precedes the catalogue . * Administrative Officer, MOONWATCH Project, Optical Satellite Tracking Program, Smithsonian Astrophyslcal Observatory. ** In charge of MOONWATCH Program, Optical Satellite Tracking Program, Smithsonian Astrophyslcal Obser vatory. 18 •4«*rONN f-O C\] t- © W\ «- t- r- co t^rjvO u>tM ocnj cn.vO On r»N,NO >r\ »r» -* r- tD & Pi K • •• • • t> t- c\ on vQ 1- On £■ nO On lA • • . • »A t- O P\ V\ ^* 0s no qnc^C-vO m-^cMntQ c"\ t\j vO >o i"T-NOryiftPMl|M»,i(MT-NOr-i-r(Nt f t- <V VNnO -4 to O vD tO CO to «Q tt> vO t\jONO<o»-ooT-ONr^<Ni»-cv}<NiCMc^c«> r~ rt— t- r- ^rt— t Rad/Yel Yel/Wh. Yellow White White White Bl./Wh. White White White White White White White White White Bad •a ♦ oo + IA »A IA • . ia ia ia g;cv 0.183 .86 0.85 1.15 .25 0.27 0.22 0.22 0.20 1.2 0.6 0.5 25• 0.17 .04 o• is! s s » ir» to S3 t- (V oo ON £~ CO O0 oo 9 >£nS >a cv va vQ cv -* ia cv -*c*\ >Jcv c»> ?to g> c^eo ™ V +" S8 r- vO 7*? 8 to 8 a 9 o O CO -4 r- o 8S 00 r— CV «- M> •AO O t> ca P? 00 o> f*N f> CV o o o o CV «A V? oo o o • M CD • H ■ i|3 • CD * 3 6n » • a] J 4» «H fj • J3 3 •H O -H »o» Li] Si 3 ia C- cv c> o iaoo + no Hp 19 i O c»\ >A in u> T- vO **> \0 f*> CV 8 P £8 36 o o o ia o CO CV •A O C\ cv f o <^«^o C*\ IA cv »A\0 t- ia »IA O cv ^ o o >♦ »A »* C> r- O O t00 rO CV t- o CV 2> cv O CV s r» *— C*> t> vO CO T- •• CV p t> C\ CV •• ~T 00 O O r- cv CA «• n e> CO a IA IA »A ia fA CV <*\ t- « «A y- O O «A «A 3* -*"«tC«>4* »a -«t q ^*cv O «^ S c^lSc^l O O O «H o o -h o o o O _ 00 g £> O hOr r CV *H o r- tT- O o o O »— O o O o o u o o u »• Cm «h VH •H O 'eo O 3 § O 8 O «H S3 •P ° g • Id * * CD o «o CD N ■P CO o q 4» « o •P CO -P CO A» 8 34 13 bp 11* 3 1 ^ Boo a) SB a) cd SB 3 H XI a) S5 XI P CD SB O M CO CO CO H «»! O CO CO O 00 00 sO i §8S?: ft ia 3 »A t> ia »oo «r» ?? 8 r»> va IA c*> o cv CO tC\ IA O «AvO r- «A c^» CV - «> t- CV a cv o a> ^ ^ s O ~* C*N o o n OO O T3 >a U t- r- O O o . »A -4 1— CV o I 5 o u r-t CD ft) CO 4* o x> cd o ■P 0 o ai c +> 2 c -P at 1 K ffe 4> CD cj j j« X> X) P SB H a) to <4 << CO CO O H 9 cS «q CD N M -ri a o Ss a) o a) +> So Vi i •¥ § *\ li o H CM o of 1 o on 1 Alti tude 1 3 3 is * £8 8 •H o m ♦> oJ o to 7^ s <? 7 <*>?J 8 •HI J3 -t-> if £88 8 c$88 s ■H x; ©' bO Ol •H CD1 OS -51 ISl O rt- CV N r- CM 4» •• c\ cv o3 g cv oo o >* cm «r\ cm M T" f\ S3 t— f\ T- o^ <*> O^ r- O r- i- O «- t- O O ■H O O O U O CM 00 CM C*\ O o o cm cv cm in en A » o <S IT o> • n «5 vc a «- « o h (8 S H P <5 IT O" :» 5 O 20 CO 4» 4 Ot H «H |I 3 -r) *H • ^3 u o o O O \D o sO vO O • • • O O »- + h + ♦ rH O iH 5 o S a) 8&<S883 <3> f> C\ v£> sD CO 3 o -4tOO^ < **\ 00 £~ I c CM 0 cd 9 t- \0 ^>43 vO O <^ (V oi iri rocA in c> o «o t> o o o a o ill 8S 4» a J3 CD bo o 8 O rvrvjo •• co cm t> © *n rA «- o ^* C> C\ "»T to to to 00 to i«AO m g (V O N i^ry to »- CO -H t- <0 00 t- «- o T-T-OUT-T-r-t— T-O c t- CM O^O^O^O OOO OOO'-rNN O 00 40 00 o o • «< • tO ■ cd • * • cd b «H • • "H tO K CHti <! rj v ,£3» i-» oO cd • • O cd •>H q *cj o -p to to gj ft •» m hO CD P CD » •> ID JJ ff&V} M C g .* ij <u <c «< • • • • to to to to «h «l «l «l a M C 60 3o N «H a & c w O B O CD 00 c o 4* ^ 1 111 cd rH o H o tp p_,+jqtpa)o3crt O bO O «r? P. D--H -H g rH-H >Z A d « X! P (OCQ3 O U O O O Jm CO •I £1 NT-r*\i-n 33333 tj i- m v£> 21 CO CM CM 00 CO t> 22 The Acceleration or Satellites 193d Alpha and 1938 Gamma by C. A. Whitney* As discussed In an earlier report,** Information about the variable acceleration of artificial satellites can be de rived from an analysis of Mini track and Moonwatch observations. Tables I and II below give the results of such an analysis for Satellites 1958 Alpha and 1958 Gamma, both of cylindrical shape The tabulated numbers are unsmoothed values. Table I Acceleration of 1958 Alpha (dP x 10? In days/rev2) dN Rev. No. x 1<>7 Rev. No. dN 50 100 150 200 250 300 350 400 450 dN -3.4 -5.2 -4.3 -3.8 -3.2 -3.6 -2.2 -4.0 -4.9 500 550 600 650 700 750 800 850 900 950 -4.3 :t:l -5.5 -M -4.2 -4.4 Table II Acceleration of 1958 Gamma Rev. No. dP x 106 dN 25 50 75 100 125 150 175 -9.3 -10.9 -12.2 -13.0 -13.4 -13.0 -13.6 * Physicist, Smithsonian Astrophysical Observatory ** (Whitney, Charles A. : "The Orbit and Variable Acce leration of Satellite 1958 Alpha." Chapter III, p. 14 in Special Report No. 11, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958) * Reproduced as IGY Satellite Report No. 2 23 The Secular Perturbations and the Orbital Acceleration of Satellite 1958 Beta Two by L. G. Jacchla* An analysis of 4l8 Minitrack observations and two visual sightings of the Vanguard Satellite 1958 P2 be tween March 19 and May 7, 1958 has revealed an acceleration of the orbital period amounting to 0.017 seconds per day. Perigee crossings and ascending nodes were first com puted from the observations using the author's sub-satellite program (1) with the following elements communicated by the Naval Research Laboratory on May 8, 1958: Epoch tQ = 1958 May I.51875 U.T. Anomalistic Period 134.277 minutes Eccentricity 0.1901d Inclination 34?25 Right Ascension l8°39 - 3?039 (t-tQ) of Ascending Node Argument of Perigee 326? 58 + 4?437 (t-tQ) Mean Anomaly at Epoch 206 ?72 Semi-Major Axis I.36185 earth's radii A plot of the residuals in the time of perigee passage showed that the best fit was obtained by the equation Time of Perigee = 1958 Mar 17.61040 (U.T.) + 0&932577 n - 9.1 X 10-9 n2 . (n = number of revolutions after 1958 March 17.61040), while the right ascension of the ascending node satisfied the equation a. = 158?60 - 3?016 (t - March 16.0) The observed nodal precession is smaller by 0.7 percent with respect to the theoretical first-order value computed using J = O.OOI6385* *in good agreement with the author's re sults for Satellite 1957 pi (2,3), for which the discrepancy was found to be 0.5 percent, in the same direction. A rough evaluation of the second-order term in the nodal precession indicates that it cannot account for the discrepancy, so the conclusion is that J must be somewhat smaller than the assumed * Physicist, Smithsonian Astrophysical Observatory ** J is the coefficient of the second-order term in the ex pansion of the earth's gravitational field in spherical harmonics. 21 value, probably around 0,001629. The observed nodal preoession was used to oorraot tha prooasslon of tha perigee, aooording to tha ratio JL m 2 - 5/2 am2 i 4^ ooa 1 (1 m lnolinatlon) Quadratic terms were oonputed for both an and u) from the observed orbital aooeleration, under the assumption of constant perigee distanoe. The following elements resulted: T ao 6d q = = = 1958 March 16.0 158?60 - 3?016 (t-T) 121?6 + 4?4o8 (t-T) 1.10285 _ 0 - lfl x 10*5 (t-T)* + 1?6 x 10"5 (t-Tr Time of Perigee = 1958 March 17.63060 + 0? 0932 5728 n - 9J x 10-9 n2. The resulting orbital acceleration is thus OsOl69 per day, with an estimated error of + 0?005. The systematic resi duals in the observed time of perigee from the above equation are very small, of the order of 1 or 2 seconds, although the total acceleration in the time of perigee during the time covered by the observations amounts to 3.9 minutes. Moreover, they seem to fit a period equal to half of the period of rotation of the line of apsides, indicating that they are due to the long-period perturbations of the major axis of the orbit (4). It therefore looks as though irregular or semiregular fluctuations of the acceleration, such as were ob served in 1957 pi (3) are absent or quite small in 1958 p2. We are thus led to the following conclusions: 1. The smallness of the fluctuations in the accleration of 1958 02 shows that gravity anomalies - which hare been suspected by some investigators to be the cause of such fluc tuations - must be discounted as a factor in producing largescale variations in the accelerations of satellites; 2. Atmospheric drag is left as the most probable cause of the variable accelerations. Since the relative amplitude of the oscillations seems to be smaller for a spherical, or symmetrically shaped, satellite, than for an elongated object such as 1957 01, it looks as though the cause should be sought in the variable attitude of the satellite rather than in a day-to-day global variation of the atmospheric density at high altitudes. The great difference in height between the perigees 2$ of 1957 pi and 1958 £2 makes it impossible to exclude the hypothesis of the day-to-day variations altogether, since these may be confined to preferential layers of the atmos phere; off hand, however, tnls hypothesis does not look realistic. Atmospheric Density Inferred from 1958 Beta One By Sterne's equations (5), we can compute the atmos pheric density corresponding to the perigee height of 1958 02. The physical characteristics of the satellite, as communicated to us by the Naval Research Laboratory, are as follows. Mass in orbit: 3.242 lb. Outside diameter of the sphere: 6.462 inches. There are six cylindrical antennae, each 12 inches long and 0.3125 inches thick, and six solarbattery cells, 2x2 1/8 inches each, protruding 1/2 inch above the surface at center and 5/8 inches at the edges. Prom these data, we derive a total area of 1457 cm2; the average presentation area is assumed to be 1/4 of the total area, or 364 cm2. The scale height of the atmosphere was , computed by successive approximations, trying to fit the new density to an extension of the Smithsonian Interim Atmos phere (6). Using the observed value of the orbital acceleration, 0?Ol69 per day, and the orbital elements given above, we obtain: At Z - 656 km, log1Qp = -15.45 (g/cm3). (d In ^>/dZ = -1.08 x 10"7). The following density profile takes into account all previously published atmospheric densities inferred from artificial satellites (7). Height log10 p (km) (g/cm3) 200 250 300 -12.18 -12 . 80 -13.28 -13.68 -14.03 450 500 550 600 650 -14.91 -15.17 -15.42 The assistance of Mr. R E. Brlggs in handling the Minitrack data for machine analysis is gratefully acknowledged. - 26 References 1. Jacchia, L. G., "Program for Determination of Geo graphic Sub-Satellite Points." Special Report No. 11, IGY Project No. 30.10, p. 26, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. * 2. Jacchia, L. G., "Satellite 1957 Beta". Harvard An nouncement Card 1391, February 5, 1958. 3. Jacchia, L. 0., "Basic Orbital Data for Satellite 1957 Beta One." Special Report No. 9, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, February 21, 1958. 4. Garfinkel, B., "On the Motion of a Satellite of an Oblate Planet." Ballistic Research Laboratories, Report No. 1018, Aberdeen, Maryland, July, 1957. 5. Sterne, T. E., "Formula for Inferring Atmospheric Den sity from the Motion of Artificial Earth Satellites." Science, in press. 6. Sterne, T. E., B. M. Folkart, and G. F. Schilling, "An Interim Model Atmosphere Fitted to Preliminary Densities Inferred from USSR Satellites.1.' Special Report No. 7, IGY Project No. 30.10, Smithsonian Astrophysical Observatory, Cambridge, December 31, 1957. 7. Sterne, T. E., "High-Altitude Atmospheric Density." Paper presented at the Meeting of the American Physical Society, Washington, D. C, May 1, 1958. (Six values of atmospheric densities from Satellites 19^7 Alpha Two, 1958 Alpha, and 1958 Gamma.) * Reproduced as I3T Satellite Report No. 2 27 Improvement! in the prediction Program for crossings or Given Latitude parallels by R, M. Adams* In Speoial Report No. 11, a diioussion of the pre diction program for crossings of a given latitude parallel was presented by John Oaustad.** A revision of this pro gram is now being considered whioh will make it more generally useful for observation teams throughout the world. As desoribed by Oaustad, this ephemeris produoes pre dictions of times, longitudes, and heights of orossings of any given latitude parallel. The predictions have been distributed by mail to observing teams in the northern hemis phere. In the oase of the Soviet satellites, the predictions have been made for crossings of 40 degrees North latitude. For American satellites, predictions have been made for cros sings of 30 degrees North latitude. In this form, the pre dictions are not of great value to observing teams In the southern hemisphere. The revision which is contemplated will . produce predictions of the times, longitudes, and heights of crossings of the equator with corrections computed for several latitudes in the northern hemisphere and also for several la titudes in the southern hemisphere. This will enable an ob server at any latitude to compute with a minimum of effort predictions for the latitude nearest his observing station. These predictions will be sent to the observing teams by Air Mail. It is hoped that the predictions can be made far enough in advance so that the time delay encountered will not be too critical. * Chief, Computations and Analysis Section, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. ** Gaustad, John: "Predictions for Crossings of Given Latitude Parallels — APO Ephemeris 5." Chapter IV, page 28 in Special Report No. 11, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. •"• Reproduced as IjY Satellite report Ho. 2 28 As mentioned In Special Report No. 11, one of the outputs of this prediction program is called a "situation report". Included here in Table I are examples of situation reports for satellites 1958 Alpha, 1958 Beta One, and 1958 Gamma. (Elements used for 1958 Alpha and 1958 Beta One were obtained by the Smithsonian Astrophysical Observatory. Those used for 19 58 Gamma were obtained by the Naval Research Laboratory with the exception that the rate of change of period and rate of change of height of apogee were obtained . by the Smithsonian Astrophysical Observatory.) It is planned to include a situation report with each set of predictions which are sent to the observing teams. Moreover, the or bital elements from which the predictions are computed will also be included. Table I Situation Report April 17, 1958 1958 a (Computed at 01*13311111. t. -based on elements of Apr 15,1958) Period Rate of change of period Latitude of perigee Rate of change of latitude of perigee Height of perigee , Height of apogee Rate of change of height of apogee Height over 30th parallel North: South -North North-South Total number of revolutions 114.18 min -.008 mln/day -27.33 degrees South -2.14 deg/day 222.8 miles 1556.2 miles -0.4 miles/day 1547 II76 miles miles 94l 1958 pi (Computed at 01h02mU.T. -based on elements of Apr 14,1958) Period Rate of change of period Latitude of perigee Rate of change of latitude of perigee Height of perigee Height of apogee Rate of change of height of apogee Height over 30th paralled North: South-North North*South Total number of revolutions 133-95 min -34.02 -O.36 409 . 3 2462.2 -0.3 degrees South deg/day miles miles miles/day 2361 2202 miles miles 325 29 Table I (cont'd) Situation Report 1958 y (Computed at 01 07 U.T. -based on elements of Apr 9,1958) Period Rate of change of period Latitude of perigee Rate of change of latitude of perigee Height of perigee Height of apogee Rate of cnange of height of apogee Height over 30th parallel North: South-North North-South Total number of revolutions 110.36 -0.347 -24.83 -2 . 62 115.5 1440.1 -19.8 min min/day degrees South deg/day miles miles miles/day 1412 968 miles miles 270 30 3. Satellite Characteristics and Scientific Results Densities of the Upper Atmosphere Derived from Satellite Observations* by G. P. Schilling** and T. E. Sterne*** Since the launching of the first artificial earth satellite in October 1957, sufficient orbital information has become available to derive values of upper atmosphere density at various altitudes. We have collected such studies as conducted by various investigators, and list here the results of all investigations known to us at this time. Complete literature references are given. Table I contains a full tabulation of numerical values, arranged according to geometric height above the earth's surface. The column headed "Satellite" refers to the object which served as the observational tool for the various authors. The values in parentheses Indicate the results of early calculations which have been superseded oy later studies, based on the same orbital information. Figure I is a density versus altitude plot on a semi-logarithmic scale. In addition to the observational values of Table I, the figure contains portions of model atmospheres between 175 km and 400 km (geometric). The values derived by G. V. Groves (11 ) are contained in the table, but were received too late for inclusion in the figure. » Pressed at the Symposium on Satellite Geophysical Studies, American Geophysical Union, National Academy of Sciences, Washington, D. C, May 6, 1958. ** Executive Assistant to the Director, Astrophysical Observatory. *** Associate Director, Smithsonian Astrophysical Observa tory, and Professor of Astrophysics, Harvard University. Smithsonian 31 It is at once apparent that all individual density values fall within an area bounded by the RAND Model I 1948 Atmos phere for 45° latitude (l) and the ARDC 1956 Model Atmosphere (2). Within this area it appears that Models 1 and 2 of the Smithsonian 1957 Interim Atmosphere (3) approximate the observations rather closely. Although the three Smithsonian interim models were based essentially on only one reliable, early density inferred from Satellite 1957 o2, each was internally consistent. (Refer to Reference 3 for the complete numerical values of pressure, temperature and density to an altitude of 500 km.) The 1952 Rocket Panel Atmosphere (4) reaches to 220 km. The NRL rocket observation, made on August 7, 1951 > and used as the basis for the Rocket Panel atmosphere at this high altitude, gave actually a value of 1.0 x 10-13 g/cnP at 219 km. Table I Atmospheric Densities Derived by Various Investigators (368) (1.5 x io-iV (1958 a) Sterne 5 368 1.4 x io-14 1958 a Sterne 5 275 8.5 x io-i* (?) 1957 a2 Harris and Jastrow 8** 241 2.5 x 10-13 1957 a2 Royal Air craft 6 233 2.2 x 10-13 1957 PI Sterne and Schilling 7 * Result of early calculations which have been superseded by later studies, based on the same orbital information. ** Harris and Jastrow have published three suggested extra polated variations of density with altitude. The value of 1.5 x 10"13 gm/cm3 appears to be the actual mean density value derived by them from Minitrack observations for the perigee altitude of 232 + 5 Ion at the epoch given. See Reference 8 for details . Tafele 1 (eentinued) Height Kilo(ineters) i Density (gm/om3) Satellite Author Referenoe 232 1.5 X 10-13(?) 1957 a2 Harris and Jastrow 8** 220 10-13 5.7 X 1957 al Sterne and Schilling 7 (1957 a2) Sterne and Schilling 7 (220) (4.5 X 10-13)* 1957 a2 Sterne 5 215 4.0 X 10-13 4.7 X 10-13 1957 a2 Prlester et al. 212 4.8 X 10-13 1957 PI Sterne and Schilling Sterne and Schilling 9 ♦»« *#* 1957 P Groves 11 220 (212) (4.4 X 10-13)* 1957 pi 211 + 4 4.6 X 10-13 206 + 7 5.4 X 10-13 7.3 X 10-13 1957 a2 Groves 11 1957 al Groves 11 6.7 X 10-13 4.0 X 10-13 1957 o2 Groves ll 1957 a2 Mullard Obs . 10 7.0 X 10-13 6.7 X 10-13 1957 P 1958 y Groves n **** 202 + 4 201 + 4 200 197 + 1 186 Sterne * Result of early calculations which have been superseded by later studies, based on the same orbital information. ** Harris and Jastrow have published three suggested extra polated variations of density with altitude. The value of 1.5 x 10-13 gm/cm3 appears to be the actual mean density value derived by them from Minitrack observations for the perigee altitude of 232 + 5 km at the epoch given. See Reference 8 for details . *** Unpublished; based on References 5 and 7. **** Unpublished; Object was given spin around long axis at launching and assumption of random orientation (see Reference 5) may not yet apply. Value of density has been derived from orbital data for the time interval 28 Maroh 1958 to 9 April 1958, provided by Dr. Charles A. Whitney, So soon after launching, this value is therefore less reliable than those for the other satellites. Comments We want to add a few critical comments of a general nature. The density values derived from the U.S.S.R. Satellites 1957 al and 1957 pi must be considered as being of rather low accuracy, Geometric Altitude (km) 34 since the technical rocket parameters have not been announced to our knowledge. (Refer also to CHAPTER I, page 3, of this report^ With regard to Satellite 1957 a2, we do not know for each case to what degree authors have taken aerodynamic drag effects on the antennas into account. In all our determinations of density from orbiting satellites, we have applied the assumption that a repre sentative sample of all possible orientations has occurred at perigee. We know that different satellites have under gone variable accelerations, and we have actually been able to deduce aspect variations from fluctuations in the drag effect. But all density points determined by us must be considered as mean values, averaged over a large number of consecutive revolutions. If and when the assumption of random orientation does not apply, density determinations should therefore spread to both higher and lower values from our mean point. So far, we have been able to study this effect satisfactorily only in the case of Satellite 1957 0. , For non-spherical objects, we are interested in the effective presentation area during its flight through perigee. For this purpose, we have used an effective mass-area ratio m/A, where m is the mass of the object in a satellite orbit, and A is the average cross-sectional area of the object projected on a plane normal to the direction of flight. If all orientations occur with equal frequency, A is the total superficial area divided by 4. It can be proved generally that the value of A, averaged over all orientations of any convex body, is exactly 1/4 of the total superficial area . All values of density listed In Table I, derived from the changes in the orbital elements of artificial earth satellites, relate to altitudes near or above the respective perigees. Since we must allow the possibility of seasonal, diurnal, latitudinal, and perhaps even sporadic variations of the air density in the upper atmosphere, the points listed in Figure 1 are not strictly comparable. They stem from observations at different geographic latitudes and are yet too few to scatter reliably about a mean. However, we are confident that artificial satellites will, in the near future, provide the most powerful tool to measure such phenomena accurately over a wide range of latitude, altitude, and time. This, we believe, is evident from our Table and Figure. It Is certainly still too early, for the various reasons Indicated above, to make definite statements to the effect that the upper atmosphere density appears to be higher than 3. was often assumed, over all latitudes at all times. Yet, all results obtained by various authors from satellite observations seem to indicate that we may have to expect such a situation. It will be obvious to our readers that — to a certain degree — these newest results seem to support the outstanding study made by Grimminger in 1948 (l), which led to the RAND atmospheric models. His numerical results were based at these altitudes to a great extent on extrapolations of results derived from one of the oldest tools of upper atmosphere research, namely meteor observations. In a sense, we may conclude that the densities furnished by the artificial satellites appear to fall between those furnished by sounding rockets and those by meteor observations. References 1. Grimminger, G.: "Analysis of Temperature, Pressure, and Density of the Atmosphere to Extreme Altitudes." RAND Report, No. R-105, 1948. 2. Minzner, R. A. and W. S. Ripley: "The ARDC Model Atmosphere, 1956." Air Force Surveys in Geophysics, Mo. 86, Geopnysics Research Directorate , SFCRC^ ARDC, December 1956. 3. Sterne, T. E., B. M. Polkart and G. F. Schilling: "An Interim Model Atmosphere Fitted to Preliminary Densities Inferred from USSR Satellites." Special Repot:io. 7, Smithsonian Astrophysical Observatory, Cambridge, December 31, 1957. (Will appear in Volume 2, Number 10 of the Smithsonian Contributions to Astrophysics in June 195^ Available from the Superintendent of Documents, Government Printing Office, Washington, D. C.) 4. The Rocket Panel: "Pressures, Densities, and Temperature in the Upper Atmosphere." Physical Review, 88, 1027, 1952. 5. Sterne, T. E. : "The Density of the Upper Atmos phere." Chapter III, p. 18 in Special Report No. Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. 6. 11, * The Staff of the Royal Aircraft Establishment, Famborough: "Observations of the Orbit of the First Russian Earth Satellite." Nature, 180, 937, November 9, 1957. * Reproduced as IOY Satellite Report No. 2 36 7. Sterne, T. E. and G. P. Schilling: "Some Preliminary Values of Upper Atmosphere Density from Observations of USSR Satellites." Special Report No. 3, Smith sonian Astrophysical Observatory, Cambridge, November 15, 1957. 8. Harris, I. and R. Jas trow: "Upper Atmosphere Densities from Mini track Observations on Sputnik I." Science, 127, 471, February 28, 1958. 9. Priester, W., H. G. Bennewitz, and P. Lengruesser: "Radiobeobachtungen des ersten kuenstlichen Erdsatelliten. 11 Westdeutscher Verlag, Koeln und Opladen, 1958. 10. The Staff of the Mullard Radio Astronomy Observatory, Cambridge : "Radio Observations of the First Russian Earth Satellite." Nature, l80, 879, November 2, 1957. 11. Groves, G. V.: "Effect of the Earth's Equatorial Bulge on the Life-Time of Artificial Satellites and Its Use in Determining Atmospheric Scale-Heights . " Nature, l8l, IO55, April 12, 1958. 37 Technical Parameters of the Artificial Satellites By G. F. Schilling* Between October 4, 1957 and the end of April 1958, a total of nine objects has been projected Into satellite orbits around our planet. With more launchings of artificial earth sa tellites scheduled for the near future, it appeared worthwhile to summarize some of the basic satellite characteristics known at this time. The following table is the result of a first attempt to collect pertinent data about these initial satellites and to present the information, most important to the analysis of tracking observations, in a concise form. The data given in the table with regard to the physical di mensions and payloads of the artificial satellites are based on announcements by the U.S.S.R. and U.S.A. National IGY Committees, respectively. Less is known with respect to the Soviet satellites, and the weight and mass-area figures in parentheses are inferred through rather speculative methods of numerical analysis. The values of orbital elements are given only for the initial launching time. While these are the important data that character ize the degree of success of a satellites launching, they are in herently less accurate than orbital data for later time periods. Since exact values of orbital elements can be computed only after a number of observations are available, these initial values are extrapolated backwards and thus not really based on the immediate observations made on the launching day. No claim as to accuracy of the tabled information can be made at this time. Indeed, I wish to ask the recipients of this report for their kind assistance in correcting possible errors and inaccuracies as well as in helping out to fill the yet too many blank spaces. I do not wish to imply, however, that any of the missing information is not available somewhere. Rather it is not known to me at this date. * Executive Assistant to the Director, Smithsonian Astrophysical Observatory. geophysical EHI XPLORER 26 March 17 04 38 05 45 17 1°W 2S.7°N 73. 19587 166 0. 1 5.91* 2, 800 138 m( onths) 5.6 (60) and 8? 200 108.03 108.00 15.3 14.1 33.5° 10 60 In lsingle given edenote values aof value. equal be those other the from signs Equal uxtocnapocmehpciontge;ndts environmental VI ANGUARD March 17 and 14years (many years) 191 0. 02 1958 134.29* at m m 34.30° 3,965 652 geophysical 108.03 108.00 16.4 16.4 1.47 (1.0) 3.97** 10 Car ier Rocket 1958 81 (many years) March 12 17 15 41 21 26 12 0.191 29* 134. 23°N 65°W 34.30° none none none PM 108.00 AM 108.03 none 3.8 145 46 23 3,965 652 SPTABLE ARTAIEMFLEITCIETRAESL OF EI XPLORER F1 ebruary 1958a 05 55 03 25.84°N 73.61°W 1 4.95* 15.3 48 03 2,540 368 geophvsical (3-5 years) 14° 0.139 33. 8.2 5.5** and 60 11 14 200 10 SO November 3 Nosecone? S2 1957 none ? ? ? 3 M ? • ? ? ? ? I Table SPUTNIK U November 3 geophysical biophysical 0.0876 61 1^57 ? 40 04 103.7 ? ? ? 40.002 508.3 65.4° ? ? ? (3,200)? 1,670 240 40.005 (17.2)? ? ■el October 4 Nosecone? 1957 a3 ? ? 7 none ? ? ? ? ■ = geophysical SPUTNIK I October 4 0.051 a2 1957 96.2 = ? ? ? 40.002 65.3° 40.005 83.6 950 225 (24.1)** ? 58 58 1,000 1,000 23 92 docket Car ier 1957 al ac ount ihrlo October 4 96.2 ? ?? ? 65.3° Q.G51 950, 225 ncr.c (14.5)? ? ? (2/590)? 58 j SATEL ITE S(days) laitfeltimte Sceixepnetrifmiecnts Battery (days) lifetime date T. (U. ) Launching tLiamuen(cUh.iTn.g) Payload (kg) weight Iecnientiraclity period Initial (km) (min) Initial perigee Iniapogee tial (km) Radio iTstriaons:m Ef emacst-iavrea *mvv>Power (rnc)Frequency(mw> Power (gm/cra^) ratio point: Injection Parainelers Time(U.T.) L(°) onjitude L(°) atitude D(cm) iameter Inclination (°) (kg) Weight (cm) Length ("'=) Frequei.cv car ied -.3 IGY Satellite Report Series Number 5 30 July 1958 IGY WORLD DATA CENTER A Rockets and Satellites NATIONAL ACADEMY OF SCIENCES RADIO OBSERVATIONS OF SOVIET SATELLITES 1957 ALPHA 2 AND 1957 BETA 1 (Scientific Report No. 10 of the High Altitude Observatory) NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington iS, P C. INTERNATIONAL GEOPHYSICAL YEAR WORLD DATA CENTER A National Academy of Sciences 2101 Constitution Avenue, N.W. • Washington 25, D. C, U.S.A. World Data Center A consists of the following eleven archives: Airglow and Ionospheres-. IGY World Data Center A: Airglow and Ionosphere Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado, U.SA. Glaciology: IGY World Data Center A: Glaciology American Geographical Society Broadway at 1 56th Street New York 32, New York, U.S.A. Longitude and Latitude: Aurora (Instrumental): IGY World Data Center A: Aurora (Instrumental) Geophysical Institute University of Alaska College, Alaska Aurora (Visual): IGY World Data Center A: Aurora (Visual) Rockefeller Hall Cornell University Ithaca, New York, U.SA. Cosmic Rays: IGY World Data Center A: Cosmic Rays School of Physics University of Minnesota Minneapolis 14, Minnesota, U.S.A. IGY World Data Center A: Longitude & Latitude U. S. Naval Observatory Washington 25, D. C, U.S.A. Meteorology and Nuclear Radiation: IGY World Data Center A: Meteorology and Nuclear Radiation National Weather Records Center Asheville, North Carolina, U.S.A. Oceanography: IGY World Data Center A: Oceanography Department of Oceanography and Meteorology Agricultural & Mechanical College of Texas College Station, Texas, U.S.A. Rockets and Satellites: IGY World Data Center A: Rockets and Satellites National Academy of Sciences 2101 Constitution Avenue, N.W. Washington 25, D. C, USA. Geomagnetism, Gravity, and Seismology: IGY World Data Center A: Geomagnetism, Gravity & Seismology Geophysics Division U. S. Coast and Geodetic Survey Washington 25, D. C, U.SA. Solar Activity: IGY World Data Center A: Solar Activity High Altitude Observatory Boulder, Colorado, U.S.A. Note: CO Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: Director, World Data Center A, National Academy of Sciences, 2101 Constitution Avenue, N.W., Wash ington 25, D. C, U.S.A.; (ii) Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate archive listed above. IGY World Data Center A fav-. Rockets and Satellites National Academy of Sciences Washington 25, D. C. IGY Satellite Report Series Number 5 30 July 1958 RADIO OBSERVATIONS OF SOVIET SATELLITES 1957 ALPHA 2 AND 1957 BETA 1 High Altitude Observatory of the University of Colorado (Scientific Report No. 10) Boulder, Colorado Note 1. This report is issued in accord with international arrange ments on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies avail able at cost to scientists upon their request. 2. These data and/or report contents are reproduced as received from the experimenter. 3. Recipients of these reports are advised to communicate with the authors prior to utilization of experimental data for further publication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites RADIO OBSERVATIONS OF SOVIET SATELLITES 1957 ALPHA 2 AND 1957 BETA 1 Table of Contents 1. Determination of Passage Parameters from Simple Interferometer Records Page 1 2. Preliminary Results of the Analysis of Ionospheric Fading and Inter ferometer Effects 4 3. Spin-Fading 30 4. Acknowledgements 50 Introduction This report presents the preliminary results of analysis of our 20 Mc/s radio observations of Soviet satellites I957a2, and 195701. So far as we know, equipment, built under this contract for studies of ionospheric absorption and refraction in the range I5 to 20 Mc/s, was virtually the only gear in the Western world immediately available without modification of any sort for detailed tracking and recording of the signals from Sputnik I. For this reason, our records include interferometer passages from as early as 0500 U.T. on 5 October 1957 » within a very few revolutions of the time of launching. Also, for this reason, we have studied in some detail the problem of reduction of tracking information from these records, taken with a simple interferometer. This problem, with preliminary results, occupies Section 1 of the report. Section 2 contains, essentially, a catologue of the various types of ionospheric fading and peculiar interf erometric effects that the Soviet satellites produced. We can present only a preliminary and descriptive interpretation of most of these phenomena. Section 3 presents an analysis of the most basic fading shown on the records, which is fading produced by the spinning of Sputnik I on an axis contained within itself (the spin of Sputnik II was not observed sufficiently long for an adequate analysis). Since this spinning appears in all the records as a fundamental and strictly periodic effect, analysis of the spin-fading necessarily precedes analysis of the other ionospheric types of fading that also appear on our records. We identify a secular change in the spin- fading rate that occurred over the three weeks of observation of Sputnik I. It seems natural to identify the effect with atmospheric drag. If' this is done, we have available a means of independently determining atmos pheric density at the perigee point of the satellite. We therefore present details of the analysis of this effect and the resulting density value. Finally, we present details on the spin-fading char acteristics of rotating, circularly polarized antenna systems. * 1957 Alpha two ** 1957 Beta one -1 1. Determination of Passage Parameters from Simple Interferometer Records The immediate problem raised by the launching of the first Soviet satellite was the determination of the satellite's orbital characteris tics. Inasmuch as the radio tracking gear that had been designed in the U.S. was exclusively intended for use at the IGY satellite frequency of 108 Mc./s, the tracking problem in initial phases of Sputnik I had to be borne by available radio equipment, in all cases improvised to give whatever tracking information it might. Our equipment had been designed for radio studies of the ionosphere, as it affects cosmic radio noise incident externally. In this sense, the satellite provided a convenient tool for the studies that we had previously planned to carry out with the much-weaker radio stars as standard sources. On the other hand, the position and motion of the radio stars are known very precisely, and the satellite orbit is a quantity to be determined as part of the analysis. For maximum results insofar as ionospheric effects are concerned, we require tracking in formation sufficiently accurate to predict the spatial position of the satellite to within a kilometer. This precision implies ephemerides accurate to about 0.1 seconds of time, and 0.1 degrees of arc, more precise than the existing information from the Smithsonian Observatory and the Vanguard computing center. Although orbit problems are not a proper part of the research under this contract, we have therefore undertaken the problem of computation of the orbital parameters of the satellite insofar as our data allow a determination. The method we use depends on complete fringe data from a well-surveyed radio interferometer, ideally at kO Mc./s. Un fortunately, our equipment for the high frequency of the Sputniks was not yet in operation at that time. We therefore have used the lessdesirable 20 Mc./s signals throughout our analysis. The method that we use consists of two parts: identification of the particular interference fringe on which the satellite lies at a given time, and determination of the direction, and distance, from the receiver to the point of closest approach of the satellite. In order to define these two problems more clearly, we compare this procedure to tne familiar Minitrack principles. In this equipment, determination of the particular fringe on which the satellite lies at a given instant is carried out through a kind of radio "vernier." Two interferometers, aligned along the same direction, but with different spacings are em ployed. Along a single line in the sky there will be a simultaneous maximum signal, for example, received in the two interferometers. -2- Minitrack uses two such pairs, crossed in the E-W and N-S directions, in order to eliminate possible difficulties in determination of direction and distance to the point of closest approach. In principle, once the lobe ambiguity is resolved, a simple inter ferometer provides as accurate data as one pair of the Minitrack system. We shall illustrate the way in which this comes about by means of a graphical construction, useful unless a refined analysis is desired. In this case, the problem can be programmed for a digital computer, which removes not only the errors in the graphical plotting of data, but also the restriction of the satellite to uniform motion in a plane (see below). We assume that, to a first approximation, the motion of the satel lite can be represented locally by uniform motion along a straight line, parallel to the surface of the (plane) earth. We construct two sets of lines on the plane that is parallel to the surface of the earth and contains the local satellite path: the intersection of the surfaces of constant phase of the interferometer system with the plane of the satellite path, and the grid representing the ordinary azimuthal coor dinate system (see Figure 1). The scale of this chart in kilometers is unknown, since we regard the satellite's height as unknown. The radii of the chart are proportional to tan z, where z is zenith distance, and the radius of the circle z = 1*5 degrees is the height of the satellite, in unknown units. The procedure now is to plot the times of lobe crossing on a flex ible scale (model airplane rubber band is especially suitable since it is flat, and has a high stretch-ratio). This scale is of unknown length, in terms of the chart. On the other hand, the times of lobe crossing must, for the correct path, coincide with the plotted fringes of the interferometer system. When, by trial and error, the correct fit is found, the plot may be sketched in on the chart (see Figure 1). Since the period of revolution of the satellite determines velocity in a circular orbit very accurately, if the eccentricity of the orbit Is small, we can scale the chart from the known times, plotted along the track. Finally, even if the period of revolution is not known, the fact that the object orbits close to the earth allows a precise determina tion of the scale of the diagram by successive approximation from an assumed period, to the consequent height, etc. From this known track it is possible to determine node and inclina tion of the orbit, as well as the radius of the (assumed) circular orbit. From tracks at two points on the orbit follow eccentricity, semi-major axis, longitude of perigee, and times of perigee passage. These two -3- FIGURE 1 - Graphical method for determination of passage constants from simple interferometer records. On two of the three tracks we indicate the data points as read from the interferometer output. -It- points, however, need to be on the same revolution of the satellite around the planet, or the perturbations of the Keplerian ellipse must certainly be taken into account. For example, evening passages of Sputnik I over Boulder were relatively low, while morning passages were high. Correspondingly, one might be tempted to use an evening passage together with the morning passage some 12 hours later to derive the shape and size of the orbit. However, the node will, in that time, move over 150 km to the west along the earth's equator, and the perigee point some I50 km in the direct sense along the orbit. Finally, or bital drag, resulting from friction of the satellite body with the residual earth's atmosphere at perigee point, contributes at least an error of JOO km to such a procedure. Table 1 contains the tracking information obtained to date from Sputnik passages near Boulder. These parameters were obtained indepen dently for each passage, although by assuming height and azimuth of nearest approach to be known, we could improve the determinations of time and range of nearest approach. More tracks will eventually be de termined from our data. 2. Preliminary Results of the Analysis of Ionospheric Fading and Interferometer Effects Out of the complex of fading effects shown by our records, we have been able to analyze completely only one effect up until the present. This is the fading produced by the spinning satellite antenna system. The last section will discuss the effect in detail. In the present section, we shall present examples of a broad range of the remaining types of fading that we have observed. In most cases, we can give little more than qualitative explanations. The core of the section, therefore, is a collection of figures, each a photographic copy of portions of' the original Sanborn records. As indicated in Section I of this report, the analysis of the tracks is not yet complete. For that reason, we have shown only ap proximate locations of the satellite on the figures, although for de tailed interpretation we need more accurate positions. Among the most characteristic records, from the standpoint of the consistency with which phenomena repeated, were the early morning passes of Sputnik I. Figures 2 through 1+ each contain a set of records on three consecutive days of the O63O MST passes. They were selected to show cypical features of the various parts of morning runs. Figures 5 through 7 show the effects for another three consecutive days of the 06:33:22.2 of NPt earest (Lat. Mc./s 140°4,52"N; 0Ifrom RPData S20 Long. HAO n5oetastdrflieu6trlco'imelotde7nre"W) of 22:10:31 NPt earest 08:06:36 of NPt earest Pt 23:43:45 of Nearest 08:10:14 of NPt earest Approach Remarks Crossed Ap5 06 39 r:oac.h-03 44 A02 2 p :roac.h-23 Ap : 10 17 roach-2 A10 p57 r:oach-08 values track because close line fringes. igiven of *Two nto symmetry tewasrference 06:30:16.5 20:31:1 .5 20:28:27-4 20:25:01.4 03:14:55 04:49:55 E- h,m,s W Angular deg/sec Rate 0.84 0.89 0.74 0.47 0.81 1.03 1.64 1.12 0.67 0.57 O.096 R1957. Notes: that listed by completed October 30 edwere uctions Height Miles 290 299 414 310 201 120 114 464 277 148 137 148 f6 ♦ 017 150 146 128 036 034 134 146 038 422(22 24 33 46 04 27 30 46 68 24 57 (.278 312 118 232 237 218 307 301+ 043 056 308 12S 35N 42 S 131S 146s 164N 169N 174s 175S 184N 06:33:23-7 06:30:1+5.0 20:31:2 .3 20:28:48.5 22:10:08 08:11:05 03:10:29 04:49:37 6 7 16 16 279 1 TABLE Course Heading degrees Distance degrees Zenith imuth Az degrees True Passage 6N No. 08:06:12.6 23:43:49 20:25:40.6 h,m, s Time MST Date 1957 Oct. I* 5 13 14 14 15 16 (7) mi/sec. 4.47 Column based that asonvu=mption rof from reading 12 bottom, lOcto The the FIGURE margins prints eto 2 top sfare, pte-c-htiavnedly, Time); (105°W Ik 0628:590653:00 0631:33 .1957: 13 I957: and October The 1957: ber MST MST; earlier these for The arecords all times crossing E-W the than minute ppasses. are one roximately of second dsmiavliseisotn 0.1 is time. rThe bottom, from reading lthe of FIGURE margins prints e3 to tap sfpare, te-c-htaivnedly, 0630:00 of these for The These aMST. the times crossings E-W pare passes. roximate Ik Time); (105°W 0634:58 0632:36 1957: and October 13 12 MST; MST dstime. of second 0.1 is imvailsieosnt of valleys minimal peaks and amplitude large with the cis into onpower. ontinues power, p(l/2 eBsecond amplitude srfading far of south the Note oato ituoeldilecirt.ety) 0633:29 tminutes and These about after MST. ctimes E-W hrtwo eare orpserfeoisrnegnst, k bottom, lreading The from prints the rof FIGURE margins eto top fsare, pte--chtainvedly, Time); (105°W lk :1U 0637:37 0635 1957: I957: and October 12 13 MST; MST of I3 second 0.1 time. for sOctober The record dshows is miatvsomeulirasteisont. -9- O63O MST passes. Each record on a given figure represents about the same position in the track as the other records on the same figure. The parameter that varies on one of these figures can be considered to be roughly the distance from the receiver to the satellite, the orientation of the satellite with respect to the line of sight, earth's magnetic field, and so forth, remaining relatively fixed, throughout a given figure. From one figure to the next, on the Figures 2 through k> the time increases, from a value early in the pass, through the ap proximate time of E-W passage, to a time late in the pass. Figures 5 through 7 are arranged in the same way. In this way, we had hoped to be able, for example, to isolate phenomena depending on the distance to the satellite from phenomena depending on the orientation of the line of sight with respect to the earth's magnetic field. It would appear that the most that can be said is that the major effects result from the differences in orienta tion of the line of sight, for example, from one part of a given pass to another part of the same pass. Variations in the distance to the satellite may produce large effects, but they are not consistent from day to day. Two additional features of the fading shown on Figures 2 through 7 should be noted. Already in Figure 2, the second strip shows a dis tinct double period in the fading, one fast period of about 1. 3 seconds, and a slower period of something more than 1+ seconds. In particular, on Figure k, showing one characteristic appearance of the late stages of south-going passes of Sputnik I near Boulder, we note again the fast fading, now with a period of considerably less than a second on all records. The long period of k seconds or so again appears, but now as half a basic period of 8 seconds. These records demonstrate the two major types of fading that appear on all of the records of south-going (high) passes of Sputnik I: a fast fading, that has different rates on different parts of the pass, and a slow fading, of almost constant period throughout the pass. The fast fading must be regarded as an ionospheric effect, which we shall not specify at the moment. The slow fading must be regarded essentially as a result of the spinning of the satellite on an axis contained within itself. We shall develop this idea in Section III of this report. The evening passes showed some similarities to morning passes inso far as the spin effects were concerned. Figure 8 shows examples of the early parts of two evening passes. Each half of the picture is a section of a complete record, i.e., the upper quarter of the figure is a portion of an ordinary radio interferometer's output, and the quarter second o lbottom, rThe from fading the of FIGURE margins prints 5 etop to fsare, tp-~ehcatnidvely, 0617: 15 athe all The MST. records than earlier crossing minute E-W p are roneoximately Time); (105°W 16 0623:^5 062Q:-50 18 I957: October 17 and 1957: MST MST; s0.1 these for times dThe is time. of second miavpasses. liseisont these for crossings the abrupt hash of record, Note stop top passes. on 6 lthe The of margins rprints from FIGURE reading etop fsare, tpe-chtainvdely, (105°W Time); 0G2h:h2 16 0621:50 bottom, 1957: October 17 MST MST; to 18 0619:15 October 1957: These and times the of aMST. E-W pareroximate 16 1957October The dssecond 0.1 is of time. miavliseisotn BstBoulder, of south The cand the E-W ahoto at teurpassage ledlfesiortp.eond lrprints The the of from reaching margins FIGURE 7 eto top sfare, pte--chtainvdely, (105°W Time); 0625:U2 0622:50 16 1957: and October 17 MST MST; bottom, IS 0619:15 than 1957: aOctober The later MST. records minute p one are roximately dsof second 0.1 is time. imvailseisotn Time); (105°W 16 bottom, 2011:00 1957: October If date; and MST time to same the of Each Note cords. pair spin morning in rate ppasses. sameresence as kc/sec dtaken strips of with r2-5 and ietwo fswas cpecirtveinvtrelsy, kc/sec k^O bThe 1 about spaced feet aE-W in direc napart dwerewan tiednthas. 8 rof from lreading The margins prints the FIGURE etop sfare, pte--chtainvdely, charac last and, and show records These MST; 2007:23 1957: strip, time date. same south) lk of approach, later time this in about minutes these than nere casearest (when ois signals of before swell the in tabetsraepilrsevitaeirdeacnce had and spthe The dtion, of second 0.1 is time. omilavsamelriszeiasotinton. -14- from the top is the corresponding part of a simple receiving system consisting of a single antenna, connected through a separate receiver to the other channel of the dual-channel Sanborn recorder. We note that the early part of evening passes (north-bound) correspond, generally, so far as the orientation of the line of sight and magnetic field is concerned, to the late parts of morning (south-bound) passes. It is not surprising, therefore, to note very much the same kind of fading on this record as on the morning passes. The spin component of the fad ing is present with, of course, its typical 8 second basic period. Another characteristic of evening passes especially was the early appearance, and sudden drop-out, of the signals several minutes before the main pass (see Figure 9)- This record again shows the characteristic 8 second spin period. We note that the two halves of the record here were used as a diversity reception system, with a base line of some 915 feet, along an azimuth of kl degrees east of north. The surprising aspect of this record is the identical fading on the two records. To within better than 0.1 seconds of time, these records agree in even minute detail. Suppose that these diversity records in volve a multi-path transmission phenomenon, in which waves propagated along two different paths constructively and destructively interfere. The characteristic frequency (to be multiplied by a constant usually < l) of such fading is v/X., where v is the speed of the satellite over the ground, and \, the wavelength of the waves (15 meters). For Sputnik I, v/X »v 500 cycles per second. Where f is the fading fre quency, we would expect to observe one cycle of such fading over dis tances on the ground amounting to about v/-f . Assume that v = 8000 m/sec and f = 20 cycles/second; we might expect to find already essentially different phases of the fading over distances as small as ^s^jflm. The similar nature of the signals received by the two antennas suggests that we are observing an interference phenomenon in plane-parallel waves, so to speak, interference fringes at infinity. The source of interference must be close to the satellite. Figure 10 shows a series of typical records from the time of closest approach of Sputnik I on evening (north-going, low elevation) passes over Boulder. These records show characteristically a slow fade with superposed small-amplitude fluctuations that in no way conceal the basic periodicity. The period of the fading varies through these passes, from, say, roughly 5 seconds on the upper two records, down to about 3 seconds, on the middle two records, and up again to about k or 5 seconds on the final two records. These records are entirely from a single passage sequence, at 2030 MST over Boulder, and show six consecutive days of this sequence. We. suggest that this fading is again essentially produced by the spinning of the satellite. As we noted earlier, the closest several sbefore The dapproach. of seconds 0.1 time minutes is imvailsieosnt Time); (105°W 18*4-2:30 with taken 1957 October and date These 17 MST time. records same were: rof bottom, lreading from The margins prints the 9 FIGURT etop to sfare, pte--chtaivnedly, ispaced cThey high the rof degrees north. in E oleoutput rcor uesiltvaretaitosen. hi iaspaced feet 9^5 azimuth along drtto iapart aefnctaecinrhvceansdlrts, time. -16- FIGURE 10 - The left-hand margins of the prints are, respectively, reading from top to bottom, 12 October 1957: 20J>k:^k MST (105°W Time); 13 October I957: 2033:45 MST; Ik October I957: 2029:51 MST; 15 October 1957 : 2028:12 MST; 16 October I957: 2025 ilk MST; 17 October I957: 2021:33 MST. These times are all roughly at the time of closest ap proach on these low, evening passes. The smallest division is 0.1 second of time. -17- spin rate shown by early parts of evening passes corresponds exactly to the spin rate derived from morning passes. We therefore identify the fading at the point of closest approach also as a spin. The lack of constancy of the period is related to the progression of the passes in this particular sequence from east (top of the figure) through overhead (central part of the figure), to west of the observer. Assume that the axis of spin remains constant in direction throughout a given pass. During a distant pass the change of orientation of the line of sight to the spin axis is small, and takes place slowly. During a nearby pass, the change may amount to as much as an additional half -rotation of the satellite, and will, of course, occur within a minute or two, near the time of closest approach. In order for the effect to speed up the fading, it is necessary that the spin axis be approximately trans verse to the direction of motion, and the spin Itself be opposite in sense to the orbital angular momentum. The records so far discussed all involved simple measures of power received by a simple antenna system. In addition, we measured the total power received by an interferometer system, oriented with its 915 foot baseline along J+l degrees azimuth east of north.* Figure 11 shows some typical records of interferometer passages from north-going (low) Sputnik I. The top strip displays simple lobe structure, in which, at intervals of about 8 seconds, the lobes appear to be broadened as a result of the spin- fading.' Timing, on records such as this, can be read to certainly 0.1 seconds. The second, or middle strip, shows the same evening passage (2030 MST) from the next night. The fringes come more rapidly, Indicating that the satellite is more nearly overhead. Finally, the last record shows an instance of lobe-doubling, or splitting. This strip can be compared exactly with the fourth strip from the top of Figure 10, which represents the power received by a simple antenna system with the same polarization as the interferometer system, during this same passage. The doubled lobes are not the result of spin-fading, in chance phase-coincidence with the times of fringe minima in the interferometer system. The evidence unmistakably points to two direc tions of arrival, differing by perhaps a degree or so. Note, however, that the lobe splitting abruptly stops, during passage of several lobes at the right-hand side of the strip. The effect may not be explained in terras of an effect continuous across the sky.** More likely, we The two identical antennae of this interferometer were connected to se parate receivers for various diversity reception measurements, as re ported above. ** Such as would result from ordinary and extraordinary ray modes of propagation. I l11 FIGURE The from the of rmargins reading bottom, prints etop to fsare, tp-e-chtainvdely, of closest sdoubled divi approach. lobes The strip. bottom the time Note in mat al est 2028:12. of irecords These the show cnhtaerpasses evening afpcetroemiastreaircnce (105°W Time); lk October 15 and 1957: I957: MST 2032:25 MST; 2030:52 0.1 is sion second of time. -19- deal here with a wavy structure in the ionospheric layers below the satellite. This structure, like the surface of a large body of water, almost but not completely at rest, causes a plane wave to split into several plane waves moving in several directions. Interferometer records from south-going (high) passes showed a somewhat different geometry of fringe-crossing. In this case, in con trast to the north-going (low) passes, the satellite crossed our fringes virtually parallel to the fringe system. This resulted in longer minima than those of north-going passes. Figure 12 shows the two re cords of a morning pass for which the rapid fading mentioned earlier proceeds at a somewhat slower rate than usual. The record was selected, however, to exhibit the typical appearance of a large section of the in terference fringes during a morning, or south-going passage. Two fea tures should be noted especially on this record. The alternating maxima that appear on the lower part of the record (receiver plus simple antenna) result from the beat between spin and rapid fading effects, the latter, in the initial part of the record, being almost commensurate with the half spin period. The second feature is the presence, in the middle interference fringe minimum on the figure, of residual signal" that is out of phase with the fading of the signal on the lower half of the record. The same effect, at the threshold of visibility, also appears in the last fringe at the right of the upper half of the record. Residual signals in the fringe minima can in general be explained in terms of unequal effective gain on the two sides of the interferometer. However, it is not apparent why, if this were the case, the rapid fading should tend to be antiphase on the two halves. This same tendency was noted on many occasions. Figure 13, the only record in this report of Sputnik II, shows samples of the first north bound (morning) and first south-bound (afternoon) passages, both, of course, very high in comparison to the Sputnik I passages. The, upper half of the figure unfortunately shows mainly the keyed ("beeping") signals initially received from Sputnik II, and the much-slower spin rate of this satellite (presumably the complete spin rotation takes about ^l8). The second record shows the detailed appearance of fringe minima during the afternoon passage of this satellite during its first day. The ionospheric fading shown on this record should be carefully distinguished from the keyed signals of the earlier, morning passage of that day. The rapid fading, which took place all through the pas sage, continues into the fringe minima, which appear to be doubled. Curiously, the fading tends to vanish at two points within each fringe shown on this figure. Moreover, the fading, as received by the simple antenna plus receiver, is precisely antiphase to the signal in the fringe minimum half way between the fading zero points, and in phase with the ciThe fringes. the shows record bottom of its with hnoutput atreaourcfteriosmteicer, rof from reading bottom, l12 The the margins prints FIGURE etop to sfare, pte-c-htiavnedly, 0621:00 the 1957: October 17 date shows, record This time. and MST; at top, output same effect beat eifading fading, spin between rapid, the and curious osnpoescpihaelriyc ipusing the receiving simple Note nosystem, atlensame ras a atfreniozmaetse.rion s0.1 The record. lower dthe time. of second is miavonliseisont also cshow how signals, the cancel ioccasion, in fringes. ontmeoncan prfleretncely eThe record, Sputnik tion. slower the shows of records spin II. stop pecial y, bottom The records effects hand, other the show, signals of fringe in minima. on lj The lFIGURE rmargins from reading the of prints etop to sfare, pte--chtainvdely, 1^56:00 simple receiver, and date The time. from records, bottom MST; to top same are (105°W Time); bottom, 1957: Ndate and MST 0553:59 time; 5 o3 vsameember the all isimple polariza of receiver, in nstate tesame rferometer, ..i"""".. ,7,.., • . :— ,„...!. a' '\ 1i ( t •■(. 1t*«J■t-vs.- s0.1 The dsecond of time. is miavliseisotn & ;v <V > I!: -22- fading on the fringe maxima. We find here, again, a similar behavior (so far as the phase of rapid fading is concerned) to the record shown in Figure 11. Even if there is a gain inequality between the two sides of the interferometer, why should the fading disappear, reappear antiphase, then disappear once more, finally to reappear inphase? Rather, we conclude that signals arrive at the interferometer from two different directions. These two signals both contain the rapid fading phenomenon, but the weaker signal shows the fading in phase opposition to the stronger signal. When the direction of arrival of the stronger signal falls in an interference fringe minimum, the weaker signal survives because its angle of arrival differs from that of the stronger signal. At a certain point a short distance removed from the center of the fringe minimum, the stronger signal and the weaker signal are of equal strength, and therefore annul each other's fading. It would appear to us, if this interpretation is correct, that we deal with two waves, each of which shows the fading characteristic in a definite phase relation to the other. Such a possibillity does not preclude the presence of some sort of Faraday rotation effect resulting from the magnetic properties of the ionized medium through which the waves pass. It would, however, suggest that the Faraday effect that actually takes place involves two separate pairs of waves of unequal amplitude but fixed phase relation. The rapid fading typical of Figure 13 was, of course, of the same nature as the characteristic rapid fading that appeared on all south bound (high) passes of Sputnik I. The feature of this fading that relates most closely to the conclusion of the preceding paragraph .is its monotonic nature, i.e., the fact that on all of our records, this fading begins (when the satellite is far to the north) slowly, a-t perhaps 1/2 cycle per second, and continuously increases in frequency until, when the satellite is no longer heard in the south, the fading may be as fast as 5 or more cycles per second (see Figure 1U). The line of sight to the satellite intercepts the lines of force of the magnetic field at right angles roughly at O628 MST, on Figure lk. The first appearance of the satellite roughly coincides with the time at which the satellite lies at right angles to the lines of force. The crucial test of the origin of the fading in terms of the magnetic Faraday effect is therefore not clear-cut on our records. The test is made even more difficult because of the hashy nature of the signals early in morning passes. We present two pictures of the records to illustrate this point. -25- 6.00h 30m 31 32m 33m 34m 35m 36m 37m 38 m TIME (06hM.S.T. I40ct. 1957) FIGURE 11* - The increase of frequency of the rapid fading through a morning passage, lk October 1957: O65O MST. This figure is com parable to the graph plotted by the Cavendish Laboratories (Nature 180, 879, 1957). -2k- Figure 15 shows the actual Sanborn charts from which Figure 1^ was constructed. Figure 16 illustrates for another pass the same monotonlc increase in fading rate, but from a slower initial frequency to a slower final frequency. In further illustration of the point that we made concerning the presence of signal in fringe minima, we present Figure 17. The top half of the figure shows a portion of the interferometer and simple receiver records. The two sides of the Sanborn tape here were recorded with identical polarization (linear, vertical). The lower half of the figure shows, on the other hand, the two sides of the chart (again, the upper side is the interferometer side, the lower side, the simple receiver) taken with crossed polarization, the upper side polarized linearly in the N-S direction, and the lower side, in the E-W direc tion. The maxima, on the two sides of the crossed polarization record, are not precisely in phase. However, there is obviously a large shift towards the antiphase condition in the fringe minima. The signals ap pearing in the fringe minima do not seem to show an obvious, or strong polarization effect that would contradict our assumption that there are two signals present, each of which shows the rapid fading phenomenon. In other words, each of the two signals shows an amplitude modulation. There were occasions, however, in which the fading appearing on a morning pass satisfied the antiphase requirement for origin in the Fara day effect. As an example of this, we present Figure 18. The two halves of this record were taken in opposite states of linear polarization, the upper half, polarized N-S and the lower half, polarized E-W. The weak maxima of the upper record correspond to the broad, bowl-shaped minima on the lower record, and unquestionably are the result of the spinning of the satellite. On the other hand, the strong maxima on the upper re cord correspond to the strong minima on the lower record. As a final illustration of another type of ionospheric fading that was frequently present on south-bound, morning passages of Sputnik I, see Figure 19. This represents a set of three passes observed in sequence one morning. The illustration is presented to show how at long ranges (for example, the top strip of Figure 19) the signals were "hashy." Undoubtedly, higher fading rates than could be followed by the Sanborn pen were present, even though the rates observed are at least 20 cycles per second. As the satellite moves closer, the record smooths out, and finally shows the characteristic smooth, rapid fading that we have discussed above. This hash frequently occurred in the early phases even on passes that came nearly overhead in Boulder. Abruptly, often, it would terminate in mid-passage, as though the satellite had emerged from a haze or cloud into a clear and smooth ionosphere. On all oc- The iand fading typical again the rapid of ^through morning lrate npcuaasrtersastge . 14 0636:11 obtained, date, which These from records Figure of data the MST. same were are 15 lfrom The prints the rof reading bottom, FIGURE margins etop to fsare, tp-e-chtainvdely, Time); (105°W 0629:44 0633:56 lit0631:38 October date, I957: MST; MST same dssecond 0.1 is of time. miavliseisotn srecords show fading into The fade. fast These imoanva slow up loserypehsetric Time); 0627:10 0625:5^ 1:16 062 and date, October MST. 17 1957: MST MST; same building 16 from bottom, lof rThe reading prints the FIGURE margins etop to sfare, pte--chtaivnedly, (105°W dtime. of second 0.1 is ivision I the antiphase be simple and minima, fading of tendency minima in to on hdthe in bottom N-S and is E-W oiriezcotniotinao.ln,y and date The polarized from bottom time. vrecords second the etwo rupper same aretical y. polarized l17 rThe the of from bottom, FIGURE margins prints reading etop to sfpare, te--chtainvdely, third and first The records both fringe riin signals the Note net care rfoeromdeste.r Time); (105°W 0630:14 lk 16 0625:11 I957: October and date 1957: MST time; MST; same precord, irof stime. dThe 0.1 is second oemilrcaverlispszveaicetsoirtnovne. 18 bottom, rof from reading lprints The the margins FIGURE etop to sfare, pte-c-htainvedly, pcrossed The phase of sharp and phase, fading rapid the minima olout aonrizations. fading show bThey spin of in pcrossed linear the minima ostates lwalr-iszahtaipoend. Time); (105°W 0k^2:hk in 16 and These records date time. 1957: October MST two aresame 0.1 time. of second dsimvailsieosnt is rlreading bottom, 19 The from the of FIGURE margins prints eto top sfpare, te--chtainvedly, seshow early records These fading of athe during vptomorn as elruoltaictoehnes (105°W Time); 0624:3U 0^52:01 date, 0312:03 I957: October 17 MST. MST; MST same The dshours. of second 0.1 ing is time. imvailsieosnt -30- casions, especially in the early morning, when distant passages were ob served, these hashy signals were a feature of the entire pass. On the other hand, the abrupt termination of the hash was a feature of morning passes coming relatively near us. The last relevant detail we should mention is that when diversity records are available, the hash is identical on the two records. This holds, as well, for records with crossed polarization. It would appear that a simple explanation for these effects lies in the fact that the south-bound morning passes must transit the vicinity of the auroral zone on their way to Boulder. We conclude that these phenomena result from the complex spatial distribution of ionization in and near the auroral zone. This affects the waves in a manner quite similar to the scintillation effects observed in radio stars. Random retardation, refraction, and possibly absorption affects all must occur near the satellite, and will combine to produce rapid fading without diversity at our receivers. 3. Spin-Fading The most obvious cases of spin-fading occurred in the final stages of south-going Sputnik I passes. Figure 20 illustrates this point with records covering a week of observations during these morning passes. We have lined up the fading so that it is inphase throughout the figure, and illustrates the periodicity of the phenomenon from one day to the next over a week of observations. The spin-fading stands out from the rapid fading because of the high rate of the latter. However, during early parts of morning passes, the spin-fading was still present at about the same amplitude, as we have had occasion to note before in this report. Figure 21 further illustrates the point with a set of records taken mid way between the point of closest approach and the last stages of morning passes. Here, the rapid fading is somewhat slower than in Figure 20. Finally, Figure 22 shows even stronger beat phenomena between the rapid fading and the spin-fading. We have attempted to align the spin-fading minima carefully, so that their basic periodicity from one record to the next will be evident. If we are correct in the identification of spin-fading, its period should be almost constant throughout a distant pass. We tested this hypothesis on a great many of the morning passes, one of which is il lustrated by Figure 25 • We have plotted the phase of the spin-fade minima from an arbitrary zero, against the whole number of spins, also reckoned from an arbitrary starting number. The phase was determined on the assumption of a constant spinning rate, P « k.h55 ± .001 seconds per one-half revolution. It is clear that, over more than 130 fading minima, the phase of the minima never changes as much as 0.5. As might -31r FIGURE 20 - The left-hand margins of the prints are, respectively, reading from top to bottom, 12 October 1957: 0635:58 MST (105°^ Time); 13 October 1957; 0636:10 MST; lk October 1957: 0636:27 MST; 16 October 1957: 0630:10 MST; 17 October I957: 0626:31 MST; 18 October I957: O62I+: 02 MST. All records from the last parts of morning passes, when the satellite was high and in the south of Boulder. These strips show the precise synchronization of the spin fading on morning passes, over an interval of one week. The smallest division is 0.1 second of time. rreading bottom, from of the l21 The prints emargins FIGURE to top sfpare, etc--thiavnedly, less cspin period, of the show They records 20. Figure htime arsame aoncteristic 0621:09 the and from between approach, closest of time records These MST. come a but (105°W Time); 062k:k2 18 0628:21 16 and 1957: October If MST; MST 0.1 cis of ibecause slower sfading dThe the omrate. nvasoilpspcieuhosentursilcy of second time. lbottom, The the from of rprints reading FIGURE margins e22 to top fstare, pe--chtainvdely, (the record) 0k^2\hk These simple the how show effect lost becomes MST. records spin top as s21. The iFigure shown than less still becomes frequency fading the moanonlosephsetric (105°W Time); 0^55:27 16 lk 0h%\\2 15 and 1957: October MST; MST dis of second 0.1 time. ivision 150 140 130 120 110 100 (105°W Ik 06j>0 1957 phase The the through of October MST minima spin FIGURE 23 pass : - * • ■• Time). U:^55 The the of period assumed sphase computing in etrue cwasonds. k. of cycles double value, the by example, for Figure Many this shown, is twice spin as ••. 1 *•. • i 1 1 • ••••. —1 I of RNumber Whole evolutions t ( approach) of is point the nearest cycle. double such show also records othera 1 • ••.. • *•. ■*. • 1. F30 20 70 10 60 50 40 90 80 • 1i "•••.. ■• •• 1.00 .80 .60 .40 .20 .00 -35be expected, the phase shows some systematic trend, probably related to the change of orientation of the spin axis and the line of sight. Note the large displacement of the point of symmetry of the phase curve from the point of nearest approach (indicated by an arrow on the horizontal axis of Figure 23). It may be that our derived period is slightly too long. If so, the curve may be modified so as to give a smoothly de creasing phase throughout the passage, although the total change in phase might then be larger than for the plotted curve. Such a change would be justified, for example, by the fact that on this pass, we ob served almost 0.1 revolution of the satellite around the entire earth. A total change of spin phase by k seconds (corresponding to 1/2 spin re volution) is possible. Moreover, the sense of the change correctly in dicates an increase in the apparent spin rate, throughout the passage. This change is consistent with the change found from the evening (low) passes . A second requirement of spin-fading is that it show a nominally constant period from day to day. We have already, in Figure 20, illus trated this point. Figure 2k further illustrates the point by summariz ing our observations of the spin period from the beginning of Sputnik I to the demise of its radio on 2k October 1957Exclusive of the first day of flight, the satellite obviously spun at a more-or-less constant rate. During the first 2k hours of flight, our observations of Sputnik I were very complete, because of the ease with which we could identify the keyed signal in the midst of noise, and probably also because of the initial strength of the transmitted signal. Furthermore, the beeping provided a very convenient artificial, fast fading in which the identi fication of the spin-fading is very straightforward. We therefore have confidence in the accuracy of these early points. The change in spin period was, as the graph shows, so sharp as to be virtually discontinuous over two revolutions of the satellite about the earth. It is tempting to identify this initial slowing of the spin rate as a result of a dis continuous increase in the moment of inertia of the satellite about the axis of spin. One way in which this might take place is through the initial failure of the satellite's antenna system to spread out to its fullest extent. If, moreover, the antennas were extended by cranks and motors within the satellite itself, it is possible that the Russians detected malfunction and corrected it during the initial phases of the flight. The possibility that this occurred depends on the fact that the antennas for the system must certainly have been large, to guarantee adequate radiation efficiency at these low frequencies, and therefore nust initially nave been stowed within the rocket assembly. -x Note added in proof: We have just received notice of the change of the orientation of Explorer I (1958 alpha) during the first day of flight; -36- Of more scientific interest is the secular decrease in the spinning rate, shown by Figure 2k, from 5 October through 2^ October. The only point failing to show the decrease in rate is 10 October 1957- The dis crepancy appears to be real, insofar as 60 spin-fade periods determined the period for this date. All remaining points show consistently a slowing-down of the spin rate. It will appear that this effect results from aerodynamic drag be tween the rotating antenna system and the residual atmosphere near perigee passage. If this interpretation is correct, then the decay of the satellite's spinning provides an estimate of atmospheric density apart from the measurement of the period of satellite revolution about the earth. Finally, the change in the spin rate is sufficiently small so that we may assume constancy of the angular rate of spin through a given passage of the perigee point. A fairly simple order of magnitude computation shows that the pre cession of the satellite spin axis caused by quite small asymmetry in the frontal area of the aerodynamic drag effect is large enough to cause a considerable change in the axis from one passage to the next. We there fore may simplify the problem still further by averaging the effects of spin drag over the possible directions of the spin axis with respect to the direction of orbital motion. This assumption is further justified by the almost uniform change of spin rate with time. We consider the dissipative torque that acts on the satellite an tenna system alone. There will also be a torque on the spherical body of the satellite, but this is minute in comparison to the torque, on the antenna system. Of course, we must proceed by guess at this juncture, since the Russians have not published the physical details of the antenna system. On the other hand, if we assume that the system is comprised of two 7-5 meter dipoles at right angles to one another, and that the dipoles are, say, made of two tapered stubs, then it is very likely, from the standpoint of the mechanical stability of the antenna system, that the dipole frontal area is comparable to the frontal area of the (reported) 23-inch sphere of the satellite body itself. The aerodynamic drag of the antennas, moreover, is an effect of purely frontal area the spin axis finally lay in the direction about which the satellite shows maximum moment of inertia. The effect that we note for Sputnik I during the first day of its flight may be similar in nature, especially if, as some announcements have suggested, the antennas of Sputnik I are swept back. This would seem a more natural explanation than our explana tion in terms of extension of the antennas under remote control. (M.S.T.) 1957 -OCT. DATE 2k Sputnik of life The sin fperiod epoch the I. FIGURE puinas ac-tfiaodning period. plotted scale ordinate the half period again, is, of spin true on 5 124 9 8 7 6 13 12 15 18 17 23 22 21 26 25 II0 14 16 20 19 -38- alone, while the torque produced by the skin drag of the rotating satellite body would appear necessarily to be a much less efficient mechanism for retarding the spin rate. The element of torque on a section of antenna x cms from the center of rotation (the center of the satellite itself) is iL- x S*<V> £.(£XR) • Here, \^ is the vector velocity of the element of antenna on which a force % (V ) is exerted. JQj is the unit vector in the direction of and is the unit vector directed out from the satellite body along antenna element. Where V,is the orbital velocity of the satellite, £J is the magnitude of the angular velocity (rads/sec), we have V- v. + . (l) drag spin, the and (2) Also, letting t(x) to be thickness of the antenna x cms from the satel lite body, we write the aerodynamic drag in the form Sdcv)- c u*)s\*r'p v^j* . (5) In equation (3), c represents the drag coefficient, which is close to unity in value, ~y' represents the angle between the vector element of length fi_dx and the velocity V, and Q is the local atmospheric density. By convention, sin'}'', in the drag formula, is always greater than zero. The torque then will have the sign of the dot product V. (-ft-X ft )• If the satellite antenna is x^ cms long, then the total torque exerted by the antenna is Xi 0 When we substitute equation (2) in equation (U), there results -39- Inspection of equation (5) shows two terms, one apparently linear in the vector R, and the other quadratic. The quadratic term introduces always a torque of fixed sign, opposed to the spin. However, the linear term in II also introduces a small torque, as we shall immediately see. The terra Vsin")^' , under the integral sign, varies as the satellite spins. We may write We now expand the square-root in terms of the small quantity KU>'/V0 . Let the angle between the orbital velocity VQ and the direction of the an tenna, JR, be £ . Then where the expansion is valid only when This con dition will be satisfied unless the spinning antenna comes within a degree of the orbital direction, and is therefore quite unrestr ictive . When equation (7) is substituted in equation (5) we find three terms, inclusive of first order terms in */Vm > L - cf \[0'(Sl XR) V.lsfc$l£\ *u>4* We have inserted the absolute magnitude signs on sin£ convention on sin^' should be preserved. in order that the We now develop the vector function £ (t). We introduce a cartesian ordinate system (see Figure 25)> with z-axis lying along the orbital velocity, and the y-z plane containing the spin axis,Jl. . The instan taneous antenna direction is defined by spherical coordinates ( £ ,\ ). Let "\ be the angle between the spin direction and the orbital velocity, foe measure time from the moment at which the instantaneous direction of the ciiiLt.ii;. j lies in the y-z plane, within 90 degrees of the orbital velocity. Finally, we let (3 represent the angle between the antenna direc- FIGURE 25 ~ Cartesian coordinate system for re presenting the components of R(t). -kltion and the spin axis. T > P>o, and (3 is assumed to be a fixed angle. In these terms, V. - ji = (o% ( o , 0 , vj s^r, , wv) (9) (10) nm (11) Substitute (9), (10), and (11 ) in the first term of equation (8). cfl V^sYviV sWt/a su,uit J x tu>4x o . then (12) This term is an oscillating function of time; since |sin&( is even, and sina t odd, its integral over one period of spin is zero. Therefore, the first term does not contribute to the slow-down of the spinning. The second and third terms of equation (8) become The integral of expression (lj) over one cycle, of length T, J o = c/> V. svu^. » J xHuU* |SUt5>( , (15) -k2- where (16) and, from (ll ), The integral, equation (16), is unfortunately elliptic, owing to the presence of the square-root in the denominator. In order to proceed further, we expand the root (to the first order) in a series in cos j , (17) ■ This approximation limits the accuracy of the remaining work to values of £ greater than about 20 degrees. With the notation (18) A(fr.r)- artUS f ].(i9) We have now to relate the drag produced by each of the four anten nas. We assume that the antennas occur in orthogonal pairs, and there fore define a plane. For a single antenna and its opposite, we have the relations ( $ , (3 ) and (180 + J? , 180 - 3), respectively. Therefore, the effect of the opposite antenna, when added to its conjugate, is simply to double the effect of a single antenna. To relate the effects of the orthogonal pairs, we must introduce another fixed angle, the azimuthal angle, a, between the conjugate antenna and the spin axis, as measured from the first antenna as a pole. Denoting the two antennas by subscripts, we find that (20) The sum of the effects of all four antennas is then a simple addition of equation (l5)j written for each of the four antennas -1*3- o 0 We have made use of the relations £ J* - Z 4 M t - J A ) ^o^<x) ; (22 ) The angles a, (3 and ^ are not known for the Soviet satellites. If we assume that Y - 90 degrees, consistent with the remarks in Section II of this report, then ja.= 0. If, without any attempt at justification for the moment, we assume j) Ss coi'ol — -Jr > then equation (21 ) takes the numerical value T ^ *» ^ r 'I (2-3) We use the equation oj it) -- c*J(o) t - £ j Lit > (?k) where I is the satellite's moment of inertia about the axis of spin, to -1*1*-- compute the change in period of spin over an interval, t. The moment of inertia is the sum of the moment for the satellite body proper, which we shall neglect, and the moment for the antenna system a (25 ) where m(x) is the mass distribution per unit length of the antennas. Let us suppose that the antennas consist of thin-walled aluminum tubing, such as, for example, U.S. 61 ST gauge, with walls 0.15 cm thick. If the tubing is of constant skin thickness, even if the antenna tapers in out side diameter, the detailed configuration cancels out of the expression for the change in period. For this example of thin-walled tubing, Ki^;= 2-7 x O.I!> IT t(x) per- c**t. (26) In equation (26), we assume the density of aluminum as 2.7 grams_ per cm5. If we now insert equations (25) and (23) in equation (2k) / Inspection of equation (27) In comparison with equation (21) shows that the leading term of the square brackets in equation (21) contains as a factor the sum that appears in the denominator of equation (27 )• This results in cancellation, in the leading terms of equation (27), of the dependence of the expression on p. and a. Their precise values should therefore not influence the result appreciably. Since (J2 X R )\ S U*Xy3 = j ->> U % f Let ' (28) S y'= cm/sec. Then equation (27) becomes 7 per spin cycle. To compare this result with observations, we compute -U5the total decrease in frequency over an interval of one day. Since the satellite moved in a slightly elliptical orbit, the density at the position of the satellite was a function of time. For a single passge of perigee point, we write i A u £ where P is half-period of the spin, with a nominal value of 4.5 seconds. This integral may effectively be limited to the immediate neighborhood of perigee as long as the scale-height of the atmospheric density is at most a few tens of kilometers. We represent the height of the satellite as a quadratic function of time (31) A, in equation (3l)> is the radial component of the acceleration of the satellite to its orbit, and is given in terms of the orbital con stants by h ■ '■ > (32) at the perigee point. hQ is the perigee altitude of Sputnik I, which we shall assume to be 220 kilometers, T is the orbital period, e, the eccentricity, and a the semi-major axis. The function yO(t) becomes />l*JV. , (33) where H is the scale height of the atmosphere at hQ, perigee point. shall assume that H = 30 km at hQ = 2P0 km. Equation (30) now may be written aw - -At,) - y- J e-*« *?4t ta and t^ effectively extend to t °o . Therefore, where Aus in satellite spin period through one perigee passage, _ We m is the change -46- (35) —-3k9 x 10 £ /J per passage^ (56) where we have substituted the values a = 6.6 x 10® cm, e = 0.05, and T = 5760 seconds. The measured value of ^w(see Figure 24), is O.5I seconds in 18 days, a change of P from 4.27 to 4-78 seconds. Since the satellite made almost exactly 15 revolutions of the globe per day, we have (37) radians per second, per passage. H --- 2-^*10 Dividing equation (36) into equation (37 )» we find - 13 Cfo = 7«6 * ' 0 grams per cm.3 (38) grams per cm 3 . / „\ (39) For a drag coefficient c = 2, -3.8*10 For a discussion of this value, see the last section of this report. The final discussion of spin in this report is concerned with the relatively simple problem of the type of fading produced by spinning, circularly-polarized, antennas. We first analyze the case in which the receiving antennas lie in a plane at right angles to the direction to the satellite. We shall assume that the polarization of the Sputnik antennas was circular, as reported by theU.S.S.R. in their preliminary literature. In this case, the received signals will correspond to the average energy absorbed from an electric vector, rotating in the equa torial plane of the satellite at angular rate , the circular frequency of the 20 Mc./s signals. This energy is the mean-square of the component of the electric vector in the direction of the receiving antenna, which we shall assume is a simple dipole. Assume that the instantaneous axis •U7- of the satellite's antenna system lies at angje i to the z axis of the receiving system whose x and y axes contain the receiving antennas, and at azimuth JP , measured with respect to the x-axis in the receiving plane. Then, the power received by orthogonal antennas, along the x and y axes of the receiving system, is Because the satellite is spinning, the angles i and are functions of time. We let iQ, <f q represent the direction of the spin axis in the coordinate system of the receiving antennas, and d represent the angle between the spin axis and the perpendicular to the plane of the satellite antennas. This angle d is related to our earlier a and (3^ by the expression 4 = si* a( iU, 4i 9 (1+1) where represents the closest antenna to the spin axis, and we do not distinguish positive or negative directions of rotation. We introduce time, measured from the moment at which the axis of the satellite antenna system comes closest to the spin axis and the direction to the receiving antennas, in the form of the azimuthal angle t*i~t , measured about the spin axis. We have three relations for i and , si** ; ctftf = cj*4 i'**i0 siuf, +• <^>4 ift iU-co t , To construct curves of the spin fading, we solve equations (k2 ) for i and , and compute equations (ho) with the results. A typical pair of curves is shown in Figure 26. Note, for example, that the curves show a phase shift of about 90 degrees between the two minima, and that the two curves have exactly the same shape. Neither of these conditions holds in general, however. We have constructed such curves for all ranges of values of the parameters iQ, <Pq, and d. The problem was generously programmed and computed by Robert S. Lawrence, of the National Bureau of Standards in Boulder. A further complication arises when the plane of the receiving antennas does not lie perpendicular to the line of sight to the satellite, 26 sTFIGURE cfor polarized The hpiaernocatu-ertfnlviacedas.rilngy lie dassumed pin plane the receiving ieto arnare peatcntdniaocsnular ^5° sspin The makes angle its and sight, of line the axis ato tpro anel ite. bisects the pof The them. jection plane receiving eto arnpontendincauslar 45° 0° 180° 135° 90° 360° 315° 270° 225° U50 splane makes of angle axis. spin the with atnanetlenitaes PHASE px +-+ 1 r —i t o1 1 o Py -OO— — but rather, in the horizontal plane. In this case, we introduce the plane of incidence, defined by the perpendicular to the plane of the receiving antennas, and the line of sight to the satellite. Suppose that the angle of incidence is Z (the zenith distance of the satellite). The azimuthal angle, between the plane of incidence and the antenna, measured in the horizontal plane, is \'. We now define the x-axis of equations (k2) as lying in the plane of incidence. Then, the received power in a horizontal antenna is a The complete specification of the spin-fading curves therefore involves two known angles, >! and Z, and three unknown angles, i0,(f0 and d. For a given direction of the satellite, at azimuth A and zenith dis tance Z, the relation giving X is X = Ao-A , (hh) where AQ is the azimuth of the receiving antenna. We can now compute the evolution of spin-fading as a function of time during a given passage, or, in the absence of precession, from passage to passage. To do this, we must take account of the variation of i0,jP0 as functions of the time of passage. We specify their values , <£' at the time when the satellite's azimuth is 90 degrees and its zenith dis tance, z' . Compute the auxiliary quantities r = >i»it' , (1*5) which are the direction cosines of the spin axis in the horizontal system. These will be fixed from passage to passage as long as the satellite does not precess. The desired angles then are given by Su*i.ux><£ = U If the values of i0»^' we should replace equations * <T cos A <-<*> Z ~ ^Siit.^ , are determined at azimuth 270 degrees^ then by the following -50- •i . n' v = - sit- .<„ 5mf. , <*7> We have not yet computed these spin-fading curves. It is important that this should be done, both in order that we might confirm the con clusions of Section II on the rate of change of spin-fading through nearby passes, and also so that we may obtain information on the orientation of the satellite antennas in space. 4. Acknowledgements It is a pleasure to again acknowledge the strong help of R. H. Lee of our staff, both in the original observations and in the reduction of the tracking data. Robert S. Lawrence, of the National Bureau of Standards Boulder Laboratories, contributed at many times in the develop ment of this report. IGY Satellite Report Series Number 6 15 August 1958 IGY WORLD DATA CENTER A Rockets and Satellites NATIONAL ACADEMY OF SCIENCES REPORTS AND ANALYSES OF SATELLITE OBSERVATIONS (Special Reports Nos. 15 and 16 and excerpts from No. 14 of the Smithsonian Astrophysical Observatory) NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, D. C. INTERNATIONAL GEOPHYSICAL YEAR WORLD DATA CENTER A National Academy of Sciences 2101 Constitution Avenue, N.W. • Washington 25, D. C, U.S.A. World Data Center A consists of the following eleven archives: Airglow and Ionosphere: IGY World Data Center A: Airglow and Ionosphere Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado, U.S.A. Glaciology: IGY World Data Center A: Glaciology American Geographical Society Broadway at 156th Street New York 32, New York, U.S.A. Longitude and Latitude: Aurora (Instrumental): IGY World Data Center A: Aurora (Instrumental) Geophysical Institute University of Alaska College, Alaska Aurora (Visual): IGY World Data Center A: Aurora (Visual) Rockefeller Hall Cornell University Ithaca, New York, U.SA. Cosmic Rays: IGY World Data Center A: Cosmic Rays School of Physics University of Minnesota Minneapolis 14, Minnesota, U.SA. IGY World Data Center A: Longitude & Latitude U. S. Naval Observatory Washington 25, D. C, U.S.A. Meteorology and Nuclear Radiation: IGY World Data Center A: Meteorology and Nuclear Radiation National Weather Records Center Asheville, North Carolina, U.S.A. Oceanography: IGY World Data Center A: Oceanography Department of Oceanography and Meteorology Agricultural & Mechanical College of Texas College Station, Texas, U.S.A. Rockets and Satellites: IGY World Data Center A: Rockets and Satellites National Academy of Sciences 2101 Constitution Avenue, N.W. Washington 25, D. C, U.S.A. Geomagnetism, Gravity, and Seismology: IGY World Data Center A: Geomagnetism, Gravity & Seismology Geophysics Division U. S. Coast and Geodetic Survey Washington 25, D. C, U.S.A. Solar Activity: IGY World Data Center A: Solar Activity High Altitude Observatory Boulder, Colorado, U.S.A. Note: (1) Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: Director, World Data Center A, National Academy of Sciences, 2101 Constitution Avenue, N.W., Wash ington 25, D. C, U.S.A.; (ii) Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate archive listed above. 1GY World Data Center A 4rfj> ^Rockets and Satellites. National Academy of Sciences Washington 25, D. C. [_IGY Satellite Report Series Number 6 15 August 1958 REPORTS AND ANALYSES OF SATELLITE OBSERVATIONS Hi.UE!37 OF sC/f LIBRARY SEP 2 iSo8 Ml RESEARCH Smithsonian Astrophysical Observatory (Special Reports Nos. 15 and 16 and excerpts from No. 14) Project Director: Fred L. Whipple Cambridge, Massachusetts Note 1. This report is issued in accord with international arrange ments on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies avail able at cost to scientists upon their request. 2. These data and/or report contents are reproduced as received from the experimenter. 3. Recipients of these reports are advised to communicate with the authors prior to utilization of experimental data for further publication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites REPORTS AND ANALYSES OF SATELLITE OBSERVATIONS Table of Contents Page 1. Moonwatch Catalogue—May Through June 1958, E. P. Bullis and L. Campbell 1 2. Preliminary Note on the Mass-Area Ratios of Satellites 1958 Beta 1 and 1958 Beta 2, G. F. Schilling, C. A. Whitney and B. M. Folkart 22 3. The Descent of Satellite 1957 Beta 1, L. G. Jacchia 25 4. Positions of Satellite 1957 Beta 1 During the First 100 Revolutions, R. M. Adams, R. E. Briggs and E. K. L. Upton 39 ERRATA IGY Satellite Report Series Number 6 "Reports and analyses of Satellite Observations" Table of Contents 2. Preliminary Note on the Mass-Area Ratios of Satellites 1958 Beta 1 and Beta 2, G. F. Schilling, C. A. Whitney and B. in. Folkart should read 2. Preliminary Note on the Mass-Area Ratios of Satellites 1958 Delta 1 and 1958 Delta 2, G. F. Schilling, C. A, Whitney and B. M. Folkart 1. Moonwatch Catalogue - May Through June 1958 E. P. Bullls and L. Campbell, Jr. Smithsonian Astrophysical Observatory This catalogue of Moonwatch observations continues from the Moonwatch catalogues contained in Special Reports No. 11 and No. 12, Smithsonian Astrophysical Observatory.(l, 2) Moonwatch observations of the U. S. satellites made during the period from May 1, 1958 through June 30, 1958 as well as observations made prior to this period which do not appear in Special Report No. 12, are included. For the U.S. S.R. Delta satellites, observa tions are listed from the date of launching on May 15 UT through June 30, 1958. The explanation of the columns in this tabulation reading from left to right is as follows: The Observation Number is assigned by the Computations and Analysis Section to every observation received according to its order of receipt. This number never changes even if subsequently some element of an observation is corrected. If any reference should be made to an observation appearing in this report please mention the observation number. The next two columns indicate the Station Name and the Station Number . The station number given contains the first three digits of the official Moonwatch team registration number preceded by a zero. When a station uses more than one observing site, the geographical coordinates of which are significantly different, the additional station numbers begin with the digit "8. " The name of the station is then indicated by a supplementary letter, for example Sacramento A, Sacramento B. The times of observation, stellar coordinates, and magnitude follow in the remaining columns. Angular velocities, directions of travel, and the observed colors of satellites were generally reported, but these are not included in this tabulation. However, this information is received at Moonwatch Headquarters since it is vital to the preliminary validation of observations. A key to the Moonwatch Station code numbers precedes the catalogue of observations. It lists those stations not previously listed (3) as well as stations where revisions have occurred. Moonwatch stations have reported a total of 131 observations of satellites 1958 4, 1958 81, 1958 02 and 1958 7. This catalogue includes all the final observations of 1958 y which ceased to exist on or about June 28, 1958. At the date of this report no observations of its actual plunge into the atmosphere have been received. - 2 A total of 536 visual observations from the 1958 Delta have been received. The breakdown by component, i.e. individual satellites, is as follows: Satellite Satellite Satellite Satellite 1958 1958 1958 1958 $1 : 459 (2: 65 £3 : 8 $4 : 4 References (t) Campbell, Leon Jr. : "Moonwatch Observations of Satellites 1958 Alpha, 1958 Beta One, 1958 Beta Two, and 1958 Comma. " Chapter II, pp. 7-13, Special Report No. 11, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958.* (2) Bullis, E. P. and L. Campbell, Jr. : "Moonwatch Catalogue. n Chapter II, pp. 24-28, Special Report No. 12, Smithsonian Astrophysical Observatory, Cambridge, April 30, 1958. •• (3) Adams, R. M. , N. McCumber, and M. Brinkman: "Processed Observational Data for U. S. S. R. Satellites 1957 Alpha and 1957 Beta. " Smithson. Contrib. Astrophys. , 2, 287-337, 1958. ••• 'Reprinted in IQY Satellite Report Series No. Z ••Reprinted In IGY Satellite Report Series No. 4. •••Reprinted in IGY Satellite Report Series No. L - 3 - STATION COORDINATES STATION NUMBER STATION LONGITUDE (E) LATITUDE HEIGHT (M) 0014 Washington, D. C. 282°47''30" 38° 45' 30" 6S 0023 Peoria, Illinois 270 24 09 40 45 19 238 0029 Wilmore, Kentucky 275 20 06.1 37 51 36.3 282 0030 New Orleans, Louisiana 269 58 34 29 57 30 0035 St. Paul, Minneapolis 266 50 01.1 44 55 03.61 306 0046 New York New York 286 01 15 40 45 28 259 0047 Rochester, New York 282 26 11 43 06 49 154 0051 Columbus, Ohio 276 57 46 40 01 49 229 0054 Tulsa, Oklahoma 26' 03 36 04 204 0060 State College, Pennsylvania 282 06 33 40 44 01.2 3*3 0065 Bryan, Texas 263 39 58.630 30 38 14.708 92 0076 Portland, Oregon 237 22 27 45 29 19 46 0078 Sunnyvale, California 237 59 40 37 22 20 17 0081 Schenectady, New York 285 58 57 42 53 32 235 0082 Dayton, Ohio 275 44 32.8 39 50 40.1 252 0087 New Haven, Connecticut 287 03 10 41 19 56.2 12 0089 San Antonio, Texas 261 30 56 29 27 48 0091 Panama City, Florida 274 24 30 05 0109 Santa Monica, California 241 20 34 04 30 853 0110 Lawton, Oklahoma 261 35 47.818 34 39 44.978 358 0116 Wake, Pacific 166 39 12 19 17 12 0119 Culver City, California 241 24 06.8 34 09 05.9 0126 Bartlesville, Oklahoma 264 03 36 36 42 18 213 0137 Agana, Guam 144 50 13 33 111 0138 New London, Connecticut 287 53 38 42 22 40 2 256 5 12 61 -4 STATION COORDINATES (cont'd) STATION NUMBER STATION LONGITUDE (E) LATITUDE HEIGHT 0139 Fort Worth C, Texas 262° 37' 30" 32° 42' 15" 0199 St. Paul B, Minnesota 266 45 59.25 44 58 30.7 0214 Fuchu 133 14 19 34 34 17 30 0274 H. S. B. 1 139 57 02 35 39 36 3 0275 H. S. B. 2 133 46 15 34 35 23 5 0276 H. S. B. 3 135 56 59 33 37 46 35 0277 H. S. B. 4 138 59 21 34 42 46 160 0278 H. S. B. 5 138 59 20 34 42 42 91 0279 Kyoto University 135 47 09 35 01 39 60 0280 Matsue 133 03 18 35 27 21 1 0401 Bloemfontein, South Africa 26 13 35.50 -29 06 19.56 1634 0405 Pretoria, B, U. of South Africa 28 12 42.58 -25 43 43.56 1311 0450 Montreal, Canada 286 22 21 45 31 10 61 0500 Quezon City, Philippine Islands 121 03 55.44 14 39 04.23 77 0501 Pasay City, Philippine Islands 120 59 30 14 33 42 0502 Taipai, Taiwan 121 30 02.6 25 02 42.7 0603 Woomera 136 47 01 -31 06 01 160 0700 Berlin-Schoneberg, Germany 13 20 30 52 28 30 50 0701 Bochum, Germany 7 13 51 58 162 0702 Hanover, Germany 9 35 42 52 18 20 110 0703 Munich, Germany 11 03 31 48 07 21 573 0704 Recklinghausen, Germany 7 11 51 37 134 0705 Ulm-Donau, Germany 9 58 48 23 500 0706 Weissenau, Germany 9 35 47 46 420 0902 Guatemala City, Guatemala 269 28 01.962 14 35 11.031 8005 Sacramento, D 239 08 36 38 38 06 204 9 22 1502 606 -5 - STATION COORDINATES (cont'd) STATION NUMBER STATION LONGITUDE (E) LATITUDE HEIGHT 8009 Washington, D. C, C 282° 47' 30" 38° 45' 30" 69 8011 Sacramento F, California 237 53 24 38 24 30 835 8040 Johannesburg, B -26 11 42 1708 8501 Sacramento C, California 238 14 58.8 38 33 05.4 8505 Cleveland B, Ohio 278 10 18 41 25 30 8512 West Palm Beach, Florida, MW, B 279 51 27 00 8513 Bartlesville, Oklahoma, C 264 00 36 36 44 18 8514 New Haven, Connecticut, MW, C 286 59 30 41 12 35 8515 Alamagordo, New Mexico, MW, B 254 02 54 32 54 49 8516 Denver, Colorado, MW, B 255 00 39 42 8517 Sacramento, California, MW, E 238 14 51.0 38 32 55.8 8518 Johannesburg, U. of S. A., MW, C 28 00 -26 07 1615 8519 Johannesburg, U. of S. A., MW, D 28 02 -26 11 1803 8520 Johannesburg, U. of S. A., MW, E 28 01 -26 08 1672 8521 Johannesburg, U. of S. A., MW, F 28 04 -26 12 1720 8522 Johannesburg, U. of S. A., MW, G 28 11 -26 14 1637 8523 Capetown, U. of S. A. , MW, B 18 29 -33 57 10 8524 Capetown, U. of S. A., MW, C 18 29 -33 59 10 8525 Johannesburg, U. of S. A., MW, H 28 07 -26 12 1704 8526 Pretoria, U. of S. A., MW, C 28 11 48 -25 45 14 1328 8527 Adelaide, Australia, MW, B 138 35 45 -34 51 50 20 8528 Adelaide, Australia, MW, C 138 40 -34 44 8529 Bartlesville, Oklahoma, MW, B 264 04 12 36 44 48 8530 Las Cruces, New Mexico, MW, B 253 12 15 32 19 16 28 08 25.5 15 15 -6 - STATION COORDINATES (cont'd) STATION NUMBER STATION LONGITUDE (E) LATITUDE 272° 06* 42" 43° 04 47" HEIGHT (M) 8531 Milwaukee, Wisconsin, MW, C 8532 Salisbury, Southern Rhodesia 8533 Idaho Falls, Idaho, MW, B 247 56 35 43 30 01 8534 Albuquerque, New Mexico, B 253 27 47 35 06 37 1667 8535 Walnut Creek, California, B 237 56 14 37 57 52 9 31 04 -17 46 1958 a R. A. h m s Declination h m i 03 54 00 -38 30 Azimuth • 1 N 180 Altitude Mag. • i n +5 08 ♦5 337 30 65 00 Obt.f 00466 00465 Station Kansas City Ten* Haute Sta. No. 0036 0025 Time(UT) Date h m s Feb. 08 00:17:30 Feb. 08 00:34:00 00641 Adelaide 0600 Feb. 17 18:26:03 00643 Fort Worth 0069 Mar. 19 11:39:09.5 00686 Wichita 0028 Apr. 04 03:13:14.0 00645 00646 Johannesburg Pretoria B 0403 0405 May 07 May 07 16:55:20 16,55:23 000 00 000 63 00 65 00 00638 00648 00649 00650 00651 00652 00653 Bloemfontein Johannesburg Johannesburg Johannesburg Johannesburg Pretoria B Johannesb. B 0401 04p3 0403 0403 0403 0405 8040 May May May May . May May May 17:43:40 17:44:23.2 17:44:24 17:44(25 17:44:25 17:44:26 17:44:20.9 000 24 000 00 180 00 180 00 000 00 180 00 76 89 54 89 48 89 48 89 54 88 06 +7 to 8 +9 00639 00662 Bloemfontein 0401 Pretoria B 0405 May 10 May 10 17:14:29 17:15:20 000 24 180 00 80 42 83 54 +7 to 8 +9.5tol0 00640 00665 00664 00667 00666 00663 Bloemfontein Johannesburg Johannesburg Johannesburg Johannesburg Pretoria B 0401 0403 0403 0403 0403 0405 May May May May May May 11 11 11 11 11 11 18:02:28 18:03:03 18:03:04.6 18:03:04.7 18:03:04.7 18:03:11.5 179 36 180 00 180 00 180 00 180 00 81 69 69 70 69 +8 to 9 49 49 00691 Pretoria B 0405 May 12 16:45:34.9 180 00 80 45 +10 00642 Bloemfontein 0401 May 13 17:32:32 179 36 80 12 +10 00677 Pretoria B 0405 May 10 17:49:45.9 00655 Capetown 0402 May 17 18:27:26 000 24 85 30 00656 00668 00064 00693 00695 00718 00696 00694 00692 Edinburg Edinburg Bloemfontein Johannesburg Johannesburg Pretoria B Johannesburg Johannesburg Pretoria B 0066 0066 0401 0403 0403 0405 0403 0403 0405 May May May May May May May May May 18 18 18 18 18 18 18 18 18 10:26:17.2 10:26:25 17:18:03 17:18:42.0 17:18:42 17:18:43.7 17:18:44 17:18:45.8 17:18:48.4 180 180 179 180 179 180 179 179 05 03 75 65 65 63 65 65 00660 00661 00698 00697 Edinburg 0066 Bloemfontein 0401 Johannesb. B 8040 0405 Pretoria B May May May May 20 20 20 20 09:56:53.5 16:46:35 16:47:13.0 16:47:19.7 00669 00705 00706 00707 Capetown Pretoria B Pretoria B Pretoria B May May May May 21 21 21 21 17:30:13.6 17:33:57.0 17:34:01.8 17:34:03.4 0402 0405 0405 0405 08 08 08 08 08 08 08 +7 to 8 17 02 +27 40 40 09 31 59 .16 00 4-3 10 41 36 11 15 11 18 10 58 10 29 54 11 28 -26 20 54 24 36 00 48 -48 30 +10 +9.5 +9.5tol0 49 49 +10.5 -53 36 00 36 00 36 36 +7 24 30 48 24 24 +8 to 9 +9.5 +9.5 +9.5 -51 48 135 179 36 81 30 75 06 +8 +11 179 24 64 18 +10.5 000 24 180 00 179 36 84 24 72 71 42 -50 54 -44 18 49 49 49 (cont'd) 1958 a Sta. Station ^hattanoog Time (UT) h m i 10:10:19 10:12:43 16:58:13.1 17:01:18 Obs.# 00703 00673 00720 00681 0062 0129 Capetown 0402 Bloemfontein 0401 Date May 23 May 23 May 23 May 23 00682 00715 00683 Albuquerque Pretoria B Konko 0103 0405 0224 May 24 10:55:30 May 24 17:49:04 May 24 18:30:36 00704 00717 00716 Chattanooga Johannesb. B Pretoria B 0062 8040 0405 00684 Terre Haute 00712 R. A. h m s Declination • IN 19 59 00 +14 00 000 24 179 36 Altitude Mag e i h +4 64 +7.5 83 54 83 36 180 000 24 59 87 48 164 87 000 24 60 36 Azimuth • ■ n 175 45 +9 +8 19 25 +02 May 25 09:42:55 May 25 18:36:38.5 May 25 18:36:43.3 12 41 06. +04 22 0025 May 26 08:35:12 18 59 16 China Lake 0098 May 27 00702 Higashlmats. 0210 May 28 17:32:25 18 51 +20 00711 00708 North Canton 0053 0028 Wichita May 30 07:26:52.5 May 30 09:24:00.6 18 33 19 28 00 -07 24 +01 54 00710 00709 Tuscon Albuquerque 0003 0103 June 01 June 01 10:49:20.5 10:50:24 20 06 +26 00713 Hifashimats. 0210 June 04 14:39:05.5 16 51 48 00719 3ftftcon 0003 June 11 10:23 00723 Sacramento E 8517 June 14 06:01:19.1 15 27 36 +19 10 +10 00724 Sacramento £ 8517 June 16 05:24:44.2 14 54 32 +19 33 +10 00725 Sacramento E 8517 June 19 15 05 57 +12 29 05:31:35.7 +8 -12 28 180 00 11:06:58.5 +9 65 00 - +8 +10 +7 180 52 35 +7 +6 +7 +21 06 180 56 +6 6- 8S6T 19 *b»S 90000 opio6ouii>[V ZOTO 'row 61 snr!l (ill) Iraq 'ii «si as £1000 opiq6ptuoxv 2010 'Wlf Z2 'XT =St 02 tTOOO ZTS8 'row OE «60 »I0 91 6T000 0120 -jdy O "H Y n in 91 S2 t uoijourpaci ^ m i qjnmriY itr* 0 ZI" f+ SI «0I 'Z2 2£ 80 iS apnjpiV -0Byf • i * 9+ 61 6Z 22+ 00 1+ T2000 22000 »Pn»T»HY £090 0090 ,jtfv a Z2 «6I Zt SS '61 «2» S"9S 081 *2 9t OEZZ ♦2000 wanxooM £090 -**Y OE '61 «8T OS 081 SI 62000 IMOfHJ, £000 *™f II «0T £2 081 9S 0E000 WIIUIIHMaDg J ZIS8 «raf 91 «0T £1 T£000 2900 «mf 6T »60 CO OS m 06 61 8* S'Z+ 9* I* 9* 60" 8S6T Si 10000 ntAmffYa** £010 '•WW 02 'TI SS ZO 20000 WW!« ZZOO '»H 92 «TI »Z0 W tOOOO OpOM|t TOW -a«Y 92 «eo *2 zt 6ZI 9E 90000 »i=»A ZOTO ton zo *0 »SS S'60 6ZT 9£ 081 61 80 9+ 62- 81 s*z+ 0+ 8T 08 8+ - 10 1958 y Azimuth • i n 00 24 179 36 Altitude Mag • 1 * 81 22 77 36 +10. S 18:40:07 18:40:49 179 36 179 36 74 39 66 +10 18:33:12 179 36 74 42 409 168 180 79 06 50 ■109 11:22:04 18:01:47.6 179 36 0 24 69 00 67 30 +10 +10 Apr. 10 18:29:11.5 00 24 53 06 0098 Apr. 16 11:32:37 179 36 76 00 Higashimats. 0210 Apr. 18 10:48:35 00137 Yuma 0107 Apr. 29 03:40:35.5 00347 China Lake 0098 May 04 04:42:20 00141 00142 SacramentoE Albuquerque 8517 0103 May 05 03:57:12.0 May 05 04:01:26 10 43 24 00145 00143 Pretoria B Albuquerque 0405 0103 May 07* 03:16:16 May 06 03:13:47 20 07 00146 00348 00342 Johannesburg China Lake Yuma 0403 0098 0107 00351 00352 00341 00354 00355 00349 Johannesburg Johannesburg China Lake 00343 00350 Albuquerque 0103 Sacramento E 8517 May 10 03:19:31 May 10 05:09:14 00356 Bloemfontein 0401 May 18 03:01:50 00362 00363 00360 00361 Johannesburg Johannesburg Pretoria B Pretoria B Ob$.# 00002 00001 00003 Sta. Station No. Capetown 0402 Bloemfontein 0401 Johannesburg 0403 Date Mar. 28 Mar. 28 Mar. 28 Time (UT) h m s 18:33:24.9 18:36:30.5 18:37:13.8 00004 00005 Bloemfontein 0401 Johannesburg 0403 Mar. 30 Mar. 30 00006 Bloemfontein 0401 Apr. 01 00008 00007 W.PalmBch.B8512 Albuquerque 0103 Apr. 05 08:56:10 Apr. 05 11:00:23 00082 00083 China Lake Capetown 0098 0402 Apr. 09 Apr. 09 00084 Capetown 0402 00128 China Lake 00086 R. A. h m s Declination • 1 M 08 56 30 -48 12 09 40 +10 +08 +32 00 402 179 36 78 45 179 36 74 12 180 00 70 30 +06.5 +08 180 00 73 30 +09 +07 May 07 03:16:14.6 May 07 04:14:14.8 May 07 04:15:08.325 180 00 179 36 179 36 64 30 61 48 73 10 +08 Johannesburg 0403 Johannesburg 0403 Sacramento E 8517 May 08 02:21:24.0 May 08 02:21:24.6 May 08 05:13:23.2 180 00 180 00 74 48 74 48 +08.5 +08.5 +08 0403 0403 0098 May 09 03:18:42.6 May 09 03:18:45.7 May 09 04:16:58 179 36 179 36 +08.5 57 00 44 22 30 +09 180 40 30 000 24 82 06 000 000 000 000 73 73 75 75 * Correction 0403 0403 0405 0405 May May May May 19 03:19:24.8 19 03:19:25 19 03:19:26.1 19 03:19:30.2 +06 46 12 -53 24 12 05 48 -18 14 20 16 36 -58 53 11 58 46 -30 08 00 00 00 24 24 30 12 30 +01 +08 +09 +08 +08.5 +09 (cont'd) - 11 1958 y Obs.# 00402 Station China Lake Sta. No. 0098 Date June 10 Tlme(UT) h m s 10: 34s 27 R. A. h m i 00396 00409 00410 Sacramento E 8517 Sacramento E 8517 Sacramento E 8517 June 14 June 14 June 14 10: 1& 22.7 lOi 16 35.3 10* 17: 05.8 19 40 50 21 23 28 21 58 34 400 12 +00 31 +00 17 +8 00397 00406 Sacramento E 8517 Sacramento E 8517 June 15 June 15 lOi 2* 20.5 lOi 2& 51.4 19 48 35 21 51 33 -02 36 -04 33 +8 00401 00407 00408 Sacramento E 8517 Sacramento E 8517 Sacramento E 8517 June 16 June 16 June 16 10j 27: 37.3 lOi 27: 47.5 Id 29t 15.9 20 04 15 20 20 05 22 07 49 -08 55 -09 20 -11 32 +8 00412 Wichita 0028 June 26 02: 43: 17.2 14 38 -36 42 +7 00415 * Walnut Crk. 0011 June 27 04* 23: 43.5 14 21 00 -40 00 +3 00418 0123 June 28 oa 31: 24 180 28 00 +8 0103 June 29 03. 07: 36 181 00 28 00 +2 MemphU 00417 * Albuquerque * (Probables) Declination e i h Azimuth o • || 180 00 Altitude • IN 66 00 Mag. +9 - 12 1958 gl Obs.# 00018 00022 00001 00024 00005 00002 00003 00004 00019 00006 00235 00007 00240 00009 00241 00236 00242 00243 00010 00244 00237 00238 00023 00021 00020 00014 00015 00016 00100 00101 Station Harrisonburg Decatur A W.Palm Bch St. Petersbg. Cambridge St. Petersbg. St. Petersbg. St. Petersbg. Albuquerque St. Paul B Albuquerque St. Paul B Edinburg San Antonio Edinburg St. Paul B Edinburg Edinburg Edinburg Edinburg St. PaulB San Jose San Jose Walnut Creek Los Altos San Francisco China Lake Whittier Miyazaki Miyazaki Sta. No. 0072 0132 0016 0121 0099 0121 0121 0121 0041 0199 0041 0199 0066 0096 0066 0199 0066 0066 0066 0066 0199 0134 0134 0011 0005 0008 0098 0012 0230 0230 Date May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 May 16 Time (UT) h m I 01:03:33 01:04:30 01:07:21 01:08 01:15 01:23:18 01:24:52 01:30:49 02:49:33 02:50:06.5 02:50:12 02:50:43.5 02:50:47.4 02:51:30 02:51:36.0 02:51:43.5 02:52:15.0 02:52:58.2 02:53:21.4 02:53 1.33. 6 02:52 30 04:36:04 04:36:47 04:38:00 04:38:16 04:40:40 04:42:46 04:43:12 11:41:17 11:42:58 0&219 00195 00090 00089 00217 00196 00280 00248 00247 00281 00197 00246 00082 00198 00094 00282 00088 00104 00060 00423 00051 00122 00114 00061 00429 00049 00058 00434 00121 00420 Bryn Athyn Bristol North Canton Washington W.Palm Bch. Bristol Whittier China Lake China Lake Whittier Whittier Los Alamos Los Alamos Whittier Las Cruces B Whittier Tucson Hiroshima Mitaka Sendai Toyohashi Tokushima Suwa Mitaka Suwa Kanaya Machi Musashino Takada Nagoya Mitaka 0055 0097 0053 0014 0016 0097 0012 0098 0098 0012 0012 0043 0043 0012 8530 0012 0003 0211 0229 0246 0255 0253 0248 0229 0248 0220 0233 0250 0236 0229 May May May May May May May May May May May May May May May May May May May May May May May May May May May May May May 01:44:10 01:44:57 01:45:53 01:47:42 01:48:16 01:50:55 03:30:35 03:30:49.5 03:30:55.9 03:34:22 03:31:36 03:32:10 03:32:27 03:32:58 03:35:00 03:35:18 03:36:24 10:32:24 10:32:35.2 10:32:43 10:33:25 10:33:27 10:33:29 10:33:30.4 10:33:41 10:33:55 10:34:01 10:34:04 10:34:14 10:34:14.8 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 R. A. h m ■ Decimation a i it 14 05 +18 30 13 14 +05 18 15 05 12 57 13 00 12 36 09 25 10 13 00 10 48 30 +40 -28 -24 +56 -10 +40 -18 11 17 30 +31 Azimuth • IN 090 00 090 090 30 48 20 00 334 335 207 12 335 335 30 225 153 30 180 08 42 09 38 10 36 30 10 50 12 06 11 38 12 20 10 06 11 25 +12 45 +04 40 -12 06 -15 -22 -34 30 -40 +11 00 -14 00 07 48 09 32 +29 -05 40 11 19 +5 +3 +2 +1 +2 +2 +1 +1 270 20 222 270 178 30 27 57 17 30 359 00 000 00 84 00 87 00 +39 36 +33 42 +06 00 +02 12 +03 36 -16 -22 11 00 +82 171 00 28 00 311 30 284 54 29 30 24 54 09 30 +53 08 14 +44 00 00 65 00 09 38 11 00 +40 +57 294 18 56 36 270 66 270 00 257 30 83 30 67 30 +24 to-l.S to 9 to 6 to 6 +4 +1 to 8 +0 +1 to 7 +1.2 +1 to 8 +55 12 06 12-08 08 56 09 11 12 52 10 47 13 22 10 14 Altitude Mag. • 1 H 90 00 +1 +2 +1.5to5 44 +2 to 4 +1 40 +2 +2 +2 +0.5 +1.5 +0.5 +1.5 36 +1 49 +1.5 17 45 63 30 81 -2 89 30 84 30 46 03 +1 -1 -1 +2 +2 -1 42 +1 4-1 4-1 44 4-1 4-1 4-1 4-1 4-1 +1 40 +1 4-1 - 13 - (cont'd) 1958 £ I Decimation h m s +32 00 +41 Obs. # 00052 00103 00435 00113 00426 00110 00055 00059 00116 00421 00425 0043" 00108 00440 00062 00054 00118 00428 00050 00105 00430 00436 00063 00427 00432 00433 00106 00422 00431 00119 00056 00123 00438 00109 00441 00111 00115 00424 00053 00120 00057 00117 00112 00107 00439 Station Yokkaichi Hashimoto Kasukabe Mizukaido Nagoya Manazuru Kurume Machi Mutashino Fukuoka II Mitaka Toyohashi Chunichi h;~j<> Kagoshima Mitaka Kiryu Mizukaido Niigata Kanaya Machi Hiroshima Suwa Kasukabe Mitaka Ikoma Tadotsu Hashimoto Higashimats. Mitaka Suwa Mizukaido Kurume Machi Otsu Otsu Honjo Yamagata Konko Asahikawa Sendai Fuchu Mizukaido Kurume Machi Fukuoka II Miyazaki Higashimats. Miyazaki Sta. No . 0258 0209 0263 0231 0236 0228 0227 0233 0206 0229 0255 0204 0212 0218 0229 0223 0231 0238 0220 0211 0248 0263 0229 0216 0249 020S 0210 0229 0248 0231 0227 0269 0269 0212 0257 0224 0201 0246 0214 0231 0227 0206 0230 0210 0230 Date May 117 May 117 May ]17 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May 17 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May 117 May ]17 May 17 May 117 May : 17 May 117 May 117 May 117 May 117 May 117 May 117 May ]17 May 117 May 117 May 117 May 117 May 17 May 117 May i17 May 117 May 117 May : 17 May ]17 May 117 Time (UT) h m s 10:34:23 10:34:25 10:34:28 10:34:31 10:34:33 10:34:35 10:34:40 10:34:42 10:34:44 10:34:51.8 10:35:03 10:35:04 10:35:20 10:35:35 10:35:42.6 10:36:01 10:36: 14 10:36:25 10:36:34 10:36:41 10:36:48 10:36:50 10:36:53.7 10:36:54 10:36:55 10:37:08 10:37:21 10:37:25.8 10:38:18 10:38:31 10:38:34 10:38:37 10:38:39 10:38:40 10:38:43 10:39:07 10:39:24 10:39:24 10:39:42 10:40:22 10:40:31 12:20:55 12:22:50 12:22:51 12:24:56 R. h 11 11 08 27 08 23 09 27 -03 -09 -20 00446 00445 00071 0006U 00443 00066 00064 00442 00070 00444 00067 00069 00072 00068 00448 Sapporo Sapporo Mitaka Kanazawa Sendai Takada Higashimats. Sendai Mitaka Niigata Kiryu Mitaka Musashino Sendai Honjo 0245 0245 0229 0221 0246 0250 0210 0246 0229 0238 0223 0229 0233 0246 0212 May May May May May May May May May May May May May May May 11: 17:19 11:17:03 11:16:55.8 11:16:32 11:16:24 11:16:02 11:15 :SS 11:15:50 11:15:24.0 11:15:18 11:14:44 11: 14:23.3 11: lit 20.9 11:14:15 11:05:25 09 43 09 31 -26 -23 09 12 -12 08 29 08 29 -02 -03 118 118 118 118 118 118 J18 1L8 118 118 118 118 118 18 118 A. ZD 1 10 05 10 10 +21 10 21 +26 11 11 10 14 25 43 05 18 13 04 13 29 12 19 13 13 13 12 00 25 03 17 12 42 195 30 Altitude Mag. o i n +2 +1 40 00 4-1 180 80 30 225 225 00 090 215 12 67 30 67 00 50 65 54 186 00 180 180 180 53 36 49 45 34 00 195 30 172 12 64 00 38 12 169 18 33 00 225 225 158 00 160 64 62 22 00 21 273 44 30 265 48 265 48 45 00 225 225 270 44 54 44.54 77 30 60 60 19 42 Azimuth • • ii +17 +15 +14 +20 -07 -08 -15 +10 -11 -12 -22 00 -26 10 05 +14 00 11 12 +55 233 12 23 54 234 00 20 12 241 54 255 24 245 00 260 00 270 54 270 00 262 00 357 00 25 00 23 48 22 00 24 00 20.54 20 42 19 12 30 30 +1 +1 +1 to 5 +1 +1 +1 +1 +0 +1 +3 +1 +0 +1 +1 +1 +1 +1 +5 +4 +1 +1 +1 +1 +2 +1 +3 +6 +3 +3 +4 45 +2 +5 +5 +3 +5 +6 43 +2 +6 +6 +3 4-3 +5.0 +2 45 +1 +3 44 +3.0 4-3 +0 +3.0 +2.0 4-1 45 (cont'd) 1958 SI R. A. h m s Declination 0 1 ft 11 30 -40 12 09 12 11 31 08 43 11 00 24 08 13 11 10 10 06 00 09 25 07 46 10 08 10 08 10 12 07 39 06 07 23 09 03 12 15 12 19 10 43 08 33 24 09 02 30 08 49 30 12 11 45 •21 -32 21 -12 -2518 -03 -21 08 -12 00 -09 00 403 30 -11 50 -12 -11 20 403 40 +09 30 +06 -00 30 -18 06 +12 48 +03 24 (OS 35 +08 03 +43 54 01:09:24 01:22:24 03:01:15 03:01:42 03:05:33 03:05:41 03:06:14 03:07:13 03:08:39 03:09:04 03:09:49 03:11:01.2 03:11:39 03:14:32 03:42:30 04:53:44.0 04:53:50 09 25 30 +25 40 01 :S7:50 02:00:30 02:01:41.3 02:01:44.8 02:02:10.0 02:12:25 03:45:03 03:45:15 03:45:41.4 03:46:05 03:46:59 03:47:47 03:48:41 03:53:44.8 10:46:08 10:49:24 10:49:38 10:50:02 10:50:35 10:50:39 07 16 10 10 34 Obs.f 00447 00250 00077 00374 00279 00373 00278 0OOS1 00361. 00085 0024!' 00372 00080 00071) 000S4 00091 00371 00277 00200 00202 00201 00083 00199 00243 00074 Station Hon jo China Lake Tucson Las Cnices B Walnut Creek Las Cnices B Walnut Crock Las Cnices B San Jose WaJnut Creek China Lake Las Cnices B San Jose Los Altos Oakland Albuquerque Las Cnices B Walnut Creek Bartlcsvillc B San Antonio San Antonio St. Louis Manhattan Manhattan Albuquerque Sta. No. TSJTT 0098 0003 8530 0011 8530 0011 8530 0134 0011 0098 8530 0134 0005 0006 0041 8530 0011 8529 0096 0096 0080 0027 0027 0041 Date May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 May 18 Time (VT) h m s 10:56:03 04:18:14.2 04:17:31 04:16:35 04:16:00 04:15:27 04:14:45 04:14:16 04:14:04 04:13:48 04:13:40.4 04:13:25 04:13:22 04:13:19 04:13:14 04:12:35 04:12:25 04:11:47.5 03:28:55 02:30:31.5 02:28:39.4 02:26:50 02:25:44 02:25:34 02:25:22 00364 00073 00381 00382 00075 00375 00076 00095 00376 00377 00378 00203 00379 00380 00369 00086 0007S Manhattan W.Palm Bch. Las Cnices B Las Cnices B Albuquerque Las Cnices B Tucson Tucson Las Cnices B Las Cnices B Las Cnices B Denver Las Cnices B Las Cnices B Albuquerque Walnut Creek Los Altos 0027 0016 8530 8530 0041 8530 0003 0003 8530 8530 8530 0013 8530 8530 0041 0011 0005 May May May May May May May May May May May May May May May May May 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 0012:. 00127 0012b 003(.5 00124 00383 00726 00128 0U3«.K 0012;' 00370 00130 00222 0031.7 001: 1 0019-1 00192 00l'.'3 00190 00223 St. Louis San Antonio Edinhurg Edinburrj San Antonio Manhattan Albuquerque B Los Anqelos China Lake Los Anneles Las Cnices B Los Anueles Las Cnices B China Lake Mi/ukaido Mic Yokkaichi Mizukaido Manazuni Suwa 0080 0089 0066 0066 0096 0027 8534 0100 0098 0100 8530 0100 8530 0098 0231 0266 0258 0231 0228 0248 May May May May May May May May May May May May May May May May May May May May 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 09 11 07 07 30 53 48 SO 34 Altitude Mag. • i it 27 42 71 208 00 IS 30 -12 -16 30 -25 11 12 08 08 08 -36 -47 +06 06 -15 00 -14 270 00 53 270 00 221 00 59 36 61 18 192 30 13 00 225 225 -04 48 +03 50 +05 42 +04 +03 06 +00 00 +05 -04 -16 06 33 +14 09 13 -13 09 24 09 37 -20 -24 3 8 3 8 7 +1 to9 +1 +4 or 5 +4 or 5 +-1 +1 to 9 -1 -1 +1 to 9 +1 to 9 +1 to 9 +2 +1 to 9 +1.0 +4 +3 to 6 +14 24 +28 30 17 11 38 07 32 07 08 30 08 40 07 56 09 20 07 34 09 35 08 36 +1 +■2 to +-2 to +-2 to +2 to +•2 +-1 to +-2 +2 to 3 +1 to 7 +2 to 6 +1 +1 -t-2 to 3 +-2 to 8 +4 or 5 +-1 to 6 +-1 to 6 +3 +1 to 8 +1 to 8 +1 +53 +43 f!9 29 +28 10 07 10 22 10 49 36 25 42 30 41 42 Azimuth • l n 257 00 82 30 81 +3 +0 +0 +1 to 6 +5 +3 +1 +1 to 7 +1 180 00 05 00 225 00 28 00 225 00 21 00 -i-l +1 +1 to 7 +2 +1 42 44 42 43 (cont'd) - 15 1958 81 Sta. No. 0215 8528 0600 Date May 20 May 20 May 20 Time (UT) h m I 10:52:49 18:45 : 23 20:32: 18.5 R. A. h m 1 10 20 02 54 03: 19: 19: 19: 19: 03 08 00 Declination • in -47 -30 30 Azimuth • i ii Altitude Mag. • IK Obs.f 00189 00221 00220 Station Ichinomiya Adelaide C Adelaide 00239 00267 00263 00264 00266 Johannesb. A 0403 Adelaide 0600 Adelaide 0600 Adelaide 0600 Adelaide 0600 May May May May May 00269 Curacao 0901 May 22 19: 19: 24 00466 00283 00292 00293 00485 00486 00487 00495 00488 0048: 00490 Pretoria B Johannesburg Kashiwabara Kashiwabara Johannesb. A Johannesb. A Johannesb. A Pretoria B Johannesb. A Johannesb. A Johannesb. A 0405 0403 0222 0222 0403 0403 0403 0405 0403 0403 0403 May May May May May May May May May May May 23 23 23 23 23 23 23 23 23 23 23 03: 03: 10: 10: 18: 18: 18: 18: 18: 18: 18: 05: 05: 58: 59: 11: 12: 13: 14: 14: 14s 15: 42 46 33 33 14.8 35 51 09 28 42.6 03 03 03 08 09 10 11 11 11 11 11 11 18 10 30 42 52 30 12 35 35 44 47 52 -43 12 -42 00 -28 00 -42 00 +34 24 +26 +15 +11 24 +08 36 +07 12 +03 30 +1.5 00491 00492 00493 00494 00496 00457 00458 00552 00719 00385 Johannesb. Johannesb. Johannesb. Johannesb. Pretoria B Johannesb. Johannesb. Konko SydneyPerth 0403 0403 0403 0403 0405 A 0403 B 0403 0224 0602 0601 May May May May May May May May May May 24 2ft 24 24 24 24 24 24 24 24 03: 03: 03: 03: 03: 17: 17: 18: 19: 21: 42: 42t 43: 43: 47: 04: 04: 30: 31: 17: 32.5 33 47 48 01 11 41 36 47.5 43 02 02 02 02 02 13 13 19 22 38 38 13 13 10 36 35 25 45 -68 -68 -51 -51 -02 +18 +16 +02 -53 +1 +1 +1 +1 +1.5 00459 00460 00461 00462 00463 Johannesb. A Johannesb. A Johannesb. A Johannesburg Johannesburg 0403 0403 0403 0403 0403 May May May May May 25 25 25 25 25 17: 17: 17: 17: 17: 40: 41: 43: 45: 46: 36.7 26 33 24 30 11 11 12 13 13 00581 00464 00465 00386 00412 00402 00403 00404 00413 00405 00406 00414 00415 00407 00724 00725 00720 00721 00387 00388 0038& Capetown Johannesburg Johannesburg Perth Pretoria B Johannesburg Johannesburg Johannesburg Pretoria B Johannesburg Johannesburg Pretoria B Pretoria B Johannesburg Sydney Sydney Sydney Sydney Perth Perth Perth 0402 0403 0403 0601 0405 0403 0403 0403 0405 0403 0403 0405 0405 0403 0602 0602 0602 0602 0601 0601 0601 May May May May May May May May May May May May May May May May May May May May May 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 03: 03: 03: Hi 16: 16: 16: 18: 18: 18: 18: 18: 18: 18: 18: 18: 18: 18: 20: 20: 20: 06: 45.4 09: 47.0 11: 47.0 18i 54.3 31: 42.4 31: 49.6 34: 49 17: 42 18: 46 22: 21 22: 57 23: 17 23: 35 23: 40 54c 38.7 57: 09 59: 21.5 59: 32 39: 09 41: 33.8 41: 51.8 A A A A 21 21 21 21 21 38: 24: 24: 24: 24: 23 26 34 36 39.5 +2 133 +3 to 8 18 18 30 18 17 +4 45 +5 +5 +5 27 +1 to 5 -24 00 154 154 156 156 30 30 30 30 270 22 30 46 26 17 00 55 00 36 +15 +06 •16 -36 -46 +2 +2 +2 +2 +2 +1 to 8 +2 +2 +2 30 30 48 48 42 12 106 48 29 38 68 28 49 18 +8 +2 to 7 +3 18 48 24 24 12 02 16 02 10 02 00 -51 42 -51 48 -30 14 13 30 14 00 14 55 09 33 09 42 10.15 10 31 10 29 10 39 10 49 19 15 21 42 01 07 30 01 25 30 -05 48 +01 48 -21 18 -03 12 -14 12 -56 30 -67 42 -61 18 -64 30 -63 54 -40 30 +09 36 -10 42 -09 12 +3 +2 +2 to 7 +2 to 7 +2 to 7 +1.2to7 +2 to 7 +2 to 7 +2 to 7 +1 to 4 150 34 131 28 126 13 28 10 29 07 29 19 +1 to 4 +1 to 4 +3 +3 +3 - 16 - (cont'd) 1958 S 1 Obi. # 00408 00409 00410 00411 00390 00573 00578 00574 00579 00575 00580 00576 00577 00722 00723 00391 00392 00393 00394 00395 Station Johannesburg Johannesburg Johannesburg Johannesburg Perth Johannesb. C Pretoria B johannesb. C Pretoria B Johannesburg Pretoria B Johannesburg Johannesburg Sydney Sydney Perth Perth Perth Perth Perth Sta. No. 0403 0403 0403 0403 0601 8518 0405 8518 0405 0403 0405 0403 0403 0602 0602 0601 0601 0601 0601 0601 Date May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 May 27 Time (UT) h as s 03: 47: 08 03: 47: 19.2 03: 49: 57.4 03: 49: 58 11: 58: 25.9 17: 05: 13 17: 08: 05 17: 08: 10 17: 10k 00 17: 10: 52.8 17: Hi 02 17: 12: 01.6 17: 12: 02 19: 33: 33 19: 35: 28 21: 15: 23.0 21: 1& 22.8 21: 19: 14.9 21: 19: 55. 1 21: 21: 07.6 R. A. ■ i it 22 28 22 37 54 00 OS 36 00 05 48 Declination • i n -33 -27 18 +28 49 +28 49 11 28 12 27 12 32 13 20 13 50 13 35 14 34 14 33 20 17 21 42 +14 42 •16 18 -15 48 -36 00 -41 48 -44 36 -49 12 -49 30 -13 54 +08 15 005S3 00467 00468 Higashlmats. Johannesburg Johannesburg 0210 0403 0403 May 28 May 28 May 28 17: 32: 25 17: 41: 47 17: 44: 34.0 18 51 09 33 00473 00469 00470 00471 00474 00472 00475 00476 00477 00478 00479 Pretoria B Johannesburg Johannesburg Johannesburg Pretoria B Johannesburg Pretoria B Johannesburg Johannesburg Johannesburg Johannesburg 0405 0403 0403 0403 0405 0403 0405 0403 0403 0403 0403 May May May May May May May May May May May 29 29 29 29 29 29 29 29 29 29 29 03: 03: 03: 03: 03: 03: 03: 16: 16: 16: 18: 22 13 22 43 06 23 11 23 11 23 15 23 43 23 55 12 12 43 14 04 14 42 08 26 -60 18 -49 14 -33 48 -32 -32 42 -04 30 ♦06 30 -15 12 -40 48 -47 24 -35 00 00511 00480 00481 00482 00483 00484 00531 00532 00507 00510 00508 00509 Johannesburg Johannesburg Johannesburg Johannesburg Johannesburg Johannesburg Adelaide C Adelaide C Johannesburg Johannesb. C Johannesburg Johannesburg 0403 0403 0403 0403 0403 0403 8528 8528 0403 8518 0403 0403 May May May May May May May May May May May May 3t* 02: 30: 54 30 03: 43: 55. 2 30 03: 44c 13 30 03: 44s 27 30 03: 45: 02.3 30 03: 45t 40.4 30 10: 09: 12 30 11: 52: 05 30 17: 04: 57.0 30 17: 06c 50 30 17: 09: 10.4 30 17. 09: 10.6 18 18 18 19 19 11 08 -14 -09 -05 +05 +18 -54 -13 00533 00534 00535 Adelaide C Adelaide C Adelaide C 8528 8528 8528 May 31 May 31 May 31 8528 0403 0403 0405 0403 8518 0403 0405 June June June June June June June June 00536 Adelaide C 00512 Johannesburg 00513 Johannesburg 00517 Pretoria B 00514 Johannesburg 00516 Johannesb. C 00515 Johannesburg 00518 Pretoria B * Correction 01 01 01 01 01 01 01 01 09: 09: 10: 10: 10: 11: 11: 30: 33: 34) 18: 00. 3 25. 6 03 06 13 10 47.5 49 41.0 48.5 52 Azimuth • • n 154 02 +1.5to7 190 02 180 05 70 02 62 08 047 04 37 28 48 05 53 10 49 07 27 12 +20 ■08 30 +1 to 4 +1 to 4 +2 to 8 +3 +3 +3 +3 +8 232 48 63 00 +7 to 1 +7 to 1 +7 to 1 109 30 54 43 55 12 23 30 48 23 11 Altitude Mag. • 1 M +2 to 7 +2 to 7 +2 to 7 +1 to 6.5 55 ; -. +3 51 36 53 24 42 30 48 18 30 +1 to 5 +4.0 +4.0 258 72 30 10 53 12 14 12 15 -SO 00 -69 30 -69 24 08: 54: 47 10: 40: 15 20: 03: 10 13 30 08 40 18 53 -28 30 -27 +17 30 +4.0 +4.0 +4.0 09: 16: 16: 16: 16: 16: 16: 16: 10 56 10 06 30 -33 30 -12 18 +4.0 10 11 12 12 16 -42 -50 12 -58 18 -59 30 -71 26c 22c 24c 25: 26: 27: 27: 31: 57 57.1 15 20.8 19.0 16 30.2 11.2 294 30 58 37 14 22 28 84 30 (cont'd) - 17 1958 8 1 Declination • I n +10 42 Obs.# 00582 00583 00401 Sta. Station No. Capetown A 0402 Capetown A 0402 Bloemfontein 0401 Date June 02 June 02 June 02 Time(UT) h m f 16: 54: 18.2 16: 58: 18 17: 00: 11 R. A. h m t 09 44 00547 00548 00549 Johannesburg Johannesburg Johannesburg 0403 0403 0403 June 03 June 03 June 03 17: 29: 00 17: 30: 16 17: 32: 13.2 07 10 24 07 08 06 49 -29 30 -39 48 -53 36 00569 00561 00562 00563 00570 00450 Pretoria B Johannesburg Johannesburg Johannesburg Pretoria B Santiago 0405 0403 0403 0403 0405 0805 June June June June June June 04 04 04 04 04 04 16: 16: 16: 16: 16: 23: 13: 13: IS: 15: 16: 26: 51.3 56.2 07.0 30 35.7 06. 5 08 08 08 09 09 20 -43 -42 -54 -58 -69 -66 00564 00565 00566 00571 00567 00568 00572 00497 00498 Johannesburg Johannesburg Johannesburg Pretoria B Johannesburg Johannesburg Pretoria B Bloemfontein Bloemfontein 0403 0403 0403 0405 0403 0403 0405 0401 0401 June June June June June June June June June 05 05 05 05 05 05 05 05 05 16: 16: 1& 1& 16: 16: 16: 16: 16: 44: 45: 45: 46t 46: 47: 49: 49: 53: 07.8 20 38.6 27.4 27.6 58 01 21 12 07 03 07 02 07 00 06 53 06 57 06 40 06 12 06 56 22 34 -30 -40 -43 -50 -49 -61 -69 -71 -80 00537 00738 Adelaide C Johannesburg 8528 0403 June 06 June 06 10: 15: 26 17: 19: 20.5 06 58 30 05 40 30 -16 -56 12 00735 00736 Johannesburg Johannesburg 0403 0403 June 07 June 07 15: 5& 14.2 15: 59: 15.0 07 07 12 07 08 30 -39 36 -49 00 00538 00739 00737 Adelaide C Pretoria B Pretoria B 8528 0405 0405 June 08 June 08 June 08 09: 27: 47 16: 26: 58.2 16: 26: 58.4 06 44 06 12 06 12 -14 18 -29 36 -29 36 00802 AlbuquerqueB 8534 June 09 10: 49: 37 00519 00530 00543 Bristol Alamagordo Tucson 0097 0102 0003 June 10 June 10 June 10 09: 34. 30 11: 17: 18 111 17: 35 00551 00550 00554 New Orleans Biloxi Whittier 0030 0090 0012 June 11 June 11 June 11 09: 59: 05 09: 59: 12 11: 43: 51 00584 00585 00710 00586 00555 00559 00711 00803 00713 00832 Edinburg 0066 Lawton 0110 Edinburg 0066 Wichita 0028 Dallas 0129 Oklahoma Cty.0135 Edinburg 0066 AlbuquerqueB 8534 Lawton 0110 Konko 0224 June June June June June June June June June June 12 12 12 12 12 12 12 12 12 12 10: 10: 10: 10: 10: 10: 10: 10: 10: 19: 26: 26: 26: 26: 27: 27: 27: 27: 2& 13: 07. 2 25 26i7 53.9 14.6 18 20.4 32 54 00 00646 00712 00604 00799 00804 00622 Sylacauga B Harrisonburg Ft. Belvoir New York AlbuquerqueB Sacramento E June June June June June June 13 13 13 13 13 13 09: 09: 09: 09: 10: 11: 08: 09: 10: 10: 53: 12: 15 38 00 15 35 47.9 8506 0072 0077 0046 8534 8517 37 41 30 55 04 23 39 30 23 56 23 54 Azimuth e i m Altutude Mag. e i ii 000 179 36 85 40 +3 30 36 36 +3 +4 34 54 00 24 30 42 36 00 25 27 +5 +4.0 +4.0 +4 103 04 42 +2 138 18 115 00 19 00 +0 -1 -2 090 2170 79 82 +lto 4 -2 to 3 -1 350 179 42 OS 20 30 40 12 11 15 -1 -1 +03 00 -28 21 18 50.9 -24 42 00 48 12 +83 28 06 02 42 21 10 01 17 49 090 00 009 30 62 00 07 15 035 42 00 000 +1.0 10 12 00 -1 40 -4 090 090 000 270 30 32 70 66 33 30 +13 54 +48 00 -03 32 24 -1 +0.5 -1 -2 to 6 +0 -1 or-2 -0.5 +2 (cont'd) - 18 1958 S 1 Obs.# 00644 00629 00642 00627 00645 00628 00643 00716 00717 00718 00813 00833 00650 Station Memphis Indianapolis St. PaulB Terre Haute Chicago Lansing Whittier Whittier Whittier Whittier Walnut Creek Suwa Suwa Sta. No. 0123 0024 0199 0025 0085 0034 0012 0012 0012 0012 0011 0248 0248 Date June : 14 June 114 June ]14 June ! 14 June ; 14 June 114 June 114 June 114 June 1L4 June 14 June 14 June 114 June ]14 Time (UT) h m s 09: 34: 26.5 09! 34: 53.3 Oft 35: 08.5 09i 35: 35 09: 36: 13 09: 36: 56.5 111 19: 10 Hi 19: 16 Hi 19: 17 Hi 19: 40 Hi 19: 47 lft 18: 00 18i 18: 36 00636 00809 00714 00639 00810 00715 00637 00805 00640 00641 00811 00812 00632 00638 00651 00835 00649 00648 00647 Bryn Athyn New York State College Dover New York State College Lawton AlbuquerqueB Oklahoma Cty. Amarillo Walnut Creek Walnut Creek Stockton Walnut Creek SacramentoX Oita Himeji Matsue Toyama 0055 0046 0060 0039 0046 0060 0110 8534 0135 0064 0011 0011 0010 0011 8517 0239 0262 0280 0254 June June June June June June June June June June June June June June June June June June June 115 15 15 ]15 115 ]15 115 15 15 115 15 115 115 IS 15 15 115 1L5 115 Oft Oft Oft Oft Oft Oft 10i lOi 10i lOi Hi Hi lit Hi Hi 1& 1& 1& 1ft 16 16 16: 16: 16: 16: 00: 00: 01: 02: 44: 45: 45: 45: 45: 43: 43: 44: 44: 20 32 33 35 39 40 28 32 09 12.9 42.6 10.5 14 18 26.8 44 48 03 39 00633 00727 00789 00800 00634 00683 00684 00685 00788 00783 00635 00686 00687 00688 00801 00784 00689 00690 00785 00786 00691 00787 00662 00663 Danville Milwaukee A State ColJbege Danville Colombus Cambridge Cambridge Cambridge State College Milwaukee Rochester Cambridge Cambridge Cambridge Red Bank Milwaukee Cambridge Cambridge Milwaukee Milwaukee Cambridge Walnut CreekB Asahikawa Otaru 0021 0074 0060 0021 0051 0099 0099 0099 0060 0074 0047 0099 0099 0099 0040 0074 0099 0099 0074 0074 0099 8535 0201 0243 June June June June June June June June June June June June June June June June June June June June June June June June 16 16 1L6 ; 16 ]16 16 16 16 116 1 16 16 116 16 16 1L6 116 116 116 16 . 16 : 16 ]16 116 116 Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft Oft 10) 17: 17: 41: 41: 41: 41: 41: 41: 41: 42: 42: 42: 42: 42: 42: 42: 42: 43: 43: 43: 43: 43: 44: 25: 24t 24: 10.5 21 30 31.6 33 45.6 53.2 01.6 03 10.2 11 11.8 17.6 27 42 06.5 11 13.0 23.3 47.3 01 23 43 52 R. A. h m s Declination • i n 22 57 -32 23 53 ■123 15 00 01 01 03 11 20 01 +57 36 +60 18 -160 48 +61 00 +20 27 +33 +68 270 Altitude Mag . • • ■ 76 50 -3 65 30 4-1 +1 86 00 -1 -2 to 5 82 -2 -2 -2 -1 -1 -1 -1.0 090 092 087 090 088 085 359 00 29 32 14 28 30 30 14 29 48 270 31 30 311 36 17 36 088 30 108 273 077 18 12 48 51 IS 263 12 269 00 273 18 000 17 30 18 18 19 00 43 284 00 288 18 298 06 358 21 30 22 00 22 30 18 340 18 343 36 18 00 18 00 357 48 1200 Azimuth e i n 270 270 180 20 07 21 25 50 00 44 SO 03 02 17 52 05 12 17 31 00 17 02 30 +31 00 +70-50 +46 42 +12 06 +23 48 16 38 00 17 20 50 12 20 +31 18 +37 09 +72 12 31 13 40 +70 00 +55 00 01 12 30 02 11 21 05 03 20 ±32 15 00 +11-20 +48 -1 +1 -1 +0 to 4 -1 +1.0 -1 -1 +1 +1 -2 +0 -3 +1 +0 40 +1 -2 -1 -2 to 5 -1 to 6 -1 to 3 -1 -3 +1 +20 22 03 33 03 53 +24 00 +26 00 01 50 00 30 +07 00 -02 00 090 00 21 30 44 40 4-1 (cont'd) - 19 1958 frl Declination • i ii Azimuth • i ii 120 00 115 54 111 06 111 48 106 54 102 42 104 18 100 12 089 54 085 42 090 082 36 077 36 074 18 068 42 064 36 297 30 301 30 003 Altitude • i n 15 00 15 12 16 36 15 30 16 36 16 36 13 12 12 30 13 06 13 06 13 11 42 11 12 10 42 09 00 08 18 46 38 29 000 00 270 283 270 87 30 40 00 56 37 30 221 24 092 06 078 30 073 24 031 48 031 00 030 30 031 42 032 18 64 30 81 54 86 18 79 12 05 42 05 00 04 00 03 02 18 235 26 30 013 30 08 06 Mag. Obs.f 006" 2 00093 006! 5 00694 00696 00697 00698 0069!> 00700 00701 O06S0 OO702 00703 00704 00705 0070(. 00806 O080S 00807 0072:00730 00681 0068 2 OOhiA Station Cambridge C ambridge C ambridge C ambridge C ambridge C ojnbridiie C ombridye C am bridge C ani bridge Cambridge Bryn Athyn Cambridge Cambridge Cambridge Cambridge Cambridge Danville Indianapolii Danville Sapporo Otare Torre Haute Danville Lansing Sta. No. 0099 0099 0099 0099 0099 0099 0099 0099 0099 0099 0055 0099 0099 0099 0099 0099 0021 0024 0021 0245 0243 0025 0021 0034 Date June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 Time (UT) h m i 07: 20: 46.2 07: 20: 52. 2 07: 20: 57.0 07: 20: 59.0 07: 21: 03.6 07: 21: 10.5 07: 21: 11. S 07: 21: 18.5 07: 21: 33.5 07: 21: 38 07: 21: 43 07: 21: 51.6 07: 21: 58.4 07: 22: 08.6 07: 22: 24.8 07: 22: 40.4 09: 05: 46.0 09: 05: 52. 3 09: 06: 31.7 17: 49: 14 17: 49: 16 09: 05: 26 09: 05: 40.5 09: 06: 29.8 00836 O0S37 OOS38 0083!' 00840 00S41 00842 00843 00S44 00728 00731 00733 00853 00732 00S59 00734 00741 Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Wichita St. Paul B St. Paul B Wichita Lemont Walnut CreekB Portland Mitaka 0099 0099 0099 0099 0099 0099 0099 0099 0099 0028 0199 0199 0028 0022 8535 0076 0229 June June June June June June June June June June June June JuneJune June June June 07: 07: 07: 07: 07: 07: 07: 07: 07: 09: 09: 09: 09: 09: 11: Hi 18: OOS54 O07ol' Milwaukee B Milwaukee 0198 0074 June 20 June 20 08: 32: 51 . 08: 34:06.6 04 00 05 37 +79 +48 00 007" 3 00S55 OU7!'S 00.S5I. 00S57 0085S Milwaukee Milwaukee St. Paul B St. Paul B St. Paul B St. Paul B 0074 0074 0199 0199 0199 0199 June June June June June June 08: 08: 08: 08: 08: 08: 14 26 +29 30 007!>1 007! >4 00792 North Canton 0053 Rochester 0047 Portland 0076 June 22 June 22 June 22 07: 33: 58 07: 34: 00 11: 02: 58 007515 007!'0 O07!'7 Cambridge Cambridge Cambridge 0099 0099 0099 June 23 June 23 June 23 06: 10: 09 06: 10: 17 06: 10: 19.6 00845 Sapporo 0245 June 24 16: 57: 16 11 30 +51 00 +2 00S61 Milwaukee B 0198 June 27 07: 31: 37 09 22 +57 30 -10 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 21 21 21 21 21 21 45: 45: 45: 45: 48: 4& 48: 48: 48: 29: 30: 30: 31: 31: 14: IS: 13: 55: 55: 55: 56: 56: 57: 16.2 31.6 33.6 35.8 12 28 36 48.4 53.0 51.8 12 55 07.1 14 18 01 27.5 02 17 25.4 08.5 18 12.4 R. A. h m l 18 58 10 41 17 40 13 30 13 25 20 48 44 +40 00 +72 54 40 -2. 5to6 -1 to 5 -2.5to6 +0 +0 ■2 -2.5to6 -1 to 4 -2 or-3 -1 +52 -3 +47 +60 06 +06 332 42 05 36 +0 40 +2.5 +1.0 -1 -1 305 24 325 006 15 009 022 15 05 22 06 08 11 00 00 +0 to 4 14 39 30 22 30 20 09 45 +46 55 +54 +58 -»0 +0 -1 -1 -1 -1 -1-1 -1 -10 055 00 053 12 049 42 05 00 03 36 03 36 45 - 20 1958 , 2 Date May 16 May 16 May 16 Time (UT) h m s 02: S3: 27 02) 55: 19.0 11: 46: 06 R. A. h m s 10 48 30 Declination h m s +18 Azimuth e 1 ii Altitude a t ii 225 85 15 178 30 178 00 80 00 76 00 Mag. Obs.# 00013 00014 00020 Station St. Paul B Edinburg Miyazaki Sta. No. 0199 0066 0230 00015 00016 China Lake China Lake 0098 0098 May 17 May 17 03: 35: 08 03: 35: 14.3 00017 China Lake 0098 May 18 04i 21: 51.2 09 29 -10 18 +4 or 5 00018 Adelaide C 8528 May 21 19: 47: 19 02 50 -40 +6 00041 0001^ oocs: Johannesburg Johannesburg Pretroa B 0403 0403 C40S May 23 May 23 May 23 03: 3€: 20 03: 36: 23 03: 36: 52 02 55 02 54 02 49 -42 -41 30 -36 12 +5 +5 +7 00028 Johannesburg 0403 May 25 18: 31: 35 10 00 00 -22 18 +7 00092 Sydney 0602 May 26 19: 39: 47.0 20 25 -27 18 +4 00055 00091 00090 Capetown Sydney Sydney 0402 0602 0602 May 27 May 27 May 27 18: OS: 25 1& 44: 32.5 18: 44: 35.5 23 44 23 58 -30 30 -29 00054 Johannesburg 0403 May 28 03: 37: 01 00038 00039 00040 Pretoria B Pretoria B Pretoria B 0405 0405 0405 May 29 May 29 May 29 02: 27: 40 02i 28: 17.3 02: 30) 27.2 02 18 01 55 01 28 -69 00 -61 54 -30 18 +4 to 8 +4 to 8 +4 to 8 00048 Adelaide C 8528 June 01 09: 12. 55 11 35 -28 +6.0 00036 oloemfontein 0401 June 02 17: 02: 53 000<*f 00097 Adelaide C Johannesburg 85 2S 0403 J-me 06 June 06 09: 05: 58.5 1C: 03: 38.8 08 15 07 42 30 -64 -38 24 00045 00047 00046 Tucson Kashiwabara Kashiwabara 0003 0222 0222 June 09 June OS June 09 11: 25 18: 56: 11 18: 56: 18 00 37 00 53 -23 00 -22 00 00070 San Antonio 0089 June 12 10: 18: 50 00110 00123 00076 00124 00125 00111 00075 00073 Sacramento E Walnut Creek Sacramento E Walnut Creek Walnut Creek Sacramento E Walnut Creek Oakland 8517 0011 8517 0011 0011 8517 0011 0006 June June June June June June June June 11: 11: 11: 11: 11: 11: 11: 13: 00072 00122 00074 Arlington 0071 Albuquerque B 8534 Oakland 0006 00093 00113 00088 00114 00107 Milwaukee WalnutCreek B Sacramento E WalnutCreek B Sacramento E 0074 8535 8517 8535 8517 11 20 000 24 179 36 +6.0 +5 104 20 30 +2 +3 +3 090 64 +1 +45 18 +62 30 +52 00 +1 +3.5 -1 00 01 01 03 +15 +26 +27 +35 June June June June June 09: 11: 11: 11: 11: 54.8 05 10.3 20 46.7 36 24 20 04 21 17 17 05 08s 45: 24.0 10: 30: 10 13: 45: 47 24: 09: 09: 09: 09: 62 +1 +1 +1 +1 +1 June 15 June 15 June 15 16 16 16 16 16 53 30 -17 02 -08 45 -08 01 -07 36 +20 29 +25 32 +39 30 +25 22 23 22 14 23 02 23 02 01 04 01 37 03 54 02 05 37: 37: 37: 37: 38t 38: 39: 29: +5 +4 +4 036 24.9 28.6 36.0 44.3 01.3 18.7 05.2 59 14 14 14 14 14 14 14 14 -18 00 +6 +0 +1 47 18 53 18 30 59 30 +1 +1 to 6 043 18 30 41 12 15 16 05 00 53 00 59 50 30 +2 +1 +2 +9 (CPnt'd) . 21 1958 f 2 Obs.# 00080 00081 00082 00083 00084 00085 00086 00087 Station Bryn Athyn Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge Sta. No. 0055 0099 0099 0099 0099 0099 0099 0099 Date June 17 June 17 June 17 June 17 June 17 June 17 June 17 June 17 Time (UT) h m s 08: 16: 29 08t 16. 51 Oft 16: 52.6 0ft 17: 04.4 0ft 17: 07.8 0ft 17: 21.0 0ft 17: 26.0 Oft 17: 52.0 00100 00101 00094 00129 00095 00096 00098 Cambridge Cambridge Chicago Chicago St. PaulB Lemont Mitaka 0099 0099 0085 0085 0199 0022 0229 June June June June June June June 07i 07i Oft Oft Oft Oft 17: 00121 Chattanooga 0062 June 19 09i 02: 50 00115 00119 00116 00120 00117 00118 Cambridge Cambridge Cambridge Cambridge Cambridge Cambridge 0099 0099 0099 0099 0099 0099 June June June June June June 06) 06: 06: 06 06: 06: 18 18 18 18 18 18 18 23 23 23 23 23 23 10i 10: 54s 54* 55) 55: 42i 46: 46: 46) 46: 47: 47: 23.6 38.4 32.0 34.9 04.6 13 26.0 R. A. h m s 19 10 19 20 01 03 58 42 15 38 32 Declination a i ii +68 Azimuth e i m Altitude 0 1 M 273 277 297 302 320 327 001 35 37 40 40 40 37 29 +1 30 18 18 36 48 42 18 30 18 30 30 30 30 30 064 42 061 12 05 30 05 00 357 30 13 30 124 90 024 42 024 00 024 54 025 1 2 025 42 026 06 16 14 14 11 10 08 +45 32 +49 20 -08 +61 36.0 42 43.2 57.2 08.4 18.4 Mag. 30 36 30 12 30 30 +3 to 6 +3 to 6 +5 +5 -1 +1 +6.0 +3 to 4 1958 h JL 00001 Edinburg 0066 May 16 02. 55: 56.3 225 85 15 00002 China Lake 0098 May 17 03: 35: 22.6 177 00 76 00019 Adelaide C 2528 June 01 09i 45* 38 00020 Tucson 0003 June 10 11: 03: 17 080 30 10 30 +4 00024 00025 New York New York 0046 0046 June 15 June 15 Oft 12: 57 08i 13: 00 090 085 30 39 34 30 +3 or 4 +3 to 4 00023 00021 Rochester Milwaukee 0047 0074 June 16 June 16 Oft 40: 49 09: 06: 45 09 56 21 05 00 00 +7 +5.5 -45 (-3 +3 +23x15 +48 1958 4 4 00001 Edinburg 0066 May 16 02: 55: 57.5 225 85 15 +7.5 00002 00003 China Lake China Lake 0098 0098 May 17 May 17 03: 36: 09.8 03: 36: 15.9 180 00 178 30 79 00 76 00 +5 +5 00004 New York 0046 June 15 03: 14: 51 090 38 +2. 5 or +3.5 - 22- 2. Preliminary Note on the Mass-Area Ratios of Satellites 1958 6l and &2 G. P. Schilling, C. A. Whitney and B. M. Polkart Smithsonian Astrophysical Observatory In order to insert reasonable values of the ballistic drag parameter into orbit prediction programs, a preliminary attempt has been made to determine the mass-area ratios of the components from the Satellite 1958 Delta launching. In addition, of course, a knowledge of these parameters permits an inference of upper atmosphere densities at the perigee altitudes concerned. Effective Mass-Area Ratios The mathematical approach used to estimate mass-area ratios was similar to the method applied earlier (1) to infer these parameters for the Soviet Satellites 1957 «1, 1957*2, and 1957 01. In the present calculation, the assumption was made that Satellite 1958 82 (Sputnik III) and its carrier rocket, Satellite 1958 Sli had negligible velocities relative to each other at the original orbit injection point and remained in the same orbital plane at equal perigee altitudes for the first 200 revolutions. Table I Orbital Data Smithsonian Astrophysical Observatory Date Perigee Distance Argument of Perigee Latitude of Perigee Rate of Change of Period Nodal Period Eccentricity Naval Research Laboratory Date Perigee Distance Argument of Perigee Rate of Change of Period Anomalistic Period Eccentricity Satellite 1958 Si June 26, 1958 4076 miles (adopted) 46.7° 4R3 N -.038 min/day (average over first 600 revolutions) 104. 21 min . 11 Satellite 1958 £ 2 J une 20, 1958 4076 miles 49.6" -.011 min/day (June 10-June 20) 105.52 . 112 -23 The orbital data of Table I give 3. 5 as the ratio of accelerations of 1958 &1 and 82. * In accord with the assumptions of the previous paragraph, we set this equal to the ratio of mass-area ratios of £1 and 6*2. Published So.iet data on {2 lead to the estimate (m/A) = 30 which gives (m/A) ■ 8 for £1. Unconfirmed speculations on Soviet Rocket performance (1) suggest (m/A) = 17, which leads to ( m/A) j 2 = 58. These values are collected in Table II . Table II Estimates of Effective Macs-Area Ratios Effective Mass-Area Ratio Satellite Minimum Maximum 1958 Si 8 g/cm2 17 g/cm2 1958 S2 28 g/cm2 2 58 g/cm* The above estimates must therefore be considered as being "reasonable" results of a mathematical exercise only. Although there is a high probability that the actual mass-area ratios of the Soviet satellite and its carrier rocket fall within the limits given, they may be in error by as much as, but not more than a factor of 2. Since the values of air d ensity at the perigee altitudes concerned are still uncertain by perhaps a factor between 5 and 10 ( 2), we have applied the given limits of mass-area ratios to infer useful, if approximate, air densities from U. S. observations of these most recent Soviet satellites. Conversely, the reasonableness of the resulting densities can be taken as a rough confirmation of the estimated mass-area ratios. Atmospheric Densities Sterne's simplified formula (3) was now used to calculate upper atmosphere densities, applying the estimated mass-area ratios and the orbital elements of Table I. The results apply to a geometric height of 118 miles (190 kilometers) above the ellipsoid at a latitude of about 40°N. Taking the "maximum" values of m/A, we find a density of 7.0 x 10"*3 gm/cc and with the "minimum" value we find a density of 3.6 x 10"^ gm/cc. Note that the density derived is independent of which object we consider since we have taken the mass-area ratios inversely proportional to the respective accelerations. Remarks These numerical results show that our rough density estimates fall definitely within an area of uncertainty (2) given by the Smithsonian Interim Atmosphere (4) and the ARDC Model Atmosphere (5). *We are indebted to Mr. E. K. L. Upton for providing us with the acceleration rate of Si resulting from his analysis of optical observations. - 24 - In conclusion we may summarize our results as follows: On the basis of rather specu lative assumptions and only indicative U.S.S.R. information, we have estimated - within reasonable limits - the effective mass-area ratios of Sputnik III and its carrier rocket. Inserting these estimates into density calculations based on radio and optical observations of these satellites, we have obtained density values which are satisfactory. Thus we con clude that our attempt may have resulted in "reasonable" numerical values of mass-area ratios. ■References (1) Schilling, G. F. and J. S. Rin chart: "Note on the Mass-Area Ratios of the U.S.S.R. Satellites." Special Report No. 1 2, pp. 20-23, Smithsonian Astrophysical Observatory, Cambridge, April 30, 1958.* (2) Schilling, C. F. and T. £. Sterne: "Densities of the Upper Atmosphere Derived from Satellite Observations. " Special Report No. 12, pp. 37-43, Smithsonian Astrophysical Observatory, Cambridge, April 30, 1958.* (3) Sterne, T. E. : "Formula for Inferring Atmospheric Density from the Motion of Artificial Earth Satellites. " Science, 127, 1245, May 23, 1958. (4) Steme, T. E. , B. M. Folkart, and C. F. Schilling: "An Interim Model Atmosphere Fitted to Preliminary Densities Inferred from U.S.S.R. Satellites." Smithson. Contrib. Astrophys. , 2, 275-279, 1958. (5) Minzner, R. A. and W. S. Ripley: "The ARDC Model Atmosphere, 1956." Air Force Surveys in Geophysics, No. 86, Geophysics Research Directorate, AFCRC, ARDC, December 1956. * Reprinted in IGY Satellite Report Series No. 4. - 25- 3. The Descent of Satellite 1957 Beta 1 L. O. Jacchia Smithsonian Astrophysics! Observatory Note The present report by Dr. L. G. Jacchia presents his analysis of ob servations of the final descent of the second Soviet earth satellite. It is based on bis on-the-spot interviews of observers who witnessed the descending flight path over the Caribbean Sea, and numerical integrations of a set of orbital trajectories. His calculations show that the burning object, with a luminous tall about 100 km long, descended to an altitude of about 40 km above sea level near latitude 9°N and longitude 57°W at 0155 U.T. on April 14. 1958. While Dr. jacchia points out that his computed 'impact or disintegration point" should not have more than academic value, he is led to the conclusion that no major frag ment succeeded in travelling much further beyond this point along an arc on the sub-satellite track. The results of a similar study by Drs. G. R. Mlczalka and E. W. Wahl of the Geophysics Research Directorate have just become available ("The Orbital Motion of the Earth Satellite 1957 P from 1 April 1958 to Its Decay 14 April 1958.' Project Space Track, GRD. APCRC-TN-58-445. ARDC. 5 June 1958), and it is interesting to compare the conclusions reached. Utilizing es sentially similar, though more limited observational data, and basing their de termination of the most probable sub-satellite path for the last revolution on the assumption of a circular orbit at a mean height of 161 km (at the equator), Drs. Miczaika and Wahl consider it quite likely that parts of significant size continued towards South America and may have touched the ground over Brazil. We must consider this as an example of the inherent ambiguity and inadequacy of the observational material available, illustrating the importance and need for obtaining as many reliable sightings as possible for studies of the future descent of other earth satellites. It also points out again the signiglcant contributions which can be and have been made by amateurs and lay men to such a complex scientific undertaking as represented by the earth satellite programs. Gerhard P. Schilling Special Assistant to the Director -26 THE DESCENT OF SATELLITE 1957 BETA ONE 1. Introduction The present paper is essentially an extension of Special Report No. 13(1) and covers the end part of the last revolution of Satellite 1957 Beta One. The observations which are at the basis of this report can be divided into three categories: 1. Observations from the Northeastern United States (Table I) 2. Observations from ships at sea ( Table II ) 3. Observations from the Caribbean Islands and from the northern coast of South America ( Table HI). While reliable observations, including altazimuth estimates of sightings, had been received at the Smithsonian Institution Astrophysical Observatory from ships at sea, only isolated and mostly descriptive observations were available from land areas. Therefore the author, at the suggestion of the Director, Dr. F. L. Whipple, undertook at the end of May 1958 a trip to the Caribbean area to collect additional information. In the course of this trip he visited Antigua, Martinique, Barbados, Trinidad, British Guiana, and Surinam. The information collected in this fashion is to be found in cluded in Table III. 2. Reduction of the Observations The observations of Table I, all made at nearly the same time from localities on both sides of the satellite path, provided the means for the computation of an excellent normal point in the trajectory. Its numerical values are given below. Longitude: 74! 00 West Latitude : 41°. 40 North Height: 101 km above sea. level Time : lh45m258 U. T. ( 14 April 1958 ) A set of orbital trajectories was computed by numerical integration starting from this normal point, with different initial radial -velocity conditions and different ( constant) drag parameters, using the ARDC model atmosphere ( 2) to compute the drag at these low altitudes. For simplicity, these integrations were performed using polar co-ordi nates in the orbital plane. One of these integrations, whose results are given in Table IV, and represented graphically in Figure 1, fitted the observations in the Caribbean area within their estimated errors and was chosen as representing the most probable trajectory of the satellite in its final plunge. The initial conditions and the drag parameter used in this integration are given below!' Orbital inclination = 65. 29° Total velocity » 7. 737 x 105 cm/ sec 27- Radial velocity ( dr/dt ) = -1 . 28 x 10 cm/sec CD A/m = K = 0.031 (e.g. ) In the last quantity, Cq is the drag coefficient, A is the presentation area of the satellite, and m its mass. The atmosphere was assumed to be rotating solidly with the earth and to have the same density at the same height above sea level, irrespective of latitude. The earth's oblateness and the precessional effects on the orbital plane were taken into account. In the other experimental trajectories radial velocities up to -2 x 10 3 cm/ sec and values of K between 0.02 and 1.0 were tried out. As should appear evident, the effect of such different conditions on the trajectory itself is to vary to a considerable extent the position of the end point, although the sub -satellite track is not greatly affected by the changes. The assumption of a constant drag parameter is of course, a little unrealistic, since the drag coefficient Crj must have been decreasing consider ably in the course of the trajectory with the formation of an air cap, while the areamass ratio A/m must have been increasing due to the continuous shedding of molten metal. Since, however, these two variations must have compensated to a certain extent, we do not feel too bad about the assumption, especially since the agreement between the resulting trajectory and the observations is quite good. 3. Phases of the Trajectory and End Point There is general agreement among practically all observers concerning the developments in the appearance of the object. When seen in the Northeastern United States, the satellite already had a faint tail in which spark-like particles could be seen through binoculars. Its visual magnitude, reduced to a standard distance of 100 km ( "absolute magnitude" ), was then about +1.0 and the tail could be followed through binoculars for 6 km behind the head, according to the Merrow, Connecticut, observa tion. After crossing over Long Island, the satellite went unreported for about 5 minutes. When it was sighted again by ships in the Caribbean, it was at latitude 23° North and had become a spectacular sight. Its tail was 60 km long as seen from Antigua, 80 km long at the latitude of Martinique, and nearly 100 km long as seen from Barbados and Trinidad. ( Of all the Caribbean Islands Barbados was the closest to the satellite's path, about 120 km from the sub-satellite track. ) When the object was at the latitude of Barbados ( 13°N), its head, according to the best estimates, had an "absolute magnitude" of about -7 or -8, and the total light emitted by head and tail must have been close to -9 or -10. The color of the head was generally described as white with tinges of blue or green, while the tail was described as white, or white -yellowish, near the head, and degrading to a deeper yellow and orange - even red - toward the far end. The "globules" described by all observers close enough to see them, were obviously drops of molten metal shed by the object; their observed splitting (A- H. C. Camp bell, Barbados ) confirms this explanation. Attention is called to the small, semiperiodic light fluctuations observed by Mr. Hart in Barbados, since they might have some bearing on similar phenomena observed in bright fireballs. Several observers observed a bright flash when the satellite reached 11° or 10s of north latitude and speak of a "shower of fragments" or "complete disintegration" of the object, but there is no unanimity on this point among the Trinidad witnesses. It seems, however, that when the satellite was disappearing from view in Trinidad, - 28much of the fiery tail had faded out in one fashion or another, and only an isolated object ( the "head, " or what remained of it) was still proceeding on its course. This object was seen in British Guiana, at closer range than from Trinidad, as a conspicuous, but not spectacular object, which faded out while still well above the horizon, in the NE. This rapid fading out in mid-air was reported by all observers who managed to follow the course of the object until that point -- i.e., the three observers in British Guiana, the vessels K. G. Lohse and Rio Atuel, and two observers in Trinidad, G. R. Robson and J. Saunders. The disappearance was seen from various directions and corresponds to a point at about 57° of longitude West and 9° North latitude, at a heigh: of some 40 km above sea level. It appears quite probable that fragments originated in the burst, including the object seen from British Guiana, fell unseen into the Atlantic Ocean along an arc of 100 km or so on the sub-satellite track, when their velocity became too low to sustain the light -producing mechanism. The "impact point" recorded in Table IV should not have much more than academic significance, although it is expected that no major fragment succeeded in travelling much more than 1° beyond that point. 4. Acknowledgements It is a pleasure to record the enthusiastic help received by the author from the U. S. Consular Authorities in the various places visited by him to collect information on the demise of Sputnik II. By giving advance publicity to his arrival and arranging for eyewitness interviews at the U. S. Information Libraries or in other suitable locales, they enormously facilitated his task. In particular the author wants to extend his thanks to Mr. Walter Orebaugh, American Consul General in Trinidad; Mr. Jesse M. MacKnight, American Consul in Surinam) Mr. A. John Cope, Jr. , American Consul in British Guiana; Mr. Knox Lamb, Consul, and Mr. Lindsay, Consular Aid, in Barbados; and Mr. Hopkins, American Consul in Martinique. Invaluable aid was given to the writer by the Barbados Astronomical Society and its President, Dr. Harry Bayley; it was shocking to receive the news of Dr. Bayley's death, which occurred on June 14, 1958, only a few days after the writer's visit to the island. A particular acknowledgement should also be extended to Pere Pinchon of the Seminaire -College in Fort de France, for his efforts to secure eyewitnesses in Martinique. The author wants to express his indebtedness to Miss Jeannie R. B. Carmichael for her help in computing many of the exacting hand integrations which led to the final trajectory . 5. References L Jacchia, L. G. : "Orbital Results for Satellite 1957 Beta One. " Special Report No. 13, Smithsonian Astrophysical Observatory, Cambridge, May 1958.* Z Minzner, R. A. and W. S. Ripley: "The ARDC Model Atmosphere, 1956." Air Force Surveys in Geophysics, No. 86, Geophysics Research Directorate, AFCRC, ARDC, December 1956. •Reprinted in IGY Satellite Report Series No. 4. -29- Figure 1 - End Path of Satellite 1957 Beta One in the Caribbean Area. Times of arrival and heights above sea level, in kilometers, are marked on the sub -satellite track. The black triangles represent localities from which quantitative positional observations were given; qualitative observations only came from the localities marked with open triangles. ( Chart reproduced through courtesy of Sky and Telescope. ) -30- 31- Table I. Observation* Over Northeastern U. S. Station U.T. h MB MB MB NH BA BA 1 1 1 1 1 1 a m s 45 OS 45 35 46 04 45 47 45 21 45 46 g Moonwatch Observers h m 5 5 + 45° 10 6 0 12 10 - 23 25' 17 15 +66 14 39 + 13 57 z h 180° 40° NW W S 25*: 45'! 15«: Isolated Observers M M M P P lh46m 1 46 OS: 1 46 25: - - 14h24m 14: +20° - 10°: Geographic Positions of the Stations Longitude(W) MB = NH = BA = M = P = Millbrook, N. Y. New Haven, Conn. Bryn Athyn, Pa. Merrow, Conn. (Mr. R. D. House) Pittsford, N. Y. (Mr. R. E. Jenkins) 73°37'22» 73 00 30 75 04 72 19.0 77 37 41 Latitude +41°S1'30" +41 12 35 +40 08 +41 49.4 +43 15 03 Station Elevation (meters) 243 Remarks Millbrook: Magnitude +1. Tail of tiny particles, about 1° long, seen more or less all the time. White. New Haven: Blue-white when first seen; magnitude +1. At lh45m42s got brighter ( mag. -1 ) and turned red. Bryn Athyn: Mag. +3 to -1 ; reddish. Tail 10' to 20' long. Merrow: Magnitude 1.5 at max. brightness; red. Faint, transparent tail 3° -5° long, visible only through binoculars. Pittsford: Magnitude +3. -32- b II 0^ 0 II 11 s s .a in & M & II -N o s E fa. (M CO •3 A m II N (Tl a 2 2 d Qo II .a a c B «1 11 us 0 IT) a ■d H N 1 Q <M8 T f*> H 3 B a 3. Si S 8 « 9 m in in -h <m + + >o ■* r> + co »-< N o w o * o fe w 3 8 b 11 a C B N 3 ■J b CM It N + w o 11 .a 8 N 3 ■ 8 P. S I f I s 11 N 8 a CM _ < 2 C E co u01 so a 3 PM .S o> 6 11 a ca) t-i a c g ■ c B co1 Si SI 11 fa 11 fa at 11 N I f a •O Q4) 9 § in in H N < M O o i s 1/1 tj' fa 11 s E J3 a 11 s E A CI C E to 01 aI a 0 CM m a S 2 vp rr 10 + o ?J in in + 8 00 m in in IO 8-# IO <t O CO m n 1 j« H a i/iv "3 I I + ro in in o t-~ ro N iH+ 00 IN + in Ol N + <o O CM + a CM in CI o 00 in S 8 o ?3 m + o ro in s CM 10 8 0> in 2 Q <B 1 5 1 * s 1 c c ina «-*B DOl 01 a01 01 2 1 in s in 10 CO in in in m o + rg CM O + «4 10 (71 in E a n I o > 3 3 2 3 -33 When d. 27°; h 90°, 133*, low. atz=mvery 20°, h 7°; 21°; d. 150°, ata.zmax■= d. 15° h 100°, (behind house ). at=z 29°; 6°; 67°, 128°, h d. ata.zz== oA15. BC. in A. 16. Babb; J. dT. WCH. 19. Stoute; b17. 18. Hassellj L. asrielbmtrcaipvdoebntrsael:.l; h<5°; 345°, 50°, 22°; h ata.z= 21° h 110°, d. 145°, atz=j 12°; 21«; h 10°, ata.maxz= h 15°; h= 10°, 18°; atz=a.max= d. clatouds. behind 119° 155°, d. •atzvery low. = ch behind 13°, lo=uds, h behind 6°, tr=e s, (h 10° obs=tacles), 40°, d. 110°. ata.i=z hmax= 30°: 25° -30°. hmax= 20°: hmax= Duration 5 2. min >1 min 2 min 4 min 2 min 20sec 35sec m lh53 lhS0r ^2 min OTable III. from bLand* servations lh4Sm lh30m +18° 21'lh4Sm 10' +17° U.T. L(W) oantigtiutduede 64° 57' 48 61 +14° 36' +13° 49' IS' +13° 04' +13* 04' +13° 06' +13° 04' 61° 60° SS' 59° 37' 35' 59° 59° 34' 27' 59° Thomai, St. Virgin Islands J Coste la de R. 7. W. 3. Novinsky P. Martinique. F.W.I. 2. H. field Me rri J. 1. Jouett H. B.W.I. Antigua. Abbe B9. J eaubrun "\ de R. 6. Reynal B.W.I. Lucia. St. 1 Theon Pere 8. 4. H. Laing 5. Y. Carty Moffat N. Mrs. 10. 14. CF. C. od ard BB.W.T. arbados. R. 11. Par is D. 13. Rufolo 12. A. Hart *a. d. dappeared; h aE); above N, (from hpositive ilto ozstria■=z=pmtzu»oedtnaeh.red; ^i:^3o}dati=io o'h=i°of appeared (2, tail the The b3). after shortly color; dead c(less body lmain region part euanm-tigrnaoelyuis)h changing white almost cend The tail. body color of aft sat became but the h"ytoemwasrearuorrnetyrv-iercnaeld, 2500 St. V.I. "Gave airplane of aThomas, ft. 5 (1 mabout dark cseemed ). Object with lat hilestaeanaway. pirt-euaydr-earnecd body, 28. 29. (5"); Scott W. Sookoo H. D. 30. (5°-7°); Aubyn St. (32. 31. Taylor oJlb5.Os°Je-ar1cvlek0Sns°":o)n;., Other 35. 46* 57° Scott 34' 6° H. North, in (h 30° d. NE, u+na.c=h-ecked), d. North; in h 60°:, behind 3°:, ata.z==» like 1/10 nB.W.I. first When NNE looked din than the that of Atail, wit object, with oinnot gtafarmihec-uogatesudtera,. dScolor pyfront, became eand lower the bin where saepart rtpseenwaslwereiaretgckioh-wctelaidlskehsyt (2). (2) paAs which 20° it tail rc30° approach of length object The (3). eat lprwasaoamoonorcsoeahiscevhtded, (2). of that than with bfirst but head the much citail, rogqat nimwasulcrmoonpaleiruantdaceibrln,eg appeared (2). composed (2, end tail the The pmainly of l3 flying could embers be in ) aikewasrseenticles (2). and lower but bThe object, the of stotal in irtpart, gniwasupper rtegahkntestdei.stry (2). "sparks" aquickly The bright would but bi'm seconds; 8-10 the quite in tail tto start, at out, wasseenweremoonnoached 55m P36. 14» 58° 29' A. 6° 1 e15°; h North, d. in ENE 10°. +rat sa.=a-ud 23. HT. 24. A. R. I26. 25. Mi27. N. W. (E. Orebaugh (15°); vSkeen nc1ikC0so°ln-e(1a65n8°)»;); 15° h= (unchec.ked). 30 h 70°, 8° 3° atseca.+z■= mountains. "a. 70°, ati■ a*a. dd. h E); N, (from hpilzto above soptaz=irsemptiazueotradnehi.dv;e Duration nRTable p(The refer the oin listed III). abuetorsmebarn-vethrkes es m lh55 U.T. TOwho in rough h bof resiegave max:tnrivmeadrtaesd, L(W) oantigtiutduede 19' +10° 39' +10° It Land^f Table cin. Ofrom b) osenrvta'iodn.s Tul och. M. 34. Lovell; G. R. 33. 2761° 61° 39' II 22. E. F. H. Beadon 2 i( sparks n) dividu.al 20. Robson R. G. TB.W.I. rinidad, E. 37. 58* Lewin+van 36' 6° 21. Saunders J. British Guiana msharply of The probably 7), (6, Jupiter than dglobe tail athe but little be could estglwasapinamicrthauetdieo,;n 20° dapproach and body c(6, At b(8, tail 7). of length the 9 30° 7) ri) color its lesotwascordwserenisentdh F.W.I. M1/3 Made greenish the of (8, white globe, (7) d9 its ) (7); ain iraortasamoonpimn-epitaqeruaenr,cnet due been have but cireal, At (6). optical body athan the brighter main Venus, lnot 10 topomay uwassomesreiosantch -6. did pof the good ehwho view not had orthe other that dsIt object is beinposmanesawwamcrevpiknearoelbsnra,ey. flareleast big behind there cloud; bank, cloud nbecame f(12) the iwhich Hart Mr. edges. atloonewasatuamsihncaetsd bright wide sof and sized medium long trail flight these large the in atprstaraaasanoreprgvamkea-renladtigsnke,g BVenus B.W.I. At approach cobject dwith head, and bthe least bright long oalratmizaoaswaselbstla-eidasniotkgsel,y which, tail mwhole, than brighter head, (12, seemed head sreltogiasawasvtlneihrtoaunldtgesh bathe less The 19). have St. 1/4 B.W.I. o"Lucia, blazing about ball, dthe of full wake (in size which rin Aiapnasaamoon, gme-eyatrlerodw) did like look apoint (12); little of d1/5 that all than less the it wsnot ieaaftmoonenmoirunesticetrdse , light 12, 16, d(16). of bright, color Its with white bluish btinge. c(13) tail The 19) ( elosunaaswaseorc-rigsrbte dnish lower the (all color their gpbN(19 e). tail, in ruaslpart imprwereorole; trbcivouacenldstresly) ffading gacolor, (19) 1ywhite dr) the from i( linto tinge pieaat gmsldoraret-orene3nauolidawscktlihegseyhr, ohead "body such 18 fthere othe (all sby tail, small of shape main bto ifsaslmweremany awaseuprolvwaientrgdisn)'g?; white 113, globules rb( became but they faded and falling behind, left the of Each 19). at eoutgwasasdwerei2,nisihng, 12 before s3 he ethe also Airport, Piarco p(23), from Hxwho Mr. chsomeipsawanoenlaekowdsmpsoaiepnornman fcvobjects the of tail sand them forming little, length The (16). time louiattwo ambwasany sedsometi-vblildked behind head, d(12). low SE, the ob3 Most object in siressawcwereorsoevery egaorhpvntednresars (12, 20° ethe ffrom Small head. od110° traced be could far 40° ( 19); lsfuyattcasisomeorusmn3) aptgiro-einosdnugts (25); long 10° sspeckled sparks, least odall with (redder body the tail The than tbatepsomeasrfwaseai-crnltviektcraesl)y, biin rapidly When appeared bright (30); Tit B.W.I. NNE, the than nrcstar irnotaganwasienvhagite-shdnreatdseg,r from othe pwof dsight, Wlflash Mr. (19 body after like ) bhiaaseglhonup ahctropvamnetidanrogen.d h6 the toward fall fade before and r5 pieces vtail object then smiles opoint aout ernorsawaway, edviezsrhoeandl of p"faded the only and lrtoward tail fiery end that reported burst. 34) omebacsany Two (30, denstrvi"eorns Git (26), Consul W. in (24), rAOwith twatching Mr. object the ewho Ivison msawironegwasribedcatluhdnge,hr R. T. Mr. sin objects it. the with tail of (27, fpinto e31 coming simply really view ) xraporanwasklg-omlseinkotens Tgive shower rin dwhat burst decide pend wof the eother is it hiastofasecwasunrtialohctsmbueilrndstogn; "d(23, 24) m(29 eSome o60° bthe tail 50°(30) of length ). sfasuaat tanireveneorxtsmivatmoe"urnmsd of (all oplanet agree). and bENE than athe vin became tail When it prstar isorany ewasiaasrgvobeahlrctesh.erd, (33). flame" welding (22) "vivid "(30), head dvThe bgreen" iwelmanuasashwasorretci-ewahiolnbsuteihsd"cly flash. the did OdmMr. quickly it which after like flash, inot big flare, erwhite msout naeatpgbinaeounsrgiehdu.m of dsparks 7, (6, o8, pnthe 9 f)elbaoustrcnorany light ornoneeatuircvthice;orlndse.s, afshortly dronly vteitoamrswgaimprnebdsnled.tas,r (Table Obcseorvnati'onds.) in. Land from by d(hidden ridge). isatant Remarks sky. 11 and (35) Scott 20 dEast the like H. light from place Gmiles of object "white eentire white lsoeasacrogutierbtsei,osc.wn, hduring the of bulb. above writer) by color dThe ethat sparks vfNo olriseanasawerewascorigrtzimbroielnced.ts E. Mr. from (37) Eboat the dLewin Steady all light white htime. above where it isoonavanarepiqzueaiorbneod,. (about tlike dplane fast, 15° Ibursts bright He fu"reto star. nasawassawascornovery vghetmlnecdnkitengsd,.) River the had seemed and hfly North wfrom sighted) first Before NE. long 1° tail parallel s( it to pohereeawasrcitazcoulna,r; dcsuddenly ENE seemed drop the in hcloser It (10°, high still while it quite ioto sreaicpzktoeinador.end, Pthe BAirport Guiana A. (36 object dAbut and bplanet, than ) it etratnot starskisawasorany cstrngai-shbuoethdnser dfrom rview". sand until it Bi"grow color the emasisawdrasnearcnlitsihbescrdhas (OTable Land from III. bcseorvnatio'nsd.) Remarks -38 Table IV. Most Probable Descent Trajectory of 1957 Beta 1 atltude Longitude (W) Height ( km MSL ) 41?40 74.°00 101 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 63.20 62. 33 61.29 60.41 59.54 58.70 57.88 57.12 88 86 83 80 78 71 88 SO 9.0 8.6 56.8 56.6 37 Time (U. T. ) l^S**' 1 1 1 1 1 1 1 1 SO SO 51 51 52 53 53 54 14 47 20 52 26 00 37 21 1 55 01 ( faopact point ) - 39- 4. Positions of Satellite 1967 Beta One During the First 100 Revolutions R. M. Adams, R. E. Briggs and E. K. L. Upton Smithsonian Astrophysics! Observatory The accuracy of determining the position of a satellite in retrospect Is Implicitly higher than the limited accuracy with which predictions of a satellite's motion can be made. The rocket-shaped Satellite 1957 Beta One had a rather low perigee and the effects of variable atmospheric drag were such as to prevent the computation of reliable predic tions for more than a few days in advance. This phenomenon, In terms of the observed variations in the rate of change of the orbital period, has been amply documented in earlier Special Reports. The present tabulation of satellite positions, in retrospect, achieves an accuracy of better than one degree in geographic latitude and longitude, and two kilometers in height above the earth's surface. While further computations could undoubtedly better this accu racy, we feel that it will suffice for most scientific studies with respect to ionospheric propagation of radio signals and evaluation of on-board Instrumentation recordings. The tabulation in this report is limited to the first eight days of the lifetime of Satellite 1957 Beta One, when radio transmission was operative. No claim is made for very high precision in the data given In this report. Pre cision is limited by the accuracy of the observations used for the analysis made in Special Report No. 13 and by the neglect of periodic perturbations of magnitude com parable to the scatter In the observations. Secular perturbations have been taken into account. Using time as the independent variable, the positions given are accurate to better than ±095 in latitude and longitude and within 2 km in height. A time interval of five minutes was chosen since it was felt that the limited accuracy did not Justify use of a smaller interval. The time origin for this ephemeris is Nov. 0, 1957. The first position given is for Nov. 3, 1957 at 0600 (GMT). However, positions given for times prior to Nov. 4, 1957 (0700 GMT) are extrapolated since observations were not available until that time. All longitudes given are degrees east and heights are In kilometers. The ephemeris gives positions of sub-satellite points in geographic latitude and longitude. A sub-satellite point is defined as the intersection of the radius vector with the geold. Thus the heights given are the actual distances between the satellite and the sub-satellite points. The equations given below were used in preparing this list of positions. They apply only to the first 100 revolutions of the satellite. The time origin is 1957.0. -40d d Time of nodal crowing = 308. 39469 + 0.072009N -ld211 x 10_6N2 - 6?40 x 10-10N3 + 4d3 x 10"l2N4 Right ascension of ascending node = 108* 2 - T. 630 ( t-TQ) - 0?002(t-To)2, To = 310.00000 Argument of perigee = S8?0 - 0*394 ( t-T0) - 2! 50 x 10"4 ( t-T0)2 ■ 3!lx lO'^t-T^3, To = 310.00000 Inclination ■ 65! 29 Perigee distance ( in earth's equatorial radii ) = 1. 02955 + 0.027 ( a-1 ) | N: Number of revolutions""! |"a: Semi -major axis ~J 1661.0 1664.9 1613.1 1507.6 1334.0 1161*6 944.3 721,6 515.9 352.2 252*0 228.1 282*0 404.0 577.2 781*1 995*2 1200.5 1381.1 1524.7 1621.9 1667.0 1656.7 1590.9 1472.6 1308.1 1108.0 887.4 666.6 469.2 320.0 238.4 234.7 307.1 443.9 626.9 835.3 1048.7 1249.1 1421.3 1553.8 1638*2 1669.3 1644.8 1565.3 1434.3 1239.7 1032.8 830*1 613.0 425.7 292.1 229.9 246.2 336.5 486.9 678.3 889.9 1101.5 1296.0 -45.79 -56.37 -63.81 -64.92 -58.50 -47.21 -33.22 -17.40 -0.19 17.97 36.33 33.29 64.48 62.25 49,76 34.46 18.94 3.91 -10.43 -24.03 -36.84 -48.63 -38.65 -64.82 -63.93 -56.0 -43.88 -29.37 -13.17 4.34 22.64 40.85 56.96 65.37 59.67 46.00 30.51 15.08 0.22 -13.94 -27.35 -39.93 -51.38 -60.70 -65.36 -62*48 -53.23 -40.40 -23.41 -8.84 8.92 27.31 45.27 60.17 65.23 56.60 42.13 26.57 11.25 -3.44 125.55 139.68 163.34 196.20 224.25 241.63 252.54 260.46 267.34 274.70 284.55 301.45 335.60 20.80 47,17 60.32 68.31 74.28 79.64 85.31 92.31 102.29 118.37 144.93 178.10 203.32 218.63 228.54 236.04 242.91 250.65 261.68 281.77 321.31 3.23 25.10 36.46 43.75 49.46 54.81 60.71 68.27 79.41 97.77 127.08 159.39 181.75 195.30 204.39 211.59 218.52 226.80 239.35 263.47 307.29 344.21 2.41 12.36 19.09 24.62 15.. 20.00 25.00 30,00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10,00 15.00 20.00 30.00 35.00 40.00 45.00 50.00 55.00 o.oc 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50,00 55.00 0.03 3.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 00 0^ 25. 10. 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 19 13 19 19 13 19 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 HEI6HTIKN) 239.0 234.3 305.8 442.0 624,6 833.0 1046.6 1247.4 1420.3 1533.3 1638.7 1670.6 1646,0 1568.0 1437,8 1263.5 1056.8 834.1 616.5 428.4 293*8 230*3 245,4 334,7 484.4 675,5 887.0 1099,0 1294,0 1457,7 1579.5 1651,6 1669,5 1631.7 1539.4 1397.3 1213.6 1001.1 777.3 565.1 388.4 270*5 226,7 261,4 367.5 529,6 727.8 941,2 1150.3 1338.6 1492.6 * 1602. BETA! 1*57 FOR EPHEMERIS ZERO LAT 40*72 56.85 65*36 59.75 46*10 30.62 15.18 0*31 -27,27 •13.86 8.74 27.13 45.09 60.05 65*25 56*73 42*28 26.71 11*39 -51.31 -60*64 -45*33 -62.53 -53*32 -40*32 •39.86 •25.55 ♦9.01 -30.31 +42.86 ♦3.31 •17.29 13.34 31,75 49.30 62,65 64.17 53,36 38.38 22.81 7.63 •53*92 ♦62.40 •63.39 •60.70 •50.37 •36.93 •21.33 •4.64 -20.68 •6.89 •33.70 1937 NOV ORIGIN 0. TIME E 6.35 26.34 65.73 107.7* 129.78 141.18 148.49 154.21 159.56 165.45 172,99 184.10 202.39 231.62 263.96 286.39 299.99 309.10 316.30 323.23 331.48 343,96 7.»0 51*39 88.73 107.07 117,06 123.81 129*35 134.75 140,93 149,14 161,62 182.47 213*94 244.47 264.24 276.37 284.82 291.82 296.90 307.83 322.26 351.00 36.83 68.45 83.68 92.76 99.07 104.49 109.99 116.54 LONG C.OJ 3.00 10.00 15.01 20.00 23.0O 30.01 35.01 45.01 50.00 55.00 60.00 5.00 15.00 20.00 25.00 30,00 33.03 40.00 45. OO 50.00 60.00 5.00 15.00 40.0"! 10.0? 55.010.0" «MT 25.00 30.0 35.00 40.00 45.00 50.00 0.00 5.00 10.00 15.00 20.00 25.00 60.00 10.0• 0^ 55. 3^.0- 35.0' 40.00 45.00 50.00 55.0) 5.00 15.0" 2C.00 10 10 10 1033*1 1252.7 1424.0 1355.3 1638.4 1668.1 1642*2 1561*4 1429.4 1253.9 1046*4 823.8 607*2 421*1 289*4 229*3 247*4339,7 491*4 683.5 893*0 1106*3 1299,9 1461*8 1381*3 1631.0 1666*4 1626*2 1331.7 1387*6 1202.6 989.4 766*2 355.2 381*0 246*5 226*3 264.8 373*9 337.9 737.0 950*3 1158*4 1343.0 1496*8 1604.0 1639.9 1661.0 1606.5 1498.6 1343.0 1149.2 931.6 709,3 505,4 344*8 248.6 229,0 286*8 411.8 IS• .01 .01 .90 .10 •37 •14 S6• 83• •38 36• 12• •09 •49 •30 •70 •63 •41 17• 33• •61 •23 93• •72 •67 87• •20 •21 •39 •34 44• 96• •44 96• •00 •42 97• •94 •86 84• •28 12• •37 13• 13• 18• •70 98• 81• 71• •62 72• S3• 73• 93• 70• •87 9i -0, -27, -40, -51, -60, -62, -53, -40. -23, •e, 27, 45, 60. 65, 56, 41, 26, 10, •3, -17 -30 -43 -54. -62, -65. -60. -49 -36. -20 •4. 14, 32, 49, 62, 63, 32, 37, 22, 7, -7, -21, -34, -46, -36 -64, -58 -46 -32. -16. 0, 18, 37, S3, 64, 61, •63 •14. •65, 03 ,17 i62 l*i .92 .31 .97 .35 »7S ,53 .63 .73 IS• .52 .93 ,00 .80 •OS •09•78 13• •63 •88 •42 •15 75• 78• •91 •24 •94 •44 51• •97 •91 •75 •44 •96 •37 •59 •68 •73 •44 •20 17• •34 72• •46 •93 •86 •67 •74 47• •66 •26 •40 •78 •87 87• •S3 •61 •37 •22 11• S3• 299, 304, 310, 316, 323, 334, 333, 22, 35, 77, 90, 99, 106, 113, 122, 134, 159, 203. 239, 257, 267, 274, 279, 265, 291 299 312. 333. 3. S3. S3, 67, 73, 62, 89, 98, 113, 142, 188 219 234 243. 249 235 260 267, 276, 290 314, 347, 15. 32, 43, 31, 38, 65, 73, 92, 128, 172. •oo .00 ,00 .00 .00 .00 .00 .00 .00 .00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 •00 •00•00 •00 •00 •00 •00 •00 •00 •00 •00 •00•00 •00 •00 •00 •00 •00 •00 •00 00• •00 00• 00• •00 •00 •00 •00 •00 •00 •00 •00 •00 •00 20, 28, 30, 35. 40, 45. 50, 55. 0, 5, 10, 15 20, 25, so, S5, 40, 45. 50, 55. 60, 5. 10 IS 20, 2S< SO S3, 40. 45. SO, S3. 60 5. 10 15. 20. 25. SO, 33. 40 43 SO. 35 0 3 10 IS 20. 25. SO, S3. 40. 45. SO, 33. 60, 3, 10, IB, 20 20 20 20 20 20 20 20 21 21 21 21 2121 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1459.0 1379.81651.0 1668.1 1629.3 1536.2 1393.4 1209.2 996.3 773.1 561.2 385.5 268*9 226.6 262*7 369.9 332*7 731.2 944*6 1153*3 1340*9 1494.0 1602.7 1660.3 1663*1 1610.3 1503.9 1349*3 1156.6 939.3 716.6 311.6 349.2 250.6 228.4 283.9 407.1 581.0 785.2 999.1 1203.8 1383.6 1326.1 1622.2 1666.0 1654.5 1587.6 1468.2 1302.9 1102*2 881*6 661*2 464.8 317.1 237.3 233.5 309*6 447,7 631.3 839.9 •OS OS• IS• .77 .22 .66 ,98 18 .21 39 47 73 24 .40 ,62 ,96 .01 ,46 .38 ,61 .23 ,77 S4• ,ST .32 •23 •71 70• •63 02• 79• 86• 86• 83• 66• 11• 87• 4i •42 98■ 77• 10• 19• •20 63• •46 83• •84 92• 48• 87• 88• 38• •00 •08 •26 •62 S3• 36• 11• 34• S4i -621 -47 -38 -33 -17 -21. 7. -7. -33 -45 -56. -63 -37, -48 -58. -65. -36. 31. 3S< -20 -64 18< 36. 18. -24. -63. -35, -29, -60. IS. 49< 62. 53. 22. 0. 62. 49. S. -10. -64, -43, -12, -42 , -50. 64. -30, -4. 64. 22* 41. 37, 65, 59, 43. 30, S3. •17, •54, 44.45 36.99 77.95 109.50 139.96 159.63 171.71 180.14 187.13 194,23 203.22 217.74 246.74 292.61 323.94 339.24 348.07 354.36 359.77 3.29 11.85 20.91 35.12 58.93 91.85 119.77 137.04 147.90 135.80 162.68 170.05 179.97 197.05 231.54 276.60 302.67 313.69 323.64 329.59 334.94 340.62 347.65 337.69 13.90 40.65 73.81 98.86 114.06 123.91 131.40 138.27 146.04 137.17 177.53 217.42 259.02 280.60 30.02i\ 36. 291.8* 25. 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 55.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15. OC 20,00 OC 20 20 20 -43- <D4iMp<mhoOHaiOOOiri«in««HOO<oi<iom<oo»»onh*io>tr'««4hHr>«h»N<Crt(g«n40Son4hHO i OKI " » * O CO c rg<^v\r-(>iHiniriio«.«io«mfi(><o«ir>(MCMCM«irtcoON<nir< I <o <£ <A in ♦ CM o e *\ * •0H(0HON4Otf><0HI^C>H«\hHN^h0tNHHm<00l0'4)MJCDO4Nff<n<0OH<0H44t00tBOO94<nC0nntkOONOh ^]r-|rt^^4o)lnlfMAOH<oa}rMOHN<r-4a)lr^lONN^40^-4fno«^H^-ONl^N«H4<cl<AH«»oo4C^(Mr^<nHwc^N<o 1 1 i 1 T 1 1 1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 11 1 1 1 1 1 1 1 *3inw3in^r*intHr~o*3f*rj»nt^o*r^^ocy»*o^fwr^in*ff*in*jo»^c>ic>iW3m^i^njtHr^.^ 7inii\oo!inoONiV'iiH4riai)«i<ir<Ht>no>4<40iAHaioiiMO<lloin«NO>MiOriHNNO(iH««iO«nM>NOh« c c f 00000c: 00000000 oocc or. ocooocooooo 00000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 n^o^oino^OAOinoAortotnoAo«oinoinoino^oiftoinoAOAOiAonoa\oAoffoAoinoiAO^o<rtotfi fNjrg(^fo^-*triir\«o f-i)-irsjrgmm<?-^inin'6 HHNnnn^^tfim r-i»-*r»jryi*ii^-#.4firtm«c HHNNttn«4in«\iO v-« r-< oootf<l0^^o^^^^^^^^^^.^^<oo)e(Offleo^)«l»o)(^c^(^c»c><^»e»(^(^(^c»e^oooooooooooOHHp< c*wjc"njC*»mrs;onifNjw5nii^inin(>o>foenf\io^t~*m^«*e)t*ni«eow)» >o^inc>f^eoininp*i^cNjin*Wfncorjinw5i**mco*3C*cocor^^«eoofsiinf-4r^*in» csc^oococ^nioincc^^^f^ir. inf^cnfntHinfn4fininf\iinfnwjf*infsi*r«nr*<*t*«>w mrsirvna)^inr^c<^rj«GONCcorvoOMtn^oC'^in<naD*c400iOcro^^o,Krkf*NirtNC^4^iO<ONCNN4inHH4^h> ^inrntno^f^c-oD^mintnajrviiAm^h-iAC^in^^p^^OiHt^inf^rg^^r^c^ai^oiniA^ino^co^ « fn ~4 H(vm4UN>(l«l(v«Nrt (\J<rm»5m*l\H-lJ>-ir>J*in>0«><0in<«>IMt N4<<<\«NH|Hr\f«l<0<4«|ltN|M|IM> 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 T 1 1 1 1 itiiTTiiii ^ccuTr-fsi<Nic^^*r~i^<r^inr>i»n^r^cDinr^<nt^cor\coinininini^*3iN(CO<o^ OHOt4Oom^ff,<AO'4O'^onHNn^in<fl^4OinHO-ooto>Hfti0ii\NGKhono<oi<tno*Aorbin«OkHHON 1 • «\ « 0> c#-ifHisj«n<^*m\oo*n«m **c>jfn*rmr^»-iinr-«ocoo»-«»-»*n*rf*-f-iin.#c\ t-ipiiAOrMn'0«0^cofrON'0(>Hf\j tn m * tr» r-ifMfN(rgrgfMr*4rsirg(M<n(*\ HHHHHNNNNtviMrgnmnin HHHHHHMrCHNNNNinnflftnKI COOOOOOOC icooocoooooooooooooooooooooooooooooooooocooooooooco 000000000000000000000000000000000000000000000000000000000000 c«oinc><o>io(>oinoinoinoino*oi>o«oi(ioino«oii<oinoiiiO(iOAO'iO(iario>io>ioino«o<>0'ioin ru N <o * •* m m *o rtriNNnm**** rtHNiMnf>< + «MA« HHnNnn«4nn'C »n-i rg rg to m * * mm mm 631.2 440*9 901*4 232*2 241*2 324*9 470.1 498*1868*0 1079.7 1273.8 1441*6 1966*3 1642*0 1663*9 1630*2 1542.0 1403*9 1223.0 1012.6 789.9 376.7 397.3 273.6 226*9 256.6 358.2 316.8 712*3 924*8 1133*9 1323.1 1478.9 1591*2 1652.8 1660*0 1611.6 1509.4 1398.9 1169.0 953.5 731.0 524*5 356.5 255.0 227.2 277.1 393.7 566.1 768.3 981.4 1186.7 1368.2 1513.2 1612.5 1659.8 1652*2 1589,1 1473.4 1311.2 -10.83 6.84 25*22 43*31 38*00 65*42 38.04 43*91 28*39 13*03 -31.97 -41.55 -52.80 -23.06 -6.26 11.66 30.09 *7.82 61.80 64.67 54.63 39.84 24.29 9.07 -5.51 -19.37 -4 .67 -63.3 -65.15 -39.31 -48.31 16.34 34.94 52.11 64.01 62.93 30.92 33.72 20.20 3.14 -9.25 -2 .92 -33.80 -47.70 -37,93 -64.35 -64.29 -56.7 -18.74 -29l.09 •1.73 •15.78 •61.69 •65.44 •61.49 •38.34 •32.47 •55.46 •34.46 •1*60 178.01 164.90 192.93 204.76 226.96 269.05 308.33 328.08 338.62 345.59 351.19 336.56 2.60 10.31 22.38 42.13 72.79 104.26 125.13 137.84 146.53 133.63 160.66 169.34 183.01 209.93 235.26 288.89 303.25 314.31 320.96 326.41 331.87 338.27 346.96 0.45 23.07 55.61 84,68 102.91 114.24 122.34 129.27 136.33 146.09 162.17 194.61 240.27 268.17 281.97 290.22 296.28 301.64 307.25 314.10 323,74 339.18 4,87 38.14 64.30 20.00 25.00 30.00 35.00 40.00 43.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 30.00 55.00 0.00 5.00 10.00 15,00 20.00 25,00 30.00 35.00 40.00 45.00 50.00 99.00 60.00 5.00 10.00 15.00 20.00 23.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 0,00 10,00 13.00 5.0<- 18 148 4 IB 4 18 148 148 4 18 148 4 21 241 4 21 146 146 146 4 16 4 16 4 16 146 146 147 147 147 147 147 147 147 147 147 147 147 148 148 4 18 4 18 4 18 4 19 4 19 4 19 4 19 4 19 4 19 4 19 4 19 240 4 20 240 240 4 20 4 21 4 16 4 19 4 19 4 19 149 4 20 240 240 4 20 4 20 4 20 4 281.0 227.6 232.7 350.5 506.2 700.5 912.5 1122.9 1313.5 1471.8 1587.0 1651.9 1662.5 1617.4 1518.4 1370.4 1182.5 968.0 745.2 536.8 367.4 259.4 226.7 271.9 386.6 554.6 755.5 968.7 1175.2 1358.7 1506.5 1608.9 1659.8 1655.6 1596.0 1483.4 1323.9 1127.5 908.8 687.5 487.0 332.1 243.1 231.2 296.1 426.7 605.3 811.4 1024.6 1226.4 1401.5 1538.0 1627.3 1663.8 1644.9 1570.8 1445.1 1274.7 1070.8 849.3 29.09 46.91 61.24 64.91 55.33 40.67 25.11 9.86 -4.76 -18.65 -31.80 -44.05 -34.94 -63.03 -65.25 -39.79 -49.01 -35.29 -19.67 -2.60 15.49 33.90 51.20 63.61 63.38 51.73 36.60 21.06 5.96 -8.47 -2 .18 -47.07 -57.43 -64.33 -64.52 -57.35 -45.63 -31.34 -15.30 2.08 20.34 38.63 55.21 65.06 61.02 47.89 32.50 17.03 2.10 -12.14 -25.65 -38.36 -50.00 -59.70 -65.15 -63.25 -54.59 -42.07 -27.27 •35.11 273.51 76 286. 312.63 357.52 32.32 49.34 58.83 65.38 70.85 76.29 82.61 91.13 104.26 126.28 158.50 188.11 206.84 218.44 226.65 233.60 240. an 250.15 265.65 296.86 342.72 11.81 26.11 34.55 40.69 46.06 51.64 58.38 67.81 82.79 107.82 141.02 167.82 184.21 194.63 202.35 209.23 216.77 227.19 245.62 282.56 326.33 330.32 2.51 10.12 15.95 21.29 27.07 34.33 44,86 62.05 90.08 123.01 146.80 161.19 170.6 .00 .00 .00 .00 .00 .00 .00 .00 .00 ,00 .00 .00 .00 ,on .00 .00 .00 .00 .00.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 »oc .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .0^ •00 •00 •00 •00 •00 •00 •00 00• •00 •00 •00 •00 •00 ,t>9 •00 20, 29.30, 35, 40, 45, 50, 55, 0, 9, 10, 15, 20, 29, 30, 35, 40, 45, 50, 55, 60, 5, 10, 19, 20, 25, 30, 35, 40 45, 90, 55, 60, 5, 10, 15, 20, 25, 30, 35, 40 45 50 99, 0 9, 10, 15, 20, 25, 30, 33, 40, 45, 50, 55, 60, 5, 10, 15, 11 1111 11 11 11 11 ri 12 12 12 12 12 12 12 12 12 12 12 12 12 IS 19 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 19 13 19 19 13 13 IS 19 19 19 19 19 19 16 16 16 1498.8 1345.2 1153.0 936.5 714.3 310.3 348.4 250.2 228.2 283.6 406.6 580.0 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C. INTERNATIONAL GEOPHYSICAL YEAR WORLD DATA CENTER A National Academy of Sciences 2101 Constitution Avenue, N.W. • Washington 25, D. C, U.S.A. World Data Center A consists Airglow and Ionosphere: IGY World Data Center A: Airglow and Ionosphere Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado, U.S.A. the following eleven archives: Glaciology: IGY World Data Center A: Glaciology American Geographical Society Broadway at 156th Street New York 32, New York, U.S.A. Longitude and Latitude: Aurora (Instrumental): IGY World Data Center A: Aurora (Instrumental) Geophysical Institute University of Alaska College, Alaska Aurora (Visual): IGY World Data Center A: Aurora (Visual) Rockefeller Hall Cornell University Ithaca, New York, U.S.A. Cosmic Rays: IGY World Data Center A : Cosmic Rays School of Physics University of Minnesota Minneapolis 14, Minnesota, U.S.A. IGY World Data Center A: Longitude & Latitude U. S. Naval Observatory Washington 25, D. C, U.S.A. Meteorology and Nuclear Radiation: IGY World Data Center A: Meteorology and Nuclear Radiation National Weather Records Center Asheville, North Carolina, U.S.A. Oceanography: IGY World Data Center A: Oceanography Department of Oceanography and Meteorology Agricultural & Mechanical College of Texas College Station, Texas, U.S.A. Rockets and Satellites: IGY World Data Center A: Rockets and Satellites National Academy of Sciences 2101 Constitution Avenue, N.W. Washington 25, D. C, U.S.A. Geomagnetism, Gravity, and Seismology: IGY World Data Center A: Geomagnetism, Gravity & Seismology Geophysics Division U. S. Coast and Geodetic Survey Washington 25, D. C, U.S.A. Solar Activity: IGY World Data Center A: Solar Activity High Altitude Observatory Boulder, Colorado, U.S.A. Note: (1) Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: Drrector, World Data Center A, National Academy of Sciences, 2101 Constitution Avenue, N.W., Wash ington 25, D. C, U.S.A.; (ii) Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate archive listed above. ^IGY World Data Center A fo-Q ■^Itockets and Satellites. National Academy of Sciences Washington 25, D. C. | IGY Satellite Report Series Number 7 1 January 1959 SIMPLIFIED SATELLITE PREDICTION FROM MODIFIED ORBITAL ELEMENTS Leonard N. Cormier Norton Goodwin Reginald K. Squires Note 1. This report is issued in accord with international arrange ments on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies avail able at cost to scientists upon their request. 2. These data and/or report contents are reproduced as received from the experimenter. 3. Recipients of these reports are advised to communicate with the authors prior to utilization of experimental data for further publication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites First Limited Draft Edition 29 August 1958 Second Draft Edition 1 December 1958 PREFACE This second draft of "Simplified Satellite Prediction from Modified Orbital Elements" is now included in the IGY World Data Center "A" Satellite Report Series. Only minor modifications from the first draft edition have been incor porated into the text, the most significant change being the addition of Appendix 2, which outlines the arrangements for communicating modified orbital elements. The word "simplified", as it appears in the title deserves some explana tion. To persons not familiar with the complexities of reducing more conven tional satellite orbital elements to local observation times and angles, the me thod described may hardly appear simplified. In fact, many observers who have attempted to make predictions either from fundamental or from incomplete data report the method to be simpler than other generally used methods. The manual, together with its tables and charts may be thought of as a complete computation program for pencil and paper, as opposed to a deck of punch-cards for programming an electronic data computer. Nevertheless, persons not necessarily familiar with celestial mechanics can compute from modified orbital element all data needed for local observations. Many of the tables are directly applicable in connection with other prediction methods. The modified elements, of course, may be used as input data for any appropriate computation program. Many simplifications, shortcuts and other suggestions will present them selves to users of the booklet after computing a few actual predictions. The authors themselves have found a number of shortcuts to the method and, by way of example, Appendix 3 includes several such shortcuts and other notes. TABLE OF CONTENTS Page Introduction Basic Assumptions Description of the Method Example : Modified Orbital Elements Schedule A Schedule B Schedule C Schedule D Schedule E Schedule F Schedule G Plotting Grid Schedule H Elevation and Slant Range Chart Table I Table II Table in -A Table III-B Table IV Polar Grid Sub -Polar Grid Mid -Latitude Grid Sub -Equatorial Grid Equatorial Grid Table V Chart for Determining Elevation & Slant Range Table VI Appendix 1 - Formulas Used In Preparing Tables Appendix 2 - How Modified Orbital Elements are Transmitted Appendix 3 - Computation Short -Cuts & other suggestions 1 3 3 4 6 7 7 9 9 10 11 11 & 12 13 15 16 & 17 18 & 19 20 & 21 22 & 23 24 & 25 26 27 28 29 30 31-43 45 46 & 47 48 49 53 ACKNOWLEDGMENTS The authors wish to acknowledge the valuable assist ance of personnel of the Smithsonian Astrophysical Observ atory, the Naval Research Laboratory, and the Army Map Service. In particular they wish to thank R. M. Adams and G. H. Conant, Jr. of the Smithsonian Astrophysical Observ atory and R. H. Wilson, Jr. of the Naval Research Laboratory. The preparations of Tables I, II and IV was greatly fa cilitated by free use of a Burroughs Model E-102 electronic computer. Table III was prepared by G. H. Conant, Jr, using free time on the Massachusetts Institute of Technology's IBM Model 704 electronic computer. Table V was provided by the Naval Research Laboratory; the part of this up to 40° lat itude has previously appeared in chart form in NRL Report #5066 by J. W. Siry, R. H. Wilson, Jr., M. de Novens, M. P. Hann, and E. L. Lady, while the part for 45° to 85° latitudes was later prepared by M. de Novens. The chart for deter mining elevation and slant range is a modification of a simi lar chart prepared by G. Veis and drawn by R. Atkinson. A number of helpful suggestions of S. W. Henricksen of the Army Map Service were employed in preparation of the plot ting grids. SIMPLIFIED SATELLITE PREDICTION FROM MODIFIED ORBITAL ELEMENTS L. N. CormieriA N. Goodwin^, and R. K. SquiresA' ABSTRACT: The problem of supplying prediction data for IGY satellite observers is discussed in terms of the need for providing a large number of stations with "fresh" data in a useful form. A straightforward method is given whereby an observer can: (a) Eliminate all but potentially significant observation periods; (b) For any such period, determine the precise time when the satellite will cross (or approach) his latitude circle, the longitude of the crossing (or approach), and the satellite height; and (c) Derive from such crossing (or approach) data the azimuth, elevation and slant range to the satellite for one or more optical observations, or comparable data for radio observations. The method is specifically designed to direct primary consideration to the times when the orbit plane (without regard to the satellite position) passes through a selected point on the observer's meridian. Modification of the or bital elements permits direct application of the observer's geographical co ordinates for first determining the times of approach of the orbit plane, and for then determining the relative position of the satellite. Prepared message forms, computation forms, tables and charts that may be used for graphic solutions are given. PURPOSE Individual observers require predictions as to when and where IGY satellites may be expected to pass near their stations. To be useful for many types of observation programming, such prediction data may have to be based upon up-to-date information as to the whereabouts of a particular satellite, and the rates of its changes of position. Some artificial earth satellites may be in such stable orbits to permit calculation of satisfactory predictions for considerably more than one week beyond current orbital information. For close-in orbits, predictions based upon week-old elements may prove of questionable value. During the terminal phase of a satellite's life, it may not be possible to make satisfactory projec tions of future position for more than half a day. Communications considera tions, therefore, will influence the form in which data is transmitted from the computing centers to the observer. 1_/ National Academy of Sciences - National Research Council, USNC-IGY Staff 2/ Director, Phototrack Program 3/ Naval Research Laboratory, (currently at National Aeronautics and Space Administration) 1 Computation and communication of satellite prediction data may take several forms. For example, the computation centers may provide predic tions tailored for specific stations. Practice has shown that if an attempt is made to provide such specialized service to more than a limited number of stations the overload on computation and communication facilities may result in delays and errors. A more general and practical procedure is to compute and to communicate schedules of predicted satellite sub -points: e.g., longi tudes where, and times when the satellite crosses over the equator or speci fied parallels of latitude. Such schedules require not inconsiderable compu tation effort on the part of the observer, and yet central computation and communication facilities may nevertheless become overloaded when several satellites are in orbit at the same time. From a communications standpoint, such prediction schedules are excessively redundant, in many cases repre senting mere interpolation between two sets of "orbital elements", each completely describing the positions of the orbit plane, and of the satellite within the orbit plane, at particular times. The practical usefulness of data based upon interpolation suggests a third form for supplying prediction data in terms of the orbital elements themselves. From computation and communications standpoints, the trans mission of orbital elements offers the simplest and most concise solution to supplying observers with the necessary data. Disadvantages to the observer include: (a) The fact that many observers are not familiar with orbital ele ments; and, (b) The computation effort required on the part of the observer, even when he does know how to use the elements for prediction purposes. The chief advantage in transmitting orbital elements to the observer is that he is more likely to receive up-to-date information in sufficient time to be conveniently useful. The purpose of this paper is to describe a prediction system which is in keeping with a practical computation and communication effort and which will at the same time provide good service to the observer. The approach is to minimize the disadvantages of using orbital elements for prediction purposes . MODIFICATION OF ORBITAL ELEMENTS The form in which orbital elements are traditionally given for stating the positions of the planets has been modified to eliminate unnecessary com putations. For example, the position of the orbit plane is given in terms of geographic longitude, rather than "celestial longitude" or "right ascension". Such modification avoids a number of confusing computations and references to almanacs. Similarly, the practice of giving the time of an actual observa tion as reference time (or "epoch"), rather than a time when the satellite is at perigee, has the effect of transferring to the observer a computation which could be better accomplished at the issuing computing center. By choosing the reference time at an instant when the satellite is at perigee, one measure serves to fix the positions of both the "ellipse" in which the satellite travels and the position of the satellite within the ellipse. 2 COMPUTATION FORMS, TABLES AND CHARTS The observer's computations can be simplified not only by modifying the traditional orbital elements, but also by solving beforehand, and in a gen eral way, many of the problems of converting the information contained in the elements into values referred to his station. These general solutions have been reduced to computation forms, tables, and charts. The computations are explicit, straightforward, and involve no operation more complicated than long division. BASIC ASSUMPTIONS The modified orbital elements described below and the method of satel lite prediction through their use are based upon certain fundamental assump tions; an understanding of these assumptions is not a prerequisite to use of the method. The assumptions are as follows: (a) That the satellite moves around the center of the earth in an ellip tical orbit of constant eccentricity, all the points of which lie within a plane whose inclination to the earth's equator is constant; (b) That the orbit plane rotates at a constant rate around the earth's polar axis; (c) That within the orbit plane, the elliptical orbit itself rotates around the center of the earth at a constant rate; and, (d) That the satellite within its orbit will sweep out equal areas in equal intervals of time. (e) That the decrease in period due to drag can be represented on a plot by a straight line over intervals of about one week. The foregoing assumptions are not altogether valid, because the earth is not a perfectly uniform sphere, and because of other factors influencing the satellite's motion. Nevertheless, computations based on such assumptions will yield prediction data of sufficient accuracy for most observational purposes, provided the data on which they are based are sufficiently "fresh". DESCRIPTION OF THE METHOD Using orbital elements given in the prescribed form, initial times are computed which place the orbit plane through a point on the observers meridian at the intersection of a nearby reference latitude. Subsequent times when the orbit plane sweeps through such reference point are then determined, from which the observer may select an appropriate sweep time for further computa tion to determine when and where the satellite will cross reference latitude. Additional optional calculations permit determination of times when the satel lite will make its closest approach to the observer and will cross specific bearings. Azimuth, elevation, slant range, visibility and apparent angular motion for such times may also be determined. Printed forms, tables and plotting grids supplied herein, a pencil, pro tractor and some long division are all that are required in applying the method. By reducing interpolation errors, extension of the tables would improve the precision of the method. Such extension might be justified in cases where the behavior of satellite period could be predicted with sufficient accuracy. 3 EXAMPLE An example is given below of the method of simplified satellite predic tion from modified orbital elements. The example is based upon the orbital elements for earth satellite 1958 Epsilon which were issued 13 August 1958 by the United States Naval Research Laboratory and which were modified to conform to the prediction methods employed. The example shows how, through use of prepared computation forms, charts and tables, orbital ele ments referred to 8 August 1958 were used in predicting the time when earth satellite 1958 Epsilon could be expected to make a meridian pass near Lima, Peru on 16 August 1958. It will be noted, in following through the example given below, that the computation forms are intended to give explicit instruc tions. Long division is the most complicated mathematical operation involved. Form for Logging Given Information and for Locating Orbit Plane Relative to Observer MODIFIED ORBITAL ELEMENTS FOR EARTH SATELLITE 195?- ^es,L0^ GIVEN ON /3 AijQr I1S~<? (date) Reference time (Greenwich Mean Time = GMT, UT or Z) 19.$?..* ...<£..m° /6h GMT Reference time (Station Time = GMT)/V(-) ...S.b) 19.5#.y ...<$.." 11.. h .^9.^.(6... ST Orbit inclination + jftf _SQM9... Longitude of northbound node at reference time West of Greenwich Prime sweep interval: ^JMZtiSJL or 1440m00 (1 day), A/(-) .JbfafSSL Perigee and satellite position at reference time (measured in degrees of arc from -» » — northbound node and in direction of satellite's motion) fti.?7«!. Change in perigee position per period +X\rf -<2?^J?».5J.;7.T../period Perigee-to-perigee period at reference time ...t.Q9™8!&!T-.. Per period change in perigee-to-perigee period — 0?.Q.£&U3/period Eccentricity of orbit Q../.JL6&*? Estimated correction to crossing times (not always given) — ■ EARLY (LATE) Radial distance of satellite from center of earth at perigee .f//.A3.^.w.. statute miles Radio transmission frequencies ...L.Q.tl. Mc .../..&£ .0.1 Mc Mc 1 Statute mile=1.609 kilometers; 1 kilometer =0 .621 1 mile; 5 miles are approximately 8 kilometers The modified orbital elements given above are largely self-explanatory. Reference time is the particular time when the satellite, its orbit, and its orbital plane were all in the precise positions defined by the orbital elements that follow. Reference time is given in Greenwich Mean Time (GMT). In the line immediately following, there is provision for converting such reference time into station time (ST). (Reference time differs from the more conventional "epoch" only in that it is a particular "epoch" at which the satellite happens to be passing through perigee.) 4 Station time (ST) is the standard or daylight time normally used by the ob server in scheduling his daily activities. Orbit inclination defines the space angle formed by the orbit plane as it inter sects the earth's equatorial plane. It is given as negative if the satellite motion is from east to west. Longitude of the northbound node at reference time defines the position of the orbit plane in geographical coordinates. There are two nodes or points at which the orbit plane intersects the earth's equator. One can be distinguished from the other by the direction in which the satellite travels when passing overhead. The northbound node is defined as the node over which the satellite will pass with a northerly heading. The longitude of the northbound node is expressed in degrees west of Greenwich. (The Northbound node differs from the "ascending node" of conventional orbital elements in that the longitude of the "as cending node" is conventionally measured eastward from the vernal equinox.) Prime sweep interval is determined by the combined motions of the orbit plane and the earth. It may be considered as the length of time it apparently takes the orbit plane to sweep completely around the earth. The interval differs by a small amount from one mean solar day. In computing the times when the orbit plane will sweep through a specified meridian point, as is done in Schedule C, below, it is convenient to think of the prime sweep interval as one day plus or minus so -many minutes. Perigee and satellite positions at reference time are identical because of the way reference time has been defined. Perigee is defined as the orbit point closest to the center of the earth. The position of perigee is defined by an angle (at the center of the earth) measured from the northbound node to the perigee location in the direction of the satellite's travel. Change in perigee position per period defines the motion of the elliptical orbit during the time interval between successive passes of the satellite through any specified orbit point. The change is given as positive if the motion is in the same direction as that of the satellite. Perigee-to-perigee period at reference time is the interval between succes sive passes of the satellite through any specified orbit point. (Perigee-to-perigee period is by definition identical to the "anomalistic period" of conventional orbital elements.) Per period change in perigee-to-perigee period gives the amount by which the satellite's period grows shorter per period. Per period change, times num ber of periods since reference time, plus period at reference time yields current perigee-to-perigee period. Over an interval, the average between current period and period at reference time is used to determine the current position of the satellite. Eccentricity of orbit defines the shape of the elliptical orbit and conforms to the normal definition of the term. Estimated correction to crossing times may sometimes be given. 5 Perigee-to perigee period is the most perishable of all the orbital ele ments and the most difficult to project for an extended period of time. During the terminal phase of a satellite's life, perigee-to-perigee period can be ex pected to change rapidly and erratically. Communication of current orbital information to observers at such times becomes increasingly difficult. By issuing corrections to crossing times computed from published orbital ele ments, communications effort can be kept at a minimum. Such corrections will also permit the observer to adjust completed predictions based on "old" orbital elements. Correction estimates based on observations can also be ap plied in the same way. Radial distance of satellite from center of earth at perigee together with ec centricity defines the size of the orbit, and also the radial distances of all points in the orbit. It is given in statute miles. Radio transmission frequencies will be needed both for radio tracking and for telemetry. The frequencies are given in megacycles. Schedule A: To Find Longitudes of Northbound Node at Sweep Times and Specific Central Angles Between Equator and Reference Latitude (Compute ONLY ONCE for given station and inclination) 0. From part of Table I showing given orbit inclination, SELECT reference latitude closest to station latitude RETURN SWEEP PRIME SWEEP STRIKE OUT ALL of line a or 6 whichever contains a false statement: 360 ?00 180?00 a. Reference latitude is South —K30TO0—0?00 b. Raforonoo latitude in North 2. ENTER: Minimum longitude of northbound node west of meridian point at sweep times (from Table I) and 0 o i W 8 ? *{ . W ADD and SUBTRACT as indicated + 3. Specific longitudes of northbound node west of meridian 3L£L:JL w / as? H. w point at sweep times 4. ENTER: Longitude of station's meridian west of Green + .Oflft g. w 017° & w wich (360° LESS east longitude) and ADD a(, 8 ? 8 w 26 6"*? 6 w 5. Longitudes of northbound node at sweep times (Note: If the orbit inclination is negative, STRIKE OUT ALL of line a or b above, whichever contains a true statement, and in entering results in Item 3, above, TRANSPOSE to opposite column.) 6. STRIKE OUT ALL of line a or 6 below, whichever contains a false statement: 360 fOO 180 fOO a. Reference latitude is South —tsoroo hi Refcronaa latitude in Pinrth 7. ENTER: Initial central angle between equator and reference latitude (from Table II) and ADD and SUBTRACT as /3 oQ S3 ?Q + indicated. 3H7°Q 8. Specific central angles between equator and reference latitude /f3 f Q In the instant example, the coordinates of a station at Lima, Peru are used: Station latitude 11978 S., longitude is 77915 W., and the station is about 3963 miles from the center of the earth. It is important to note that Schedule A provides two different sets of answers, one under a column marked "Prime sweep" and the other under a column marked "Return sweep". Two sets of answers are required because two different parts of the orbit plane of 1958 Epsilon sweep through Lima, Peru, and it is important to distinguish between them. 6 The part of the orbit plane through which a satellite passes from equa tor to pole (whether North or South) is always identified with prime sweep, and the part through which a satellite passes in returning from pole to equator is always identified with return sweeps of the orbit plane through any specified meridian point. The distinction between prime and return sweeps disappears for meridian points whose latitude is numerically equal to orbit inclination — a fact that simplifies computation in Schedule A for observers whose latitude is numerically close to or greater than the orbit inclination. Schedule A need only be computed once for a given station and orbit inclination. A 10° S reference latitude was selected because it is the reference lati tude nearest to the station's latitude for which data on the given orbit inclina tion is computed in Tables I, II and IV. The intersection between the station's meridian and reference latitude (10° S) defines the meridian point for which sweep times are computed in Part I, below. Schedule A can be used for either southern or northern latitudes, and covers the possibility of a negative orbit inclination. Tables I and II are used in the same way whether the latitude is north or south, and whether the orbit inclination is positive or negative. PART I — TO LOCATE ORBIT PLANE Schedule B: To Find Orbit Plane's Relative Westward Motion 1. Degrees of longitude between successive prime sweeps 2. DIVIDE BY: Prime sweep interval in minutes (given) 3. Orbit plane's relative westward motion (degrees of arc per minute) 360?00 0° £.$'3&../m Schedule C: To Find Times When Orbit Plane Sweeps Through Meridian Point PRIME SWEEP _ ^ ««>..$.?...».. W 1. Longitudes of northbound node at sweep times (Schedule A, Item 5) 2. SUBTRACT: Longitude of northbound node at reference time (given) (ADD: 360° if needed to avoid negative balance) - RETURN SWEEP / 7Z ° 7 W - ..<?..•£ ?..fi... W 428. 8 /•<•/• !.J.Z.° "... W 3. Longitude to be traversed before first sweeps after reference time 4. DIVIDE BY: Orbit plane's relative westward motion (Schedule B, Item 3) 4- 0? £S3g ,/m + 0° ZST3.Z ../m 5. Equivalent times in minutes before first sweeps 6. CONVERT: Item 5, above, to hours and minutes 7. ADD: Reference time (from given data) 8. Times of first sweeps after reference time #.h ..UJa..%... o + ° O a V * ..././. h 7 7? Me ST - A // 3ft m &,i /6>> 57? Ob ST 7 .J£> Q + .0 ."■.//'■ Q I * (L ST a/ il <*/.» TP ST 8. Times of first sweeps after reference time 8 m« 9. ADD: Prime sweep interval (given) 10. Times of SECOND sweeps 8. /(, > 37 - oc ST 8 mo k 19. ADD: Prime sweep interval 1 II, c ST +ld/tf(-o/i ST ST -Of ST 23. ADD: Prime sweep interval 24. Times of NINTH sweeps 8 m o W*/f 25. ADD: Prime sweep interval 26. Times of TENTH sweeps 27. ADD: Prime sweep interval 28. Times of ELEVENTH sweeps - 3y ST ST k 3i.?2 ST » ST If *?o - .JSt- .7f ST +imk--) 8 m 0 n/3 +ij+f-•) d k 57 . 5/ +1V(- +i*&<- mo ST +i^(- 8 m c le* if 30 +ij^(- ) 18 22. Times of EIGHTH sweeps |3d^2 k +1-/M-. +1'* (- )/a -« ST 21. ADD: Prime sweep interval ST il' +l*f (- .8 m t■ \l< I* .8 m 1...ft- ts +id*f (- ST +id^(- )/f.-.Q?. 8 m « /f - /? +i*fi )/0 20. Times of SEVENTH sweeps ST (--)/*.- «l ) IB 17. ADD: Prime sweep interval 18. Times of SIXTH sweeps ST $ M ( 10 * Ik - <*? » <?£ ST 15. ADD: Prime sweep interval 16. Times of FIFTH sweeps te )/* .0?.. 13. ADD: Prime sweep interval 14. Times of FOURTH sweeps ST )/* -.<??. + 11. ADD: Prime sweep interval 12. Times of THIRD sweeps H*03 k ST m m ST k /a +ij+(--) d h ST * m ST Part I is self-explanatory. The purpose in finding out when the orbit plane sweeps through the selected meridian point will be apparent when it is realized that satellite 1958 Epsilon must pass closest to the meridian point within 55 minutes of sweep time. As a general rule, the time when any IGY satellite passes closest to any point on the earth's surface is bound to be within half a period of the time the orbit plane itself sweeps through or closest to such point. It will be noted in the above example that the sweep times keep changing. The time limits within which the satellite will pass closest to the observer are also changing in a like manner because of the general rule mentioned above. Without further computation an observer can inspect a filled -in Schedule C to determine which of the close passes for the ensuing week will occur at inopportune times. He can determine without further ado which passes are obviously going to occur at the wrong time of day for visual sighting. He can also pick out a sweep time that seems favorable, and using that sweep time, work out a detailed prediction with the help of a form for locating the satellite first within the orbit plane, then relative to the observer, as is shown below. I Form for locating satellite—first within the orbit plane, then relative to observer. PART II—TO FIND WHEN AND WHERE SATELLITE 19-5tf - ErsiLQU CROSSES REF ERENCE LATITUDE ON 8 ™ /* d, 19^8 Schedule D. To Find Minutes Elapsed between Reference Time and a 1. Selected sweep time (from Schedule C, above) 2. SUBTRACT: Reference time (from given data) - . 8 <"> 3. Elapsed time from reference time to selected sweep time 4. ENTER: Minutes from Item 3 (above) 5. ENTER: Hours from Item 3 (above) MULTIPLIED BY 60 6. ENTER: Days from Item 3 (above) MULTIPLIED BY 1,440, and ADD: Items 4, 5&6 7. Time in minutes elapsed since reference time Selected Sweep Time .(4>.A J.¥.> ST .8 * ft > ..#&../£. ST B d Q7> h 23™ %5..<?Z.... /..ZQ.iOO + l./.SZQ.^fy ..../../..&.!6>. 3... The computations involved in Schedule D, above, are self-explanatory. Schedule E. To Find Time when Satellite is Last at Perigee prior to Selected Sweep Time 1. Time in minutes elapsed since reference time (Schedule D, Item 7) /../..(.4>.3.. 2. DIVIDE BY: Average* perigee-to-perigee period -h /.0.9. "7.48 3. ENTER: Quotient (number of periods completed since reference time) /.tt.h... and 4. ENTER: Remainder in minutes 5. ENTER: Selected sweep time (Schedule D, Item 1) and _ SUBTRACT Item 4 from Item 5: Q>• ./*.« /Xh /2^37 ST 6. Time when satellite is last at perigee prior to a / i/ de selected sweep time ...P..mo ./y.d ,/3> Z7j?...t!. ST *In predicting satellite positions for only one or two days from given ref erence time, the small changes in period that occur during the interval may normally be disregarded. Substantial errors in crossing times will result if changes in period are not taken into account in predicting for more than one or two days from reference time. The difference between period at reference time and the period current at the time for which prediction is being made can be determined as follows: dcLpscci time APPROXIMATE number of whole periods completed = —■ given period (rounded off) 1 166 3***2 '. = 106 periods* (slide rule accuracy is sufficient) 109^9 /period CURRENT period = lOg1!^? - 106 periods(0r?00225/given period) = 109m887 - 0m239 - 109™648 (used in Schedule F, Item 9) AVERAGE period = 109m887 - °™239 = 109m768 2 === In determing the Remainder (Schedule E, Item 4), it is essential to com pute as precise a value as possible for the AVERAGE period and to carry out the division completely. Equivalent precision can be obtained by multiplying the pre cise AVERAGE period by an approximate number of whole periods and subtracting the product from the total elapsed time. Elapsed Time Less : 106 x 169^68 Remainder 11 663^2 11635?^ 27^8 If the Remainder is negative, add whole average periods; if it exceeds one period, subtract. 9 Schedule F. To Find Time when Satellite Crosses Reference Latitude 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14 15. Number of whole periods completed since reference time (Schedule E, Item 3) MULTIPLY BY: Change in perigee position per period (given) X + (^#^ Change in perigee position since reference time ADD: Perigee position at reference time (given) Current perigee position relative to northbound node ENTER: Appropriate central angle between equator and reference latitude, (from Schedule A, Item 8) and SUBTRACT: Item 5 from Item 6, adding 360° to item 6 if necessary Perigee distance from crossing point, measured within orbit plane ENTER: Equivalent fraction-of-period for given orbit eccentricity (from Table III) MULTIPLY BY: Current* perigee-to-perigee period Time required for satellite to travel from current perigee position to crossing point. CONVERT above to hours and minutes ADD: Time when satellite is last at perigee (Schedule E, Item 6) Time when satellite crosses reference latitude ST NOTE: If time computed in item 13 differs from selected sweep time by more than one-half perigee-to-perigee period, then determine alternative time as shown below: ADD (SUBTRACT) as appropriate: One whole perigee-toperigee period (given) Alternative time when satellite crosses reference latitude ST gf 222 /period 2.3° At + /.Of °.QG>- ..£1.3: 2/ 0 » 24 3 3 7fk 0S"t 8 ST ST ST To BRING ABOVE UP-TO-DATE, Determine from the most recent data that the satellite will cross reference latitudes minutes early, SUBTRACT this amount from Item 13 or 15, and ENTER corrected timt in appropriate box. {If satellite is late—ADD) If the time when the satellite crosses reference latitude found in Item 13, Schedule F, differs from selected sweep time by more than one-half period, the crossing that occurs one whole period earlier (or later, as the case may be) will actually constitute a closer approach. In such case, it will be sufficient to add or subtract one whole period, whichever reduces the dif ference between crossing time and sweep time, as indicated in Item 14, Schedule F. In the case of satellites passing high near the station, it may be possible to observe the satellite as it crosses reference latitude one whole period after or before the crossing closest to sweep time. The times of such crossings are found by adding or subtracting one whole period, as indicated in the form. How predictions can be brought up-to-date with estimated or subsequently issued correction data is explained at the foot of Schedule F, above, and at the foot of Schedule G, below. 10 Schedule G. To Find Relative Longitude of Point Where Satellite Crosses Reference Latitude 1. Time when satellite crosses reference latitude (From schedule F, Item 13 or 15 uncorrected): 2. SUBTRACT: Selected sweep time 3. Time difference (note whether plus or minus) 4. CONVERT above to minutes + (-) 5. MULTIPLY RY: Rate of orbit plane's relative westward" motion (Schedule B, Item 3) 6. Relative longitude of point where satellite crosses reference latitude. (If time difference in Item 3 is positive, the observer's station will be East; of crossing point. + (-) 8 8 .5. ,3 3 If,..* h ST ST (3 m 4» (-) ...£.?.<£l X0?..&r,3.&,./rnin. *(-) To BRING ABOVE UP-TO-DATE, SUBTRACT from time given in Item 4, the correction used in bringing Schedule F up-to-date, and ENTER result in Box. MULTIPLY corrected time by Item 5, and ENTER pro duct in box opposite Item 6. The orbit plane apparently sweeps from east to west. Thus a crossing that occurs before sweep time will occur when the plane is to the east of the observer's meridian. The computation in Schedule G, above, is obvious. Normally, an observer will not be directly interested in merely observ ing the satellite when it passes across reference latitude; he will probably want to know when and where to look to observe the satellite as it passes nearest his station or directly across his meridian. Information of this type was in the instant example derived through use of a plotting grid as shown below. „ oUc -c, 20 re5tive longitude of JOI =5 5° WEST OF REFERENCE POINT oO 0° 5' RELATIVE LONGITUDE OF OBSERVER EAST OF ST3TTVHMU H±02 QNV HiZ IV "IWVHOdNOO 11 25° Reference point The grid was prepared in accordance with the following instructions ap pearing at the beginning of the third and last part of the computation forms. In preparing the plotting grid it should be remembered that a straight line rep resents the satellite track for only a short segment near the reference point. If it is desired to use the grid for drawing a longer portion of the satellite track, points may be plotted by means of Tables I and II, by assuming a mean angular velocity for the satellite (as seen from the center of the earth) and by making the corresponding correction for the relative westward motion of the orbit plane. PART HI—OPTIONAL ADDITIONAL DETERMINATIONS Preliminary Preparation Of Plotting Grid (for use with any Pass of a given Satellite near Observer's Station) 1. SELECT a plotting grid showing latitude both of observer's station and of reference latitude used in Part II. 2. LOCATE Reference latitude used in Part II on central meridian (0° relative longitude). This is reference point. 3. ENTER Heading along satellite track for given orbit inclination and reference latitude *n (from Table IV) ..A.L°J.. 4. ALSO ENTER: 180° less Item 3, above J^.° 7 5. DRAW straight line(s) through reference point on heading(s) (measured clockwise from North) shown above. EXTEND the resulting satellite track(s) on both sides of the reference point and MARK satellite direction(s) with arrowhead(s). In the example given above, the grid appears to be upside-down. Inspection will show, however, that the latitudes along the right-hand margin are correct for a station that is south of the equator. Note that both arrows point to the east. The grid for a westward-moving satellite (negative orbit inclination) would be plotted in a similar way. Table IV should not be used for deriving the heading of satellites having negative inclination, since correction for the observer's motion has been subtracted from rather than added to the eastwest component of the satellite's motion. The line that points away from the equator and toward the pole will in either event represent the path of the satellite at prime sweep times. Where reference latitude is numerically equal to orbit inclination, there is only one heading, and only one line cross ing the central meridian at 90°. The satellite tracks for 1958 Epsilon may be used for any pass of the satellite near Lima, Peru. The additional marks on the grid shown above are pertinent only to the specific pass under consideration. It is suggested that observers mark specific positions for a specific pass described in a Schedule H computation with a grease pencil on a transparent overlay. In this way, one grid may be used again and again for a given satellite and station location. How the grid is used is illustrated in the following: 12 Schedule H—To Obtain Azimuth, Elevation, Slant Range and Passage Times 1. LOCATE Observer's relative position on plotting grid using station latitude (given) and relative longitude (from Schedule G, Item 6). 2. SELECT Point (s) of observational Sub-Satellite Point(s) of Observational Interest interest along satellite track Point of 3. DRAW LINE(S) from observer's Nearest Meridian relative position to selected point (s) Approach Passage Alt #1 Alt ^2 4. MEASURE clockwise from North the angular distances(s) from ob server's position to point(s) of in000° or terest, and ENTER as Azimuth ° 4W> 0 ° 5. MEASURE distance(s) from ob server's position to point(s) of in terest, SCALE OFF on meridian to read in degrees of arc and ENTER as Distance(s) from observer in degrees f.... 3* 6. MEASURE along satellite track from reference point to point(s) of interest, SCALE OFF on meridian to read in degrees of arc and ENTER as adjustment(s) to position +(-) !.... Jf(-).A.°3. + (-) +(-) 7. ADD Current perigee distance (from 83?? Schedule F, Item 7) + ". . . 8. Perigee distance(s) relative to points of interest TURN TO Table III opposite perigee position(s) found in Item 8 (above) and under given orbit eccentricity, FIND and ENTER: 9. Equivalent fraction(s) of period 0. 0. /° 7.. 0. 0. 10. Radial distance factor s 11. MULTIPLY radial distance factor (Item 10, above) by radial distance at perigee (given) X m' X V/23.^m j X "J X 12. Radial distance(s) of satellite from center of the earth "1 13. SUBTRACT Mean radius of Earth (3959 mi.) or radius at station »1 - 3lp3 - i - 1 -. Satellite height(s) above point(s) of interest m1 14. USING Satellite heights (from Item 13, above) and distance(s) from ob server in degrees (from Item '5, above) ENTER "Chart for Deter mining Elevation and Slant Range" . a. . adtmv i Elevation(s) ?.... k±?.Q to OBTAIN^. L*4r\ *■ (Slant range(s) " 1. ...M..1.U.. 15. MULTIPLY Equivalent fraction of period (Item 9, above) by (Current perigee-toperigee period) and ENTER 16. SUBTRACT Time required for satellite to travel from current peri gee position to reference point (Schedule F, Item 10) - Z! ? 3. ?.17. Time interval (s) between satellite passage over point(s) of interest and satellite passage over reference point +( — ) if (— ) ....(f..9.8. +( — ) "... +( — ) t— 18. ADD Time when satellite passes over reference latitude (from Schedule F. Item 13 or 15) + h ?. - + M Q5? 8. + h ?.... + h ?... 19. Time(s) of satellite passage over point (s) of interest h /JL\.j05VQ h ? h ».„ 20. Satellite in sunlight (from Table V) Yes No (Yep No Yes No Yes No 21. Sky Dark at station (from Table VI) Yes (Ro) 13 Item 19 of Schedule H, above indicates that the satellite was predicted to pass across the station's meridian at 14*1 05 m0, station time. The station time of the pass as actually observed at Lima, Peru was 14" 04^4. Items 20 and 21 of Schedule H, above, are of interest only to persons making photographic or visual sightings. Although the tables are extensive, the answers required are of the yes -no type. The sky is either dark enough to make an observation or it isn't. In general, the sky will be too bright after the end of nautical twilight in the morning, and before the beginning of nautical twilight in the evening. These times may be found in Table VI. Similarly, the satellite will not be visible (unless it is self-luminous because of friction or for other reasons) except when the sun is shining at the latitude and height through which the satellite is traveling. The longitude of the satellite is taken into account in determining local mean time for Table V. The longitude of the station is taken into account in determining local mean time for Table VI. In the example shown, the local mean time of the subsatellite point of interest was identical to the local mean time of the observer. Local mean time varies uniformly, increasing four minutes of time for every degree of easterly longitude; but in the example given, both the observer and the subsatellite point of interest were on the same meridian. The relation between station time and local mean time of the observer was found through the following generalized formula: TO FIND RELATION OF LOCAL MEAN TIME OF OBSERVER TO STATION TIME (ST) 1. ENTER: Number of hours Greenwich mean time is ahead of station time (ST) + 05^00 2. MULTIPLY above by 15° /hour 3. Longitude of central meridian of station time zone 75 ? 00 W 4. SUBTRACT station longitude - 5. Longitude of station east of central meridian , ^(-) 6. MULTIPLY above by 77? 15 W 2? 15 E 4^00 /° 7. Local mean time of observer EQUALS station time (ST) 4/ (-) 8™6 The plotting grid will always show on its face how far the observer is expected to be east or west of subsatellite points of interest. If the observer is N degrees east of a subsatellite point of interest, then the local mean time of that subsatellite point is (4 TIMES N) minutes earlier than the local mean time of the observer. Similarly, if the observer is N degrees west of a subsatellite point of interest, then the local mean time of that subsatellite point is (4 TIMES N) minutes later than the local mean time of the observer. 14 CHART FOR DETERMINING ELEVATION 8 SLANT RANGE OF SATELLITE ALL DSTANCES ARE IN STATUTE MILES - 5 STATUTE MILES EQUAL APPROXIMATELY 8 KILOMETERS. The above reproduction illustrates how the computed height of 590 miles (Item 13) and the measured angular distance from observer to the subsatellite point of interest of 3?4 (Item 5) were used in finding that the satellite would appear at an elevation of 65. 0 above the observer's horizon, and would be at a slant range distance of 630 statute miles from the observer. 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20° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 20° NORTH LATITUDE SUNRISE. (20* R) Satellite JAN 19 FEB 22 HAS 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 Heights h m h m h m h m h m h m b m b ■ h m h ■ h ■ 05 21 05 12 04 52 04 27 04 02 03 58 04 11 04 28 04 36 04 42 04 56 200 ml 300 ml 05 05 04 56 04 36 04 10 03 43 03 38 03 53 04 11 04 20 04 27 04 40 400 ml 04 51 04 43 04 22 03 56 03 27 03 22 03 37 03 57 04 06 04 14 04 26 500 ml 04 39 04 31 04 11 03 49 03 13 03 06 03 23 03 45 03 55 04 02 04 14 04 29 04 21 04 00 03 32 03 00 02 53 03 10 03 33 03 44 03 52 04 04 600 sd 700 ml 04 20 04 12 03 52 03 23 02 48 02 41 02 58 03 24 03 36 03 43 03 55 800 ml M 12 04 05 03 43 03 14 02 37 02 29 02 47 03 15 03 27 03 36 03 47 900 ml 04 05 03 57 03 36 03 05 02 28 02 17 02 38 03 06 03 20 03 28 03 40 1000 ml 03 58 03 50 03 29 02 58 02 18 02 06 02 28 02 59 03 13 03 21 03 33 1100 ad 03 51 03 44 03 22 02 50 02 08 01 55 02 18 02 51 03 06 03 15 03 26 03 45 03 38 03 16 02 43 02 00 01 44 02 10 02 44 03 00 03 09 03 20 1200 ml 1300 mi 03 40 03 32 03 10 02 36 01 50 01 33 02 00 02 37 02 54 03 03 03 15 03 35 03 28 03 03 02 30 01 42 01 22 01 52 02 31 02 49 02 59 03 10 1400 ml 1500 sd 03 29 03 23 03 00 02 24 01 33 01 10 01 43 02 26 02 44 02 54 03 04 swsr: (20* H) Satellite JAN Heights h 200 ■1 19 19 300 ml 400 ■1 19 19 500 ad 600 ml 19 700 mi 20 800 ml 20 20 900 al 1000 ml 20 20 1100 mi 1200 ml 20 20 1300 ml 20 1400 ml 1500 ml 20 DATES DEC h 05 04 04 04 04 04 04 03 03 03 03 03 03 03 22 ■ 11 56 42 30 20 10 02 54 47 41 34 29 24 19 19 FEB 22 MAI 21 APR 16 max 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 m h m h ■ b m h m h m h m h m h m h m h m h m 00 19 16 19 24 19 34 19 53 20 06 20 06 19 34 19 08 18 47 18 36 18 45 17 19 32 19 40 19 so 20 09 20 26 20 19 19 51 19 24 19 03 18 52 19 00 31 19 45 19 54 20 04 20 25 20 42 20 35 20 05 19 38 19 16 19 06 19 14 43 19 57 20 05 20 16 20 39 20 58 20 49 20 17 19 49 19 28 19 18 19 26 53 20 07 20 16 20 28 20 52 21 11 21 02 20 29 20 00 19 38 19 28 19 36 02 20 16 20 24 20 37 21 04 21 23 21 14 20 38 20 08 19 47 19 37 19 46 10 20 23 20 33 20 46 21 15 21 35 21 25 20 47 20 17 19 54 19 45 19 54 17 20 31 20 40 20 55 21 24 21 47 21 34 20 56 20 24 20 02 19 52 20 02 24 20 38 20 47 21 02 21 34 21 58 21 44 21 03 20 31 20 09 19 59 20 09 31 20 44 20 54 21 10 21 44 22 09 21 54 21 ll 20 38 20 15 20 06 20 15 37 20 50 21 00 21 17 21 52 22 20 22 02 21 18 20 44 20 21 20 12 20 22 42 20 S6 21 06 21 24 22 02 22 31 22 12 21 25 20 so 20 27 20 17 20 27 47 21 00 21 11 21 30 22 10 22 42 22 20 21 31 20 55 20 31 20 22 20 32 53 21 05 21 16 21 36 22 19 22 54 22 29 21 37 21 00 20 36 20 28 20 37 TABLE V - 20° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 20° SOUTH LATITUDE SUNRISE (20* S) Satellite JAN 19 FEB 22 MM 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCX 20 NOV 22 DEC 22 h m h m h m h ■ h m h m h m Heights h m h m h ■ h ■ b ■ 50 05 06 05 200 ■d 04 14 04 40 04 04 37 OS 14 16 05 00 04 36 04 05 03 52 03 54 03 58 04 24 04 36 04 42 04 50 05 00 05 00 04 43 04 20 03 55 03 33 03 34 300 ml 03 42 04 10 04 22 04 29 04 36 04 46 04 46 04 30 04 06 03 41 03 17 03 18 400 mi 500 mi 03 28 03 58 04 11 04 17 04 24 04 34 04 34 04 18 03 55 03 29 03 03 03 02 600 ml 03 15 03 46 04 00 04 07 04 14 04 24 04 24 04 08 03 44 03 17 02 50 02 49 700 mi 03 03 03 37 03 52 03 58 04 05 04 14 04 15 03 59 03 36 03 08 02 38 02 37 02 52 03 28 03 43 03 SI 03 57 04 06 04 07 03 52 03 27 02 59 02 27 02 25 800 mi 900 ml 02 43 03 19 03 36 03 43 03 50 03 58 04 00 03 44 03 20 02 50 02 18 02 13 1000 ml 02 33 03 12 03 29 03 36 03 43 03 51 03 53 03 37 03 13 02 43 02 08 02 02 02 23 03 04 03 22 03 30 03 36 03 45 03 46 03 31 03 06 02 33 01 sa 01 51 1100 ml 02 15 02 57 03 16 03 24 03 30 03 38 03 40 03 23 03 00 02 28 01 so 01 40 1200 ml 1300 ■1 02 05 02 50 03 10 03 18 03 25 03 33 03 35 03 19 02 54 02 21 01 40 01 29 1400 sd 01 57 02 44 03 05 03 14 03 20 03 28 03 30 03 15 02 49 02 IS 01 32 01 18 1500 ml 01 48 02 38 03 00 03 09 03 14 03 23 03 24 03 10 02 44 02 09 01 23 01 06 surerr (20* s) Satellite JAN Heights h 200 sd 20 20 300 sd 400 sd 20 20 500 sd 21 600 al 21 700 ml ml 800 21 900 sd 21 1000 ■1 21 21 1100 sd 1200 sd 22 22 1300 ■1 1400 sd 22 22 1500 ad 19 FEB 23 MAI 21 API 16 KAY 21 JUN 22 JUL 24 AUG 28 8D 24 OCT m h ■ h m h m h m h m b m h m h h m 07 19 46 19 23 19 03 18 35 18 48 18 56 19 08 19 13 19 24 20 04 19 40 19 18 19 02 19 04 19 12 19 19 19 24 19 40 20 18 19 54 19 31 19 16 19 18 19 26 19 32 19 38 19 54 20 30 20 05 19 43 19 28 19 30 19 38 19 44 19 49 20 07 20 42 20 16 19 53 19 38 19 40 19 48 19 54 20 00 20 19 20 51 20 24 20 02 19 47 19 50 19 57 20 03 20 08 20 30 21 00 20 33 20 19 19 55 19 58 20 05 20 10 20 17 20 39 21 09 20 40 20 17 20 02 20 06 20 12 20 18 20 24 20 49 21 16 20 47 20 24 20 09 20 13 20 19 20 25 20 31 20 59 21 24 20 54 20 30 20 16 20 19 20 26 20 31 20 38 20 07 21 31 21 00 20 36 20 22 20 26 20 32 20 37 20 44 21 17 21 38 21 06 20 42 20 37 20 31 20 37 20 43 20 SO 21 25 21 44 21 11 20 46 20 42 20 36 20 42 20 47 20 55 21 34 21 50 21 16 20 51 20 48 20 41 20 48 20 52 21 00 21 "For locoI moon Mm of ■ofolllto, SUBTRACT from locoI moon tlmo of ooaorvor 4m/° thai obsorvo* U EAST. 33 20 NOV 22 DEC 22 m h m b ■ 20 19 43 19 56 35 19 59 20 22 49 20 15 20 38 01 20 29 20 54 13 20 42 21 07 22 20 54 21 19 31 21 OS 21 31 40 21 14 21 43 47 21 24 21 54 55 21 34 22 05 02 21 42 22 16 09 21 52 22 27 13 22 00 22 38 21 22 09 22 50 319V1 A - 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"1SV3 TABLE V - 35° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 35° NORTH LATITUDE SUNRISE (35* H) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 BET 24 OCX 20 NOV 22 Heights h m h m h ■ h m h m h m h m h m h ■ h m h ■ 200 ml 05 38 05 15 04 39 04 00 03 13 02 56 03 22 03 59 04 24 04 45 05 12 300 ml 05 19 04 56 04 21 03 38 02 47 02 31 02 57 03 39 04 05 04 27 04 54 400 ml 05 04 04 41 04 05 03 20 02 24 02 04 02 34 03 21 03 49 04 12 04 39 500 mi 04 51 04 28 03 51 03 04 02 02 01 36 02 12 03 05 03 35 03 59 04 26 600 ml 04 39 04 16 03 39 02 50 01 40 01 03 01 50 02 51 03 23 03 47 04 14 700 mi 01 26 02 37 03 12 03 37 04 04 04 29 04 06 03 28 02 36 01 16 III 800 mi 00 57 02 24 03 01 03 27 03 55 04 20 03 56 03 17 02 23 00 47 III 900 mi 04 12 03 47 03 08 02 10 02 11 02 52 03 18 03 47 III III III 1000 mi 04 04 03 40 02 59 01 58 01 59 02 43 03 11 03 39 III III III 03 37 03 32 02 50 01 46 1100 mi 01 47 02 34 03 03 03 32 III III III 1200 mi 03 50 03 25 02 42 01 33 01 34 02 26 02 56 03 25 III III III 1300 mi 03 43 03 19 02 34 01 20 01 21 02 18 02 50 03 18 III III III 03 L2 02 26 01 1400 mi 03 37 10 01 11 02 10 02 43 03 12 III III III 03 1500 ml 32 03 06 02 19 00 49 00 so 02 03 02 37 03 07 III III III SUNSET (35'' N) Satellite JAN Heights h 18 200 mi 300 ml 19 400 mi 19 19 500 mi 19 600 ml 700 mi 19 20 800 ml 20 900 mi 1000 ml 20 1100 ml 20 1200 mi 20 1300 ml 20 1400 mi 20 20 1500 mi DATES DEC h 05 05 04 04 04 04 04 04 03 03 03 03 03 03 22 ■ 33 16 59 46 34 24 15 06 59 52 41 38 33 27 19 FEB 22 MAR 21 APR 16 HAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 m h m h m h m h ■ h m h m h m h m h m h m h m 02 20 42 21 04 20 50 20 02 19 16 18 44 18 20 18 24 43 19 14 19 37 20 03 19 32 19 55 20 22 21 05 21 33 21 15 20 23 19 39 19 03 18 38 18 40 18 19 47 20 11 20 40 21 28 22 00 21 38 20 41 19 53 19 18 18 S3 18 57 31 20 00 20 25 20 56 21 50 22 28 22 00 20 57 20 09 19 31 19 06 19 10 43 20 12 20 37 21 10 22 12 23 01 22 22 21 11 20 21 19 43 19 18 19 22 22 46 21 26 20 32 19 S3 19 28 19 32 53 20 22 20 48 21 24 22 36 III 02 20 32 20 59 21 37 23 05 23 15 21 38 20 43 20 03 19 37 19 41 III 10 20 41 21 08 21 50 21 51 20 52 20 12 19 45 19 50 III III III 18 20 48 21 17 22 02 22 03 21 01 20 19 19 53 19 57 III III III 22 15 21 10 20 27 20 00 20 04 25 20 56 21 26 22 14 III III III 32 21 03 21 34 22 27 22 28 21 18 20 34 20 07 20 15 III III III 39 21 09 21 42 22 40 22 41 21 26 20 40 20 14 20 18 III III III 45 21 16 21 50 22 50 22 51 21 34 20 47 20 20 20 23 III III III 50 21 22 21 37 23 11 23 13 21 41 20 53 20 25 20 29 III III III TABLE V- 35° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 35° SOUTH LATITUDE SUNRISE (35* S) Satellite JAN 19 FEB 22 MAR 21 APR 16 MAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h m h ■ h m h m h m h m n m h m h m h ■ h ■ 200 mi 03 24 04 10 04 38 04 59 05 22 05 36 05 33 05 02 04 23 03 42 03 03 02 57 300 mi 03 02 03 52 04 21 04 42 OS 04 05 20 05 14 04 43 04 OS 03 23 02 37 02 27 400 mi 02 39 03 34 04 05 04 27 04 49 05 03 04 59 04 28 03 49 03 05 02 14 02 00 500 mi 02 17 03 18 03 51 04 14 04 36 04 50 04 46 04 IS 03 35 02 49 01 52 01 32 600 mi 01 55 03 04 03 39 04 02 04 24 04 38 04 34 04 03 03 23 02 35 01 30 00 59 700 mi 01 31 02 50 03 28 03 52 04 14 04 28 04 24 03 53 03 12 02 21 01 06 /// 800 ml 01 02 02 37 03 17 03 42 04 05 04 19 04 15 03 43 03 01 02 08 00 37 /// 900 mi 02 24 03 08 03 33 03 57 04 10 04 07 03 34 02 52 01 55 /// III /// 1000 mi 02 12 02 59 03 26 03 49 04 03 03 59 03 27 02 43 01 43 III III /// 02 00 02 50 03 18 03 42 03 56 03 52 03 19 02 34 01 31 1100 mi III III /// 1200 mi 01 47 02 42 03 11 03 35 03 45 03 45 03 12 02 26 01 18 III III /// 1300 mi 01 34 02 34 03 05 03 28 03 42 03 38 03 06 02 18 01 05 III III /// 1400 mi 01 24 02 26 02 58 03 22 03 37 03 32 02 59 02 10 00 55 III III /// 1500 mi 01 03 02 19 02 52 03 17 03 31 03 27 02 53 02 03 00 34 III III /// SUNSET (35'' 8) Satellite JAN 19 FEB 23 MAR 21 APR 16 KAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT Heights h m h m h m h m h ■ h ■ h ■ h m h ■ h 20 56 20 14 19 41 19 00 18 30 18 26 18 42 19 03 19 23 19 200 mi 300 ml 21 20 20 36 19 55 19 18 18 48 18 44 18 58 19 19 19 37 20 21 43 20 54 20 11 19 33 19 03 19 01 19 13 19 34 19 55 20 400 mi 22 05 21 10 20 15 19 46 19 16 19 14 19 26 19 47 20 08 20 500 mi 22 27 21 24 20 37 19 58 19 28 19 26 19 38 19 59 20 21 20 600 mi 700 mi 22 51 21 38 20 48 20 08 19 38 19 36 19 48 20 09 20 32 21 800 mi 23 20 21 51 20 59 20 18 19 47 19 45 19 57 20 19 20 43 21 900 mi 22 04 21 08 20 27 19 55 19 54 20 05 20 28 20 52 21 /// 1000 mi 22 16 21 17 20 34 20 03 20 01 20 13 20 35 21 01 21 /// 22 28 21 26 20 42 20 08 20 08 20 20 20 43 21 10 21 1100 mi /// 22 41 21 34 20 49 20 17 20 19 20 27 20 so 21 18 22 1200 ml /// 1300 mi 22 54 21 42 20 55 20 24 20 22 20 34 20 56 21 26 22 /// 23 04 21 40 21 02 20 30 20 27 20 40 21 03 21 34 22 1400 mi /// 1500 mi 23 25 21 57 21 08 20 35 20 33 20 45 21 09 21 42 22 /// 'Fof local nMn tin* of sotolllto, SUBTRACT from local nan timo of obtorvor 4m/° rhot obsorvor U EAST. 35 20 NOV 22 DEC 22 m h m h ■ 48 20 30 21 01 07 20 55 21 29 25 21 18 21 56 41 21 40 22 24 55 22 02 22 57 09 22 26 /// 22 22 55 /// 35 III /// 47 III /// 59 III /// 12 III /// 25 III /// 50 III /// 56 /// III TABLE V - 40° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 40° NORTH LATITUDE SUNRISE (40* I) Satellite JAN 19 FEB 23 MM 21 APE 16 HAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OR 20 NOV 22 DEC 22 Heights h ■ h m h ■ h m h m h ■ h m h m b m h m h m h m 200 ml 05 44 05 14 04 33 03 32 02 48 02 28 02 56 03 45 04 17 04 44 OS 17 05 40 300 mi 05 23 04 54 04 13 03 22 02 17 01 51 02 27 03 23 03 57 04 25 04 58 05 21 400 ml 05 07 04 38 03 56 03 01 01 46 01 05 01 56 03 02 03 40 04 09 04 42 05 05 500 mi 04 33 04 24 03 40 02 43 01 13 01 23 02 44 03 24 03 55 04 28 04 50 III 600 ml 04 43 04 11 03 26 02 25 00 20 00 30 02 26 03 10 03 42 04 18 04 38 III 700 ml 04 30 04 00 03 14 02 08 02 09 02 58 03 31 04 05 04 29 III III III 800 ml 04 20 03 50 03 02 01 52 01 53 02 46 03 21 03 55 04 17 III III III 900 ml 04 11 03 41 02 51 01 34 01 35 02 35 03 12 03 46 04 08 III III III 1000 ml 04 03 03 32 02 41 01 16 01 17 02 25 03 03 03 38 04 00 III III III 1100 ml 03 55 03 24 02 30 00 54 00 55 02 14 02 55 03 30 03 52 III III III 1200 ml 03 48 03 16 02 21 III 02 05 02 47 03 23 03 45 III III III III 1300 ml 03 41 03 08 02 11 01 57 02 39 03 16 03 38 III III III III III 1400 ml 03 35 03 01 02 02 III 01 46 02 32 03 10 03 32 III III III III 1500 mi 03 29 02 54 01 32 III 01 36 02 25 03 04 03 26 III III III III SUNSET (40* H) Satellite JAH Heights h 200 ml 18 300 mi 18 400 mi 19 500 ml 19 600 ml 19 700 ml 19 600 ml 20 900 ml 20 1000 ml 20 1100 ml 20 1200 mi 20 1300 mi 20 1400 mi 20 1500 mi 20 19 FEB 22 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 m h m h m h m h m h m h m h ■ h ■ h m h m h m 39 19 12 19 44 20 16 21 06 21 35 21 14 20 16 19 26 18 44 18 14 18 16 59 19 34 20 03 20 38 21 35 22 11 21 45 20 39 19 47 19 05 18 34 18 35 75 19 so 20 20 20 59 22 06 22 59 22 16 21 00 20 04 19 21 18 50 18 51 29 20 04 20 36 21 17 22 39 22 49 21 18 20 20 19 35 19 04 19 06 III 23 42 21 36 20 34 19 48 19 14 19 18 39 20 17 20 50 21 35 23 32 III 52 20 28 21 02 21 52 21 53 20 46 19 59 19 27 19 27 /// III III 02 20 38 21 14 22 08 22 09 20 58 20 09 19 37 19 39 III III III 22 27 21 09 20 18 19 46 19 48 11 20 47 21 25 22 26 III III III 22 45 21 19 20 27 19 54 19 56 19 20 56 21 35 22 44 III III III 27 21 04 21 46 23 06 23 17 21 30 20 35 20 02 20 04 III III III 34 21 12 21 55 21 39 20 43 20 09 20 11 III III III III III 41 21 20 22 05 21 49 20 51 20 16 20 18 III III III III III 47 21 27 22 14 21 58 20 58 20 22 20 24 III III III III III 53 21 34 22 24 22 08 21 05 20 28 20 30 III III III III III TABLE V - 40° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 40° SOUTH LATITUDE SUNRISE (40* S) Satellite JAN 19 FEB 22 MAR 21 APR 16 HAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h m b m h m h tn h m h m b m h m h m h m h m 02 58 03 56 04 31 04 58 05 27 05 43 05 39 OS 03 04 17 03 33 02 38 02 25 200 ml 300 mi 02 32 03 36 04 13 04 40 05 04 OS 25 05 18 04 41 04 05 03 07 02 07 01 47 02 01 03 IS 03 56 04 24 04 52 05 09 05 02 04 25 03 48 02 46 01 36 01 01 400 ml 01 28 02 57 03 40 04 10 04 38 04 54 04 48 04 11 03 32 02 28 01 03 500 mi /// 600 mi 00 35 02 39 03 26 03 57 04 28 04 42 04 38 03 58 03 18 02 10 00 10 /// 700 mi 02 22 03 14 03 46 04 IS 04 33 04 25 03 47 03 06 01 53 III III /// 02 54 01 37 800 mi 02 06 03 02 03 36 04 OS 04 21 04 IS 03 37 III /// III 02 43 01 19 900 ml 01 48 02 SI 03 27 03 56 04 12 04 06 03 28 III /// III 03 02 18 58 03 19 33 01 01 1000 mi 01 30 02 41 03 03 48 04 04 III /// III 22 00 02 39 02 30 03 10 03 40 03 56 03 so 03 11 1100 ml 01 08 III /// III 02 02 02 03 49 03 43 03 03 13 1200 mi 21 03 03 33 III III /// III III 02 26 03 42 36 02 02 03 1300 mi 02 11 54 03 03 55 III III III /// III 03 30 02 48 02 03 20 36 03 01 54 1400 ml 02 02 47 III III III /// III 1500 mi 01 52 02 40 03 14 03 30 03 24 02 41 01 48 III III III /// III SUNSET (40* S) Satellite JAN 19 FEB 23 MAI 21 APR 16 MAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h ■ h m h m h ■ h m h m h m h m Heights h m h m b m 21 22 20 28 19 39 18 65 18 25 18 20 18 29 19 06 19 35 20 13 20 56 21 38 200 mi 21 50 20 52 20 03 19 20 18 44 18 39 18 54 19 21 19 47 20 23 21 25 22 09 300 mi 22 21 21 13 20 20 19 36 19 00 18 55 19 10 19 37 20 04 20 44 21 56 22 55 400 ml 22 54 21 31 20 36 19 50 19 14 19 20 19 24 19 51 20 20 21 02 22 29 /// 500 mi 600 mi 23 47 21 49 20 SO 20 03 19 24 19 22 19 34 20 04 20 38 21 20 23 22 /// III 700 mi 22 06 21 02 20 14 19 37 19 31 19 47 20 15 20 46 21 37 /// III 22 22 21 14 20 24 19 47 19 43 19 57 20 25 20 58 21 53 III /// 800 ml III III 22 40 21 25 20 33 19 56 19 52 20 06 20 34 21 09 22 11 /// 900 ml III 22 58 21 35 20 42 20 04 20 00 20 14 20 43 21 19 22 29 III /// 1000 ml III 23 20 21 46 20 50 20 12 20 08 20 22 20 51 21 30 22 51 III /// 1100 mi III III /// 21 S3 20 58 20 19 20 15 20 29 20 59 21 37 /// 1200 ml III III 22 05 21 06 20 26 20 22 20 36 21 07 21 49 /// III /// 1300 mi III III 22 14 21 13 20 32 20 28 20 42 21 14 21 58 III /// 1400 ml /// III III 1500 mi 22 24 21 20 20 38 20 34 20 48 21 21 22 08 III /// /// III III ■For local moon tint* of ■atollrto, SUBTRACT from local moon tlmo of obiorvor 4m/° thot obrtorvor It EAST. 36 TABLE V - 45° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 45° NORTH LATITUDE SUNIISE (45* N) Satellite JAM 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 on 20 ■Of 22 h m h m h m h ■ h m h ■ h ■ h m b a h m h m Heights 05 49 05 13 04 2 5 03 28 02 13 01 40 02 22 03 27 04 09 04 42 05 22 200 mi 01 39 03 01 03 46 04 22 05 02 300 mi 05 27 04 51 04 02 03 00 01 29 /// 00 32 02 37 03 27 04 05 04 44 400 mi 05 09 04 34 03 43 02 36 00 22 III 02 14 03 10 03 49 04 29 III 500 mi 04 54 04 18 03 26 02 13 III III 01 50 02 54 03 35 04 16 600 ml III 04 41 04 04 03 10 01 49 III III 01 25 02 39 03 23 04 04 700 mi 04 29 03 52 02 55 01 24 III III III 00 54 02 25 03 11 03 54 04 19 03 40 02 41 00 53 800 mi III III III 02 12 03 01 03 44 III 900 mi 04 09 03 30 02 28 III /// III III 01 38 02 51 03 35 1000 mi 04 00 03 20 02 14 III III III III /// 01 45 02 42 03 26 03 51 03 11 02 01 1100 mi III III III III III 01 32 02 33 03 18 1200 mi III 03 43 03 02 01 48 III III III III 01 18 02 24 03 11 III 1300 mi 03 36 02 53 01 34 III III III III 01 02 02 16 03 04 1400 mi 03 29 02 45 01 18 III III III III III 00 45 02 08 02 57 1500 mi III III 03 22 02 37 01 01 III III III SUNSET (45* N) Satellite JAN h Heights 200 mi 18 18 300 mi 19 400 ml 500 mi 19 600 mi 19 700 mi 19 20 800 mi 20 900 mi 20 1000 mi 20 1100 ml 1200 mi 20 20 1300 ml 20 1400 mi 21 1500 ml DATES DEC h 05 05 05 04 04 04 04 04 04 03 03 03 03 03 22 ■ 46 27 10 54 41 29 18 09 00 51 44 36 29 23 19 FEB 22 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 ■0* 22 DEC 22 h m h ■ h m b m h m h m h ■ b ■ m h m h m h m 32 19 15 19 52 20 34 21 42 22 23 21 48 20 32 19 33 18 46 18 09 18 09 22 33 21 01 19 58 19 08 18 30 18 29 55 19 37 20 14 21 00 22 23 /// 23 40 21 25 20 17 19 25 18 48 18 46 13 19 54 20 33 21 24 23 30 /// 21 48 20 34 19 41 19 03 19 02 28 20 10 20 50 21 47 /// III III 22 12 20 50 19 55 19 16 19 15 41 20 24 21 06 22 11 III III III 22 37 21 05 20 07 19 28 19 27 53 20 36 21 21 22 36 III III III 23 08 21 19 20 19 19 38 19 38 03 20 48 21 35 23 07 III III III 21 32 20 29 19 48 19 47 13 20 58 21 48 III III III III III 21 46 20 39 19 57 19 56 22 21 08 22 02 III III III III III 17 21 59 20 48 20 06 20 05 21 15 31 21 III III III III III 22 22 12 20 57 20 14 20 12 21 26 28 39 III III III III III 22 26 21 06 20 21 20 20 46 21 35 22 42 III III III III III 22 42 21 14 20 28 20 27 53 21 43 22 58 III III III III III 22 59 21 22 20 35 20 33 00 21 51 23 15 III III III III III TABLE V - 45° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 45° SOUTH LATITUDE SUNRISE (45* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 HAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h Heights h m h m h m h m h m h m b in h m h m h ■ h m 200 mi 02 22 03 39 04 24 04 57 05 32 05 49 OS 45 OS 01 04 10 03 13 02 03 01 37 300 mi 01 44 03 14 04 02 04 37 05 12 05 31 05 22 04 38 03 46 02 45 01 19 III 400 mi 00 37 02 50 03 43 04 20 04 54 05 14 05 04 04 21 03 27 02 21 00 12 III 02 27 03 26 04 04 04 39 04 58 04 49 04 05 03 10 01 58 500 ml /// III III 600 mi 02 00 03 10 03 50 04 26 04 45 04 36 03 51 02 54 01 34 /// III III 700 mi 01 38 02 55 03 38 04 14 04 33 04 24 03 39 02 39 01 09 /// III III 800 mi 01 07 02 41 03 26 04 04 04 22 04 14 03 27 02 25 00 38 /// III III 900 ml 02 28 03 16 03 54 04 13 04 04 03 17 02 12 /// /// III III III 1000 mi 02 14 03 06 03 45 04 04 03 55 03 07 01 58 /// III III III III 1100 mi 02 01 02 57 03 36 03 55 03 46 02 58 01 45 III /// III III III 1200 ml 01 48 02 48 03 28 03 48 03 38 02 49 01 32 III /// III III III 1300 mi 01 34 02 39 03 21 03 40 03 31 02 40 01 18 III /// III III III 1400 mi 01 18 02 31 03 14 03 33 03 24 02 32 01 02 /// III III III III 1500 mi 01 01 02 23 03 07 03 27 03 17 02 24 00 45 III /// III III III SUNSET (45* 8) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights li m h m h ■ h m b m h m h m h m b m h m h m h m 200 ml 21 57 20 44 19 48 19 01 18 29 18 12 18 29 19 03 19 37 20 19 21 32 22 20 300 mi 22 38 21 14 20 14 19 23 18 40 18 33 18 so 19 24 19 58 20 45 22 13 /// 400 mi 23 45 21 38 20 33 19 40 18 58 18 50 19 08 19 41 20 17 21 09 23 20 /// 500 ml 22 01 20 50 19 04 19 13 19 06 19 23 19 37 20 34 21 32 /// /// /// 21 28 21 06 20 10 19 26 19 19 19 36 20 11 20 50 21 56 600 ml /// III /// 21 21 700 mi 22 50 20 22 19 38 19 31 19 48 20 23 21 05 22 21 /// III /// 800 mi 23 21 21 35 20 34 19 48 19 42 19 58 20 35 21 19 22 52 /// III /// 44 900 ml 21 48 20 19 58 19 51 20 04 20 45 21 32 /// /// III III /// 22 1000 mi 02 06 20 07 00 20 20 17 20 21 20 46 55 III /// III III /// 22 20 1100 ml 03 20 21 15 21 20 16 09 26 04 21 59 III /// III III /// 1200 mi 22 21 12 20 20 28 20 24 16 12 34 21 22 III 13 /// III III /// 1300 mi 22 20 24 42 21 21 31 20 21 22 26 III 20 41 22 /// III III /// 1400 mi 22 58 21 29 20 38 20 31 20 48 21 30 22 42 /// III III III /// 1500 ml 23 15 21 37 20 45 20 37 20 SS 21 38 22 59 III /// III III /// •For local mon tlmo of •atolltto, SUBTRACT from local mean rime of obitfvw 4m/° thai obtarvor It EAST. 37 TABLE V - 50° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 50° NORTH LATITUDE SUNRISE (SO* N) Satellite JAN 1* FEB 22 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 0CI 20 ■Of 22 Heights h m h m a m h ■ h ■ h m h m h m h m h m h m 200 ml 05 55 05 10 04 14 03 05 01 11 01 20 03 04 03 57 04 40 OS 27 /// 300 ml 05 31 04 47 03 48 02 30 02 31 03 32 04 18 OS 06 III III III 400 mi 05 11 04 27 03 26 01 58 01 59 03 10 03 58 04 46 III III III 500 ml 04 55 04 10 03 05 01 22 01 23 02 49 03 41 04 30 III III III 600 ml 00 27 02 30 03 25 04 15 04 40 03 54 02 46 00 26 III III III 04 27 03 40 02 28 700 mi 02 12 03 11 04 02 III III III III III 800 mi 04 15 03 27 02 09 01 53 02 58 03 50 III III III III III 04 04 03 14 01 50 900 ml III 01 34 02 45 03 39 III III III III 03 54 02 58 01 30 1000 mi 01 14 02 29 03 29 III III III III III 00 SO 02 23 03 20 1100 ml 03 45 02 52 01 06 III III III III III 1200 mi 03 35 02 40 00 25 00 09 02 11 03 10 III III III III III 03 27 02 30 02 01 03 02 1300 mi HI tit III III III III III 1400 mi 03 19 02 19 01 50 02 54 III III III III III III III 1500 mi 01 40 02 46 03 11 02 09 III III III III III III III SUNSET (50* N) Satellite JAN Heights h 200 mi 18 300 mi 18 400 ml 19 500 ml 19 600 mi 19 700 ml 19 800 ml 20 20 900 ml 1000 ml 20 20 1100 mi 1200 ml 20 1300 ml 20 1400 mi 21 1500 mi 21 DATES DEC h 05 05 05 04 04 04 04 04 03 03 03 03 03 03 22 m S6 34 14 57 42 30 18 07 57 48 39 35 23 16 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 ra h m h m h m h ■ h m b m b m b m h m h m h tn 22 48 20 55 19 44 18 48 18 04 18 00 28 19 19 20 04 20 58 22 47 III 21 30 20 12 19 12 18 26 18 22 SI 19 41 20 28 21 30 III III III 22 02 20 34 19 32 18 46 18 42 11 20 01 20 50 22 02 III III III 22 38 20 55 19 49 19 02 18 59 27 20 18 21 11 22 38 III III III 23 34 21 14 20 OS 19 17 19 14 42 20 34 21 30 23 34 III III III 21 32 20 19 19 30 19 26 55 20 48 21 48 III III III III III 07 21 01 22 07 21 SI 20 32 19 42 19 38 III III III III III 18 21 14 22 26 22 10 20 45 19 53 19 49 III III III III III 28 21 30 22 46 22 30 21 01 20 03 19 59 III III III III III 22 54 21 07 20 12 20 08 37 21 36 23 10 III III III III III 23 35 21 19 20 22 20 17 47 21 48 23 51 III III III III III 21 29 20 30 20 21 55 21 58 III III III III III III III 21 40 20 38 20 33 03 22 09 III III III III III III III 21 50 20 46 20 40 11 22 19 III III III III III III III TABLE V - 50° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 50° SOUTH LATITUDE (50* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 ma 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h m h m h m h ■ h m h m h m h m h m h ■ h m 200 mi 01 16 03 16 04 10 04 34 OS 37 05 59 05 49 04 SB 04 56 02 53 01 01 /// 300 mi 02 44 03 48 04 33 05 16 05 38 05 26 04 34 03 32 02 15 III /// /// 02 12 03 26 04 13 04 56 05 18 05 06 04 14 03 10 01 43 400 mi /// III /// 500 ml 01 36 03 05 03 56 04 40 05 01 04 50 03 57 02 49 01 07 /// III III 600 ml 00 40 02 46 03 40 04 25 04 46 04 35 03 41 02 30 00 11 /// III III 02 28 03 26 04 12 04 34 04 22 03 27 02 12 700 ml /// III III III III 800 mi 02 09 03 13 04 00 04 22 04 10 03 14 01 53 III III III III III 900 mi 01 50 03 00 03 49 04 11 03 59 03 01 01 34 III III III III III 1000 mi 01 30 02 44 03 39 04 01 03 49 02 45 01 14 III III III III III 01 06 02 38 03 30 03 52 03 40 02 39 00 50 1100 ml III III III III III 00 25 02 26 03 20 03 43 03 30 02 27 00 09 1200 ml III III III III III 12 22 02 17 1300 mi 02 16 03 03 39 03 III III III III III III III 06 1400 mi 03 03 27 03 02 02 OS 04 14 III III III III III III III 1500 mi 01 03 20 03 01 02 ss S6 06 56 III III III III III III III SUNSET (JO* S) Satellite JAN 19 FEB 23 MAR 21 API 16 NAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h m h m Heights h m h m h m h m h m h m h m b m b m 200 mi 23 00 21 07 20 01 19 05 18 14 18 03 18 25 19 07 19 51 20 51 22 37 /// 300 ml 21 44 20 28 19 27 18 36 18 26 18 46 19 28 20 12 21 15 III /// /// 400 ml 22 16 20 50 19 47 18 56 18 46 19 06 19 48 20 34 21 47 III III /// 22 52 21 11 20 04 19 12 19 03 19 22 20 05 20 55 22 23 500 ml III /// III 23 48 21 30 20 20 19 27 19 18 19 37 20 21 21 14 23 19 600 mi /// III III 700 mi 21 48 20 34 19 40 19 30 19 50 20 35 21 32 /// III III III III 22 07 20 47 19 52 19 42 20 02 20 48 21 51 800 mi III III /// III III 22 26 21 00 20 03 19 53 20 13 21 01 22 10 900 mi III III /// III III 22 46 21 16 20 13 20 03 20 23 21 17 22 30 1000 mi III III /// III III 1100 ml 23 10 21 22 20 22 20 12 20 32 21 23 22 54 /// III III III III 20 20 32 20 21 42 21 35 23 35 1200 ml 23 51 21 34 /// III III III III 44 40 20 50 45 20 25 21 1300 mi 21 20 /// III III III III III III 21 20 20 56 20 37 58 21 1400 mi 48 SS III III III /// III III III 05 56 20 44 21 22 06 22 06 1500 mi 20 III III III III III /// III •For local fftaan tlmo of sotolllto, SUBTRACT front local moan tiato of oooarvor 4m/° that obaorvor is EAST. 38 TABLE V - 55° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 55° NORTH LATITUDE SUNRISE (55* H) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 Heights h m h m h ■ h ■ h m h a h m h m h m h m h m 06 01 05 07 04 00 02 30 200 ml 02 28 03 37 OA 33 05 32 /// III /// 05 33 04 40 03 28 01 41 300 ml 01 42 03 12 04 11 05 08 /// /// III 05 11 04 17 03 01 00 28 400 ml III III 00 29 02 45 03 48 04 46 III 500 ml 04 53 03 57 02 35 III III III 02 19 03 28 04 28 III III 04 37 03 39 02 08 600 ml III III III III III 01 52 03 10 04 12 04 22 03 22 01 41 700 mi III III III III III 01 25 02 53 03 57 04 09 03 06 01 07 800 ml III III III III 00 51 02 37 03 44 III 900 ml 03 56 02 51 III III III III III III 02 22 03 31 III 1000 ml 03 44 02 36 III III III III III 02 07 03 19 III III 03 J3 02 21 1100 ml III III III III III III 01 52 03 08 III 0J 23 02 06 1200 ml III III III III III III III 01 37 02 58 1300 mi 03 13 01 50 III III III III III III 01 21 02 48 III 03 03 01 33 1400 mi III III III III III III III 01 04 02 38 02 54 01 13 1500 mi III III III HI III 00 44 02 29 III III SUNSET (55* H) Satellite JAN Heights h 18 200 ml 300 mi 18 400 mi 19 500 mi 19 600 mi 19 2U 700 mi 10 800 ml 900 mi 20 Hi 1000 ml 20 1100 ml 1200 mi 20 21 1300 mi 1400 ml 21 1500 mi 21 DATES DEC h 06 05 05 04 04 04 04 04 03 03 03 03 03 03 22 ■ 05 40 18 59 43 28 15 05 52 41 31 22 13 04 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m m h m h m h m h m h m h m h m fa m h m h m 22 19 24 20 20 21 36 III /// 21 30 20 00 18 32 17 58 17 52 III 49 19 48 20 48 22 19 III /// 22 20 20 32 19 19 18 24 18 16 III 11 20 11 21 15 23 32 III III 23 33 20 59 19 42 18 46 18 38 III 29 20 31 21 41 III III III III 21 25 20 02 19 04 18 57 III 45 20 49 22 08 III III III III 21 52 20 20 19 20 19 13 III 00 21 06 22 35 III III III III 22 19 20 37 19 35 19 28 III 13 21 22 23 09 III III III 22 53 20 S3 19 48 19 41 III III 26 21 37 III III III III III III 21 08 20 01 19 51 III in 38 21 52 III III III III III 21 23 20 13 20 04 III 49 22 07 III 21 38 20 24 20 15 III III III III III III 59 22 22 III II' III III III 21 53 20 34 20 25 III III 09 22 38 III III III III 22 09 20 44 20 34 III III III 19 22 55 III III III 22 26 20 54 20 43 III III III III 28 23 13 III III III III III III 22 46 21 03 20 52 III TABLE V - 55° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 55° SOUTH LATITUDE SUNRISE (5S* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h ■ h m h m h m b m h m h m h m h m h m h m 200 mi 02 40 03 54 04 48 05 42 06 08 05 55 04 55 03 52 02 24 /// III III 300 mi 01 55 03 28 04 26 05 18 05 44 05 28 04 27 03 12 01 26 /// HI III 400 mi 00 42 04 03 01 03 05 22 /// 04 56 05 06 04 04 02 45 00 13 III III 500 mi 02 35 03 43 04 38 05 03 /// 04 48 03 44 02 19 /// /// III III 600 mi 02 08 03 23 04 22 04 47 04 32 03 26 01 52 /// /// III /// III 700 mi III 01 41 03 08 04 07 04 32 04 17 03 09 01 25 /// III III III 800 ml 01 07 02 52 03 54 04 19 04 04 02 53 00 51 III /// III III III 900 mi 02 37 03 41 04 09 03 51 02 38 /// III /// III III III III 1000 ml 02 22 03 29 03 56 03 39 02 23 III III III III III III III 1100 mi III 02 07 03 18 03 45 03 28 02 08 III III III III III III 1200 ml III III 01 52 03 08 03 35 03 18 01 53 III III III III III 1300 mi 01 36 02 58 03 26 03 08 01 37 III III III III III III III 1400 mi III 01 19 02 48 03 17 02 58 01 20 III III III III III III 1500 mi III 00 39 02 39 03 08 02 49 01 00 III III III III III III SUNSET (55« Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h m h m h m h ■ h m h m h m h m h m h m h m 200 ml 21 42 20 18 19 09 18 08 17 60 18 20 19 12 20 08 21 17 /// III III 300 ml 22 33 20 48 19 34 18 34 18 20 18 44 19 35 20 32 22 04 /// III III 400 mi 23 46 21 15 19 57 18 56 18 42 19 06 19 58 20 59 23 17 /// III III 500 mi 21 41 20 17 19 14 19 01 19 24 20 18 21 25 /// III /// III III 600 ml 22 08 20 35 19 30 19 17 19 40 20 36 21 52 /// III III /// III 700 mi 22 35 20 52 19 45 19 32 19 S3 20 53 22 19 /// III /// III III 800 mi 23 09 21 08 III 19 58 19 43 20 08 21 09 22 53 III III III III 900 ml III 21 23 20 11 19 20 21 21 24 III III S3 III III III III 1000 mi 21 38 20 23 20 08 20 33 21 39 III III III III III III III 1100 ml III 21 53 20 34 20 19 20 46 21 54 III III III III III III 1200 mi III 22 08 20 44 20 29 20 54 22 09 III III III III III III 1300 ml III 22 24 20 54 20 38 21 04 22 25 III III III III III III 1400 ml 22 41 21 04 20 47 21 14 22 42 III III III III III III III 1500 mi III 23 01 21 13 20 56 21 23 23 02 III III III III III III •Fo. loci .mn linw of ■Molllfa, SUBTRACT from locol mMl liM of Ob.efy«r 4*V° tKot obtorvor Is EAST. 39 TABLE V - 60° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 60° NORTH LATITUDE SUNRISE (60* N) Sat-allie* JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 h m h m h m h ■ h ■ h m li ■ h m h m h ■ h m Heights 38 04 29 05 01 25 03 19 /// III III 200 mi 06 08 05 00 03 37 01 22 02 42 04 00 05 11 III /// III 05 M 04 29 02 58 300 mi III III 02 05 03 33 04 4o III III III /// 05 11 04 02 02 21 400 mi III 01 24 03 00 04 24 III III III /// 04 49 03 29 01 40 500 mi III 00 21 02 47 04 05 ill III III 04 30 03 16 00 37 III III 600 ml 02 25 03 48 /// III III III III 700 mi 04 13 02 54 III /// 02 04 U3 32 III /// III III III 03 57 02 33 III 800 mi III 01 42 03 18 III III III III III 900 mi 03 43 02 11 III III ill 01 19 03 04 III III III III III 03 29 01 48 III 1000 mi 00 51 02 50 ill III III III III 03 15 01 20 III III 1100 ml 00 05 02 37 III III III III III ill 03 02 00 34 1200 mi III 02 24 III III III III III III 02 49 III 1300 mi III III 02 12 III III III III III III 02 37 III 1400 mi III III 02 00 III III III III III 02 23 III III 1500 mi III III SUNSET (60* N) Satellite JAN Heights h 18 200 ml 300 mi 18 19 400 mi 19 500 ml 19 600 ml 20 700 mi 20 800 mi 20 900 mi 20 1000 mi 21 1100 mi 1200 mi 21 1300 mi 21 1400 mi 21 1500 mi 21 DATES DEC h 06 05 05 05 04 04 04 03 03 03 03 03 02 02 22 ■ 15 46 21 00 41 24 09 55 42 29 17 06 55 44 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h ■ h m h m h m h m h ■ h m h m h m h m m h ■ 17 41 18 58 54 22 29 20 21 17 /// III III 15 19 30 20 43 22 51 21 02 19 30 18 21 18 10 III III ill 46 19 59 21 18 III III 21 39 19 57 18 46 18 35 III hi III III III 11 20 26 21 55 22 20 20 30 19 08 18 56 ill III III 33 20 59 22 36 III III 23 23 20 43 19 27 19 15 ill III 52 21 12 23 39 III III III 21 05 19 44 19 32 III III III III III 09 21 34 III III 21 26 20 00 19 47 III III III III III III 25 21 55 III 21 48 20 14 20 01 III III ill III III III 39 22 17 III 22 11 20 28 20 14 III III III III 53 22 40 III III III 22 39 20 42 20 27 III III III III III 07 23 08 III III 23 25 20 55 20 39 III III III III III 20 23 54 III III 21 08 20 50 III III III III III III III 33 III III 21 20 21 01 III ill III III III III III 45 III III 21 32 21 12 III III ill III III III III III 57 III TABLE V - 60° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 60° SOUTH LATITUDE SUNRISE (60* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 NAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h ■ h m h m h m h ■ h m h m h m h m h m h m Heights h m III /// 01 37 03 31 04 42 05 48 06 18 06 01 04 48 03 18 01 15 200 mi III III /// 02 58 04 15 05 21 05 50 05 31 04 16 02 42 /// 300 mi /// III III /// 02 21 03 48 04 56 05 25 .15 06 03 49 02 05 /// 400 mi III /// III /// /// 01 40 03 15 04 34 05 04 l<4 44 03 16 01 24 500 mi III III /// III 00 37 03 02 04 15 04 45 U4 25 03 03 00 21 III 600 mi III III III III 02 40 03 58 04 28 04 08 02 41 III /// 700 mi III III III III III /// 02 19 03 42 04 13 03 52 02 20 III 800 ml III III III ill III 01 57 03 28 03 59 U3 38 01 58 III /// 900 ml III III III 'II III /// 01 34 03 14 03 46 03 24 01 35 III 1000 mi III III III /// 01 06 03 00 03 33 03 10 01 07 III III III 1100 mi III III III ill III III III 00 20 02 47 03 21 02 57 00 21 1200 mi III III III III 02 III III 02 03 10 44 III 34 HI III III 1300 ml III III III III III 02 22 02 59 02 32 III III III 1400 mi III III III 02 10 02 48 02 20 III III III III III 1500 mi III III III III SUBSET (60* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 NAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h ■ h m h m h m h m b m h ■ h m h m h m h m Heights 22 28 20 32 18 19 18 III 04 14 17 51 III 22 41 20 40 19 16 18 200 ml III III III 21 18 19 45 18 31 18 14 18 41 19 46 21 02 /// 300 mi III III III III 21 55 20 12 18 56 18 39 19 06 20 13 2i 39 /// 400 mi III III III III /// 22 36 20 45 19 18 19 00 19 28 20 46 22 20 500 mi III III III III III 23 39 20 58 19 37 19 19 19 47 20 59 23 23 600 mi III III III III II' III 21 20 19 54 19 36 20 04 21 21 700 mi III III III III III III III 21 41 20 10 19 51 20 20 21 42 800 ml III III III III III III III 22 03 20 24 20 05 20 34 22 04 III 900 ml III III ill III III III III 22 26 20 38 2 0 18 20 48 22 27 III 1000 ml III III III III III 22 54 20 52 20 31 21 02 22 55 III 1100 mi III III III III 23 40 21 05 20 43 21 15 23 41 III III III III 1200 ml III •II III III 21 18 20 54 21 28 III III III III /// 1300 mi III III III III III 21 30 21 05 21 40 III III III III 1400 mi III 21 42 21 16 21 52 III III III III III III III 1500 ml III III 'For local man ti™ of ••folllto, SUBTRACT from local moan timo of obvorvor 4m ° that obaorwor la EAST. 40 TABLE V - 65° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 65° NORTH LATITUDE SUNRISE (65* N) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 h m h m h m h ■ Heights h m h m h m h ■ h ■ h m h d 200 mi 06 11 04 48 03 00 02 44 04 19 03 46 III III /// III III 300 mi 05 37 04 12 02 05 01 49 03 43 05 12 III HI III III III 400 mi 05 08 03 39 00 40 00 24 03 10 04 43 III III III III III 04 42 03 08 500 mi III 02 39 04 17 III III III III III III 04 19 02 36 600 mi 02 07 03 34 III III III III III III III 700 mi 03 58 02 03 01 34 03 33 III III III III III III III 800 mi 03 39 01 23 00 54 03 14 III III III III III III III 900 mi 03 20 02 55 III III III III III III III III III 1000 mi 03 02 III 02 37 III III III III III III III III 02 43 1100 mi III III 02 18 III III III III III III III 02 24 1200 mi III 01 39 III III III III III III III III 02 06 1300 mi III III III 01 41 III III III III III III 01 1400 mi 44 III III III III III III III 01 19 III III 1500 mi 01 21 III III III III III III III III 00 56 III SUNSET (65* N) Satellite JAN Heights h 200 mi 18 18 300 mi 19 400 mi 500 mi 19 20 600 ml 20 700 mi 800 mi 20 21 900 mi 21 1000 mi 1100 mi 21 1200 ml 21 22 1300 mi 22 1400 mi 23 1500 mi DATES DEC h 06 05 05 04 04 04 03 03 03 03 02 02 02 02 22 ■ 29 54 24 59 37 17 58 41 24 09 55 38 23 08 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 m h ■ h m h a h m h ■ h m h m h m h m h ■ h m 21 00 19 11 17 46 17 27 11 19 40 21 16 III III /// III /// 45 20 16 22 11 III 21 55 19 47 18 20 18 02 III III /// III 14 20 49 23 36 23 20 20 20 18 49 18 32 III III III III III 20 51 19 15 18 57 40 21 20 III III III III III III III 03 21 52 21 23 19 38 19 19 III III III III III III III 24 22 25 III III III 21 56 19 59 19 39 III III III III 43 23 05 III 22 36 20 18 19 58 III III III III III III 02 20 37 20 15 III III III III III III III III III 20 20 S3 20 32 III III III III III III III III III 39 III III 21 14 20 47 III III III III III III III 58 21 33 21 01 III III III III III III III HI III 21 51 21 18 16 III III III III III III III III III 38 III 22 13 21 33 III III III III III III III III 01 III III 22 36 21 48 III III III III III III III TABLE V - 65° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 65° SOUTH LATITUDE SUNRISE (65* S) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h ■ h m h m h ■ Heights h m h m h m h m h ■ h m h m h m 02 60 04 34 05 56 06 33 06 06 04 35 02 44 200 mi III III /// III /// 02 05 03 58 05 22 05 58 05 32 03 59 01 49 300 mi III /// III /// III 00 40 03 25 04 53 05 28 05 03 03 26 00 24 400 mi III III III III /// 02 54 04 27 05 03 04 37 02 55 500 ml III III III III III III /// 02 22 04 04 04 41 04 14 02 23 600 mi III III III III III III III 01 49 03 43 04 21 03 53 01 50 700 mi III III III III III III III 800 mi 01 09 03 24 04 02 03 34 01 10 III III III III III III III 900 mi III 03 05 03 45 03 15 III III III III III III III III 02 47 0J 28 02 57 1000 ml III III III III III III III III III 02 28 03 13 02 38 1100 mi III III III III III III III III III 02 09 02 59 02 19 1200 mi III III III III III III III III III 1300 mi 01 51 02 42 02 01 III III III III III III III III III 01 29 02 27 01 39 1400 mi III III III III III III III III III 01 06 02 12 01 16 1500 mi III III III III III III III III III SUNSET (65* S) Satellite JAN 19 FEB 23 h m Heights h m 200 mi III III 300 ml III III 400 mi III III 500 mi III III 600 mi III III 700 ml III III 800 ml III III 900 ml III III 1000 ml III III 1100 mi III III 1200 mi III III 1300 mi III III 1400 mi III III 1500 ml III III ■Fo. M MAR 21 APR 16 HAT 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h m h m h ■ h m h m h m h m h m h ■ 21 16 19 26 17 36 17 31 18 06 19 27 21 00 III III III 22 11 20 02 18 30 18 06 18 40 20 03 21 55 III III III 23 36 20 35 18 59 18 36 19 09 20 36 23 20 III III III 21 06 19 25 19 01 19 35 21 07 III III /// III III 23 21 38 48 19 58 21 39 19 19 III III III III III 22 11 20 09 19 43 20 19 22 12 III III III III III 20 28 02 20 38 22 52 22 51 20 III III III III III 20 47 20 19 20 57 III III III III III III III 21 05 20 36 21 15 III III III III III III III 21 24 20 51 21 34 III III III III III III III 21 43 21 05 21 53 III III III III III III III 22 01 21 22 22 11 III III III III III III III 22 23 21 37 22 33 III III III III III III III 22 46 21 52 22 56 III III III III III III III Hi— ol MtalllM. SUBTRACT hwm 1«<ol n»oi> tl"» •< oki«tv« <"/• lKo« ob>..... Ii EAST. 41 TABLE V - 70° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 70° NORTH LATITUDE : (70* H) SATELLITE HEIGHTS 200 ml 300 mi 400 mi 500 mi 600 mi 700 ml 800 mi 900 mi 1000 mi 1100 mi 1200 mi 1300 mi 1400 mi 1500 mi JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h ■ h m h ■ h m h ■ h a h ■ h ■ h ■ h m h ■ h ■ 04 02 06 46 01 34 05 55 06 20 04 31 01 50 /// III /// /// /// 03 15 05 12 06 03 III III 05 37 03 44 III III III III III 02 25 04 36 05 26 05 01 02 54 III III III III III III III 01 38 04 04 04 55 04 29 02 07 III III III III III III III 00 24 03 34 04 27 III 03 59 00 53 III III III III III III 03 07 04 02 III III 03 32 III III III III /// III III 02 40 03 38 III III /// 03 05 III III III III III III 02 12 03 15 III /// 02 37 III III III III III III III 01 43 02 52 III III 02 08 III III III /// III III III 01 08 02 30 III III III III III 01 33 III III III III 00 10 02 10 III III III III 00 35 III III III III III III 01 39 III ill III III III III III III III III 01 08 III III III III III III III III III III III III 23 58 ,11 III III III III III III III III III SUNSET (70* N) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h ii h m h m h m h ■ h m h m h m h m h m h m HEIGHTS 19 28 17 10 22 10 17 37 200 mi 18 02 19 57 22 26 III III III III /// 20 15 18 20 17 53 18 45 20 44 III 300 mi III III III III III III 21 05 18 56 18 30 III III 19 21 21 54 III 400 mi III III III III 21 52 19 28 19 01 III 500 ml 19 53 22 21 III III III III III III 23 06 19 58 19 29 III 20 23 23 35 III 600 mi III III III III III 20 25 19 54 III III 700 mi 20 50 III III III III III III /// 20 52 20 18 III III 21 17 III III 800 mi III III III III /// 21 20 20 41 III III 21 45 900 mi III III III III III III III 21 49 21 04 ill III III 22 14 III III 1000 mi III III III III 22 24 21 26 22 49 III III 1100 ml III III III III III III III 23 50 21 46 III III III 23 47 III 1200 mi III III III III III 22 17 III 1300 mi III III III III III III III III III III 22 48 III 1400 mi III III III III III III III III III III 23 58 III III III 1500 mi III III III III III III III III TABLE V - 70° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 70° SOUTH LATITUDE (70* S) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h ■ h m h m h m h m h ■ h m h m h m h m h m h m HEIGHTS /// 01 50 04 17 06 05 06 50 06 15 04 18 01 34 /// 200 mi III /// III /// 03 30 05 21 06 07 05 31 03 31 III 300 ml /// III /// ill 30 02 41 /// 04 56 02 40 04 46 05 III 400 mi III III III /// III 01 53 04 14 04 59 04 24 01 54 III 500 mi III III III III III /// III 00 39 03 44 04 31 03 54 00 40 600 mi III III III III 03 17 04 06 03 27 /// III III 700 ml III III III II! III 02 50 03 42 03 00 ill /// III III 800 mi III III Ill III 02 22 03 19 02 32 III III 900 mi III III III III ill III 01 53 02 56 02 03 III III III III III III 1000 mi III III 01 18 02 34 01 28 III III III III 1100 ml III III III 00 20 02 14 00 30 II! III III III 1200 mi III III III III III 01 43 III III Ill III II! III III 1300 mi III III III 01 12 III III III III 1400 mi III III Ill III III 00 02 III III ill ill ill III III 1500 mi III III SUNSET (70* S) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h m h m h m h m h m h m h m h m h m h m h m HEIGHTS /// III /// 22 26 19 43 17 47 17 14 17 57 19 44 22 10 200 ml III III III /// /// /// 20 30 18 30 17 57 18 40 20 31 300 mi III III 11 / III III 21 20 19 06 18 34 19 16 21 21 /// /// 400 mi 1 '/ III III III HI 22 07 19 38 19 05 19 48 22 08 /// /// 1 '/ 500 mi III III III III /// 23 21 20 08 19 33 20 18 23 22 /// 600 mi 1 / III III III III III 20 35 19 58 20 45 /// /// 700 ml III 1 / III III III III 21 02 20 22 21 12 m /// /// III 800 mi III 1 / III III III 21 30 20 45 21 40 /// /// III III 900 mi III 1 / III III 21 08 22 09 21 59 in III /// /// III 1000 mi 1 '/ III III III III 22 34 21 30 22 44 in /// /// III III III 1100 ml 1 / III III 23 32 21 50 23 42 in /// /// 17 1200 mi III III III III 22 21 in III /// /// ill III III 1300 mi III 1 / III III 22 52 III l/i III in /// /// III III 1400 mi li / III III 00 02 III /// /// III III III 1 / III 1500 mi III III To- local rrwMn Hrrw of •ot.ll.t., SUBTRACT loco) kni IN of obt«'«»r 4"V° that ob«.«.ver ,t EAST. 42 TABLE V - 80° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED FOR 80° NORTH LATITUDE SUNRISE (80* N) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 h m h ■ h m h. m h m HEIGHTS h m h m h m h ■ h m h ■ 200 mi 06 50 02 39 02 10 06 25 III III III /// /// III /// 300 mi 05 26 05 01 III III III III III III III III /// 400 mi 04 11 03 46 III III III III III III III III /// 02 55 500 mi 02 30 III III III III III III III III /// 01 02 600 mi III 00 37 III III III III III III /// III 700 mi III III III III III III III III III /// /// 800 mi III III III III III III III /// III III /// 900 mi III III III III III III III III /// III /// 1000 mi III III III III III III III III III /// /// 1100 mi III III III III III III III III III /// /// 1200 mi III III III III III III III III /// III /// 1300 mi III III III III III III III III III III /// 1400 mi III III III III III III III III III III /// 1500 mi III III III III III III III III III III /// DATES DEC 22 h ■ 08 05 06 33 05 21 04 18 03 16 02 08 /// /// /// /// /// /// /// /// SUNSET (80* N) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 :SEP 24 OCT 20 NOV 22 DEC 22 h m h m HEIGHTS h ■ h ■ h ■ h ■ h m h m h m h m h m h ■ 200 mi 17 32 21 49 21 20 17 07 15 51 III /// III III III III /// 300 ml 18 56 18 31 17 23 III III III /// III III III III /// 400 mi 19 11 19 46 18 35 III III III III III III III /// III 21 27 500 mi 21 02 19 38 III III III III III III III III /// 600 mi 23 20 22 55 20 40 III III III III III III III III /// 700 mi 21 48 III III III III III III III III /// III /// 800 mi III III III III III III III III /// III /// /// 900 mi III III III III III III III III III III /// /// 1000 mi III III III III III III III III III /// III /// 1100 mi III III III III III III III III /// III III /// 1200 ml III III III III III III III III /// III III /// 1300 mi III III III III III III III III III /// III /// 1400 mi III III III III III III III III III III /// /// 1500 ml III III III III III III III III /// III III /// TABLE V - 80° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 80° SOUTH LATITUDE SUNRISE (80* S) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 HEIGHTS h m h m h m h m h m h m h m h m h m h m h ■ h m 200 mi 02 25 06 35 08 09 06 45 02 26 III III /// III III /// /// 300 mi 05 11 06 37 05 21 III III III /// /// III III /// /// 400 mi 03 56 05 25 04 06 /// III III III III /// III /// /// 500 mi 02 40 04 22 02 50 III III III III III III /// III /// 600 ml 00 47 03 20 00 57 III III III III III III /// III III 700 mi 02 12 III III III III III III /// III III /// III III 800 ml III III III III III III III III III III /// 900 mi III III III III III III III III III III /// III 1000 mi III III III III III III III III III III /// III 1100 mi III III III III III III III III III III /// III 1200 mi III III III III III III III III III III III /// 1300 mi III III III III III III III III III III III III 1400 mi III III III III III III III III III III III III 1500 mi III III III III III III III III III III III III SUNSET (80* 8) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 HEICHTS h ■ h m h ■ h ■ h m b d h m h m h m h m h ■ h m 200 mi 21 35 17 17 15 55 17 27 21 36 III III /// III /// /// III 300 mi 18 41 17 27 18 51 III III III III /// /// III /// III 400 mi 20 06 19 56 18 39 III III III III /// /// III /// III 500 mi 21 12 19 42 21 22 III III III III III /// /// /// III 600 ml 23 05 20 44 23 15 III III III III III III III III III 700 ml 21 52 III III III III III III III III III III III 800 ml III III III III III III III III III III III III 900 mi III III III III III III III III III III III III 1000 mi III III III III III III III III III III III III 1100 ml III III III III III III III III III III III III 1200 ml III III III III III III III III III III III III 1300 mi III III III III III III III III III III III III 1400 mi III III III III III III III III III III III III 1500 mi III III III III III III III III III III III III •For local Ilea of .ot.1111., SUBTRACT t'om loco! mwr timo ol obi ■row 4"/° ll«n obury. la EAST. 43 TABLE V - 85° NORTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 85° NORTH LATITUDE SUNRISE (85° N) SATELLITE JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h ■ h m HEIGHTS h m h m b m h m h ■ h m h m h m h m 7 42 7 17 200 ml I /// /// /// /// /// /// /// /// /// ■•// /•',/ '/■' .'.'/ 4 27 7 18 300 ml 4 52 /// /// /// /// /// /■-.' 4 56 7 00 400 ml 1 25 /A/ /// 7/ /// /// 7/ /// /// ''A' 2 31 500 ml /// Y/ Y7 Y/ /// /// /// /// 7 /// //•/ '.•'/ '// 600 ml 7" /// 7/ /7 /// /// /// •AY AY 700 ml 77 /// 7/ 7/ /// /// /// /// 7/ /.■•'.' 800 mi .7/ /// 77 7/ /'/ /// // 7/ /// Y/ /// 900 ml 77 /Y Y/ /// /// /// /// 7/ /// Y/ 1000 ml AY Y /// /// 7/ /// /// /// /// //'■ 77 AY 1100 mi /// ,7/ Y/ AY /// /// 7/ 7/ 7/ //•' 1200 mi '// /// '// Y/ 7/ Y/ /// /// Y/ /// .AY .AY 1300 mi 7/7 ///' /// /// AY /// Y/ 7/ /// /// 1400 mi .AY .AY /// 7/ /// /// 77 // // 7 /// 1500 mi /// /// /// /// /// /// /// /// /// /// /// /// SUNSET (85° N) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h m h m h m h m h o h m h m h m h m h m h m Heights 16 40 200 mi 16 15 § /// /// /// /// /// /// /// /// /// Y/ 300 mi 19 30 19 05 16 38 '/,' AY /// /// /// Y/ /// ■■/■' ■'/•' 77 22 32 19 00 400 mi 22 57 /7/ '// /// 7/ /// " 77 77 ''// 500 ml /// 21 25 /// 7/ 7/ /// /// 600 mi /// /// /// /// 7/ 7/ /// /// /// 7/ 700 mi /// Y/ /// 77 Y 7/ 7/ 7/ /// /// 7/ /// ■7/ 800 mi 7/7 /// 77 .77 //,' .7/ /// /// Y/ 7/ /// 900 mi AY /// /'// 77 /// 7/ Y/ /// /// /// /// AY 1000 mi 77 7/ /// /// /// 7/ /// /// /// Y/ /// ■// 1100 mi Y/ Y7 /// /// 77 7/ /// /// /// /// 7/ 1200 mi .7/ 7/ 7/ 7/ /// /// //' 7/ /// /••/ //■ ■'/■' 1300 mi ,7/ /// AY 7/ /// /// /// /// /// /■■•/ ■'/■■■ ,77 AY 1400 mi 77 7/ AY /// 7/ /// /// /// 1500 mi AY /// /// /// /// /// /// /// /// /// /// /// TABLE V - 85° SOUTH LOCAL MEAN TIMES* OF SUNRISE AND SUNSET AT VARIOUS SATELLITE HEIGHTS ON SELECTED DATES FOR 85° SOUTH LATITUDE SUNRISE (10° S) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 h m h m h m h m Heights h m h m h m h m h m h m h n h m 200 ml 7 27 7 37 f /// /// /// /// /// /// /// /// /// 300 mi 4 37 7 22 4 47 AY //A 7Y AY /// /// /// /// /// 400 mi 1 10 5 00 1 20 .Y/ AY 77 ,77 /// /// /// /// /// ■'// 500 mi 2 35 /// /// /// /// /// /// /// /// /// /// Y A/ 600 mi AY /,'/ /// /// /// /// /// /// /// /// 77 700 mi 77" AY Y/ AY /// /// /// /// 77 /// A7 7Y 800 mi 77 //A 77 /"' /// 7/ /// /// 7/ /// /// YV 900 mi 77 77 .7/ 77 /// /// /// 7/ /// /// 77 1000 ml 7Y /// /// /// /// /// /// /// /// /// AY 1100 mi 77 AY /// /// /// /// /// /// /// /// /// 1200 mi AY AY 77 Y7 77 /// /// /// /// /// /// /// .AY AY 1300 mi t/f /// /// /// '// /// 7/ /// 7/ /// Y/ AY 7/ 1400 mi YA t/t 7/ /// /// /// 7/ '// AY 1500 mi /// /// /// /// /// /// /// /// /// /// /// SUNSET (85'> s) Satellite JAN 19 FEB 23 MAR 21 APR 16 MAY 21 JUN 22 JUL 24 AUG 28 SEP 24 OCT 20 NOV 22 DEC 22 Heights h m h m h m h m h m h m h m h m h m h m h m h m 16 25 16 35 200 mi 0 /// /// f/ /// /// /// /// /// "/ ,7/ 19 15 16 42 19 25 300 mi 77 7/ Y7 /// /// 77 /// /// AY 22 42 19 04 22 52 77 .AY 400 mi ,77 /// 77 /// /// '// Y/ 7Y 500 mi /// 7/ /// 7/ /// 7/ 77 /// 21 29 /// ,7/ AY AY AY 600 mi AY /// /// /// /// /// /// /// /.Y AY AY AY 700 mi AY ,7/ //./ /// /// /// 7/ 7/ 11/ 77 800 mi AY 77 /// 77 77 /// 77 7/ /// /// 77 900 mi '// 7/ /// /Y fff /// /// /// 77 7/ AY 77 1000 mi AY AY .AY A// 77 /// /// /// /// /!/ AY 77 /./.' AY 1100 mi /'// 7/ AY 7/ /// /// /// /// AY 77 AY 1200 mi /// f'f ,7/ Y/ /// 7/ /// /// .AY 1300 ml 77 /// AY 7/ 77 7/ /// /// /// /// /// AY 1400 ml A/7 /// 77 /// AY 7/ /Y 7/ /// /// 1500 mi .7/ /// /// /// /// /// /// /// /// /// /// /// •F« local won IIm »f ■•MllHs, SUBTRACT hoi- local Man tin.* •( obsafvar 4m/o thai abaarwar l> CAST. aNa*ar Sunlit. 44 CHART FOR DETERMINING ELEVATION 8 SLANT RANGE ALL DISTANCES ARE IN STATUTE MILES - 5 STATUTE MILES EQUAL APPROXIMATELY 8 KILOMETERS. 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3 OZ TZ EZ v x a i 17G SO 170 SO VE 9G •ZS qm 10 6Z 61 OZ SZ VS IZ EG tstnoaa ivhoimhvanl 8Z ZZ OZ 90 LI 61 tsons moniwx voimvn "856T m 17*7 10 ZS VE 91 017 q ZO VO VO SO 90 90 9Z 9E 8E 90 SO VO to 6T 8T 6S EO VO VO EE 80 8Z SO 90 90 LI VE SV 90 SO 170 9S EV EO ZO ZO m W ZG SO .OV q EO VO SO TE 00 L\ VO OZ El SO 90 90 60 EE OS 90 SO 170 m EO EV 60 q VO VO SO OE ES 80 ZO IE VS SO SO 90 90 SO VO m 61 ZS ZT 9S 6Z LS SO SO VO vz ss ss q VO VO SO 8Z 9V 6S SO SO SO D W 90 9T q VO so so EZ ££ EV so so so ZV SZ ZO OZ 8E VZ VO VO VO .OZ a EO 9T 6T q so so so 8T 6T 9Z so so so OZ 6Z VO so so so L*l 8V 6E VO VO VO .01 OZ SZ 61 •0 m q SO SO SO 11 SO 60 SI El SO SO SO SO SO SO SO 9S SS 90 VO VO SO •0 m q 9T HJV V3 inr 03 100 ZZ AON .05 vg ZZ LS Ul SZ TZ q 9G TZ OZ 6T VZ 9E vz 8T LI LI Ul ZO 80 VT S17 9Z q TZ OZ 6T 9E LI 8T LI 9S 6Z LI 8T 6T 017 8E VT TZ 6T OZ n LZ VS 60 LZ ES 170 TE LZ ET OZ 6T 6T 9V 8T LI ZT 8T 8T 8T 00 TT ZZ ZS 9S 8T 8T LI 8T 8T 8T m ZO SE ZO TE LO VO 8T V£ 8V LO 8£ ZO q OZ 6T 61 8T 8T 8T 8T 8T 8T 6T 6T OZ TZ 8S 9£ OZ TZ TE 8£ ES ET EE 6T 6T 8T 8T 8T 8T 8T 8T 8T 8T 6T 6T 8T IT 9S 61 61 81 TV EE LZ vv w TV 81 81 8T ZV ES OT ZO ZO SS 8V 8V VS 81 81 81 LS OS ov VE LZ IS 81 81 81 81 81 81 zz mir VZ TOT 8Z aas onv vz AON zz 02a OZ 130 ZZ .OS EO ZO TO 89 80 8Z LI 8T 6T 85 Zl 00 TZ 6T ZZ ail! .sv TS SOI .S17 TO V s I .SG .OG .03 ,01 aiva aai 13 HVW 61 Nvr 33 so so so vz aas .OV VO GO GO ST LZ 6E VO EO EO q SO •SG B 8T V* q OZ 6T 6T 6Z .OG VO EO EO in 8E Ul M 61 61 81 83 onv 33 oaa aai 61 NVf 33 13 WW W 6T OZ OZ 9T ES OZ 61 OZ 6T W 81 81 81 aiva NOT 13 AVW 33 9S 91 HiV 13 AVW 81 8T 61 lilO APPENDIX 1 - Formulas Used In Preparing Tables Table It A « arcsin (tan <f> / tan i); Table II: a = arcsin (sin <f>/ sin i); and, Table III a: EPP»-^-»^ = E - e sin E T 2* 2" Table III b: RDF = r/r * Table IV*: y = = -Li® 1 + e cos v arcsin ( 1440 cos i - T cos2 <f> \ 1440 cos 4> - T cos i cos \ / Where: A is minimum longitude of northbound node measured westward from foot of observer's meridian on the equator; <t> is latitude of meridian point; i is orbit inclination; a is initial central angle within orbit plane between equator and refer ence latitude; EPP is equivalent percent of period; t is time in minutes since perigee; T is period in minutes; M is mean anomaly measured in radians; E is eccentric anomaly; e is eccentricity. RDF is radial distance factor. rv is radial distance of satellite at v. rp is radial distance of satellite at perigee. y is heading along satellite track. v is true anomaly: the current position of satellite within orbit plane measured at the center of the earth from perigee in the direction of the satellite's motion and is related to E as follows: ♦Table IV is computed for a 105 minute period; note that the formula does not take into account the effect of precession of the orbit plane, which would not significantly affect the accuracy of the table. 41 APPENDIX 2 - Communication of Modified Orbital Elements A. SUMMARY — Modified orbital elements are communicated by radio and by mail. The world-wide radio teletype channel is the IGY World Warning Agency. Data are sent over this channel in the SATOR code explained below in section B. Within the United States (including Alaska), Hawaii, Puerto Rico and adjacent portions of Canada and Mexico, the radio channel is the Civil Air Patrol voice communications network, which broadcasts modified elements in uncoded form (see section C). In addition to these radio services, many vol unteer participants receive modified elements by mail from the appropriate volunteer headquarters (see section D). Section E explains the relationship between modified orbital elements and a more traditional form. B. IGY WORLD WARNING AGENCY : WORLD-WIDE RADIO TELETYPE SERVICE TO REGIONAL IGY WARNING CENTERS - This communication channel carries various types of IGY information, e.g. solar activity. The Comite' Special Annee Geophysique Internationale (CSAGI) has issued a new code which is specially designed for transmission of modified orbital ele ments. The code was drafted by the USNC-IGY and edited by the CSAGI Re porter. It was issued as the Fifth Supplement to the Draft Manual for World Days and Communications, compiled and produced at the Central Radio Pro pagation Laboratory, National Bureau of Standards, Boulder, Colorado, U.S.A. As with other codes in the Draft Manual, it must be replaced with the final, corrected version when available. This code is reproduced below for the convenience of users of this prediction booklet. SATOR (Modified Orbital Elements for Prediction Purposes) Code word: SATOR Symbolic form: SATOR jkkkk ppppp sssbs aabbc deeff ggggZ hhhhX NOWES ARPER 11111 mnnnX PERIOD ECCEN qqqqq PERRA rrrrr (ssssa repeated as necessary) RAD EG iiiii ooooo RAFRE ttttt Key: aa bb c d ee ff gggg Z hhhh X NOWES iiiii j kkkk ARPER 11111 m nnn X PERIOD = ■ = * last two digits of year satellite launched Greek letter designation, 01 = Alpha, 02 ■ Beta, etc. component reference time (epoch): last digit of numerical notation for month; i.e. 1 = January_or November, 2 ■ February or December, 3 * March, etc. • reference time (epoch): date ■ reference time (epoch): hour ■ reference time (epoch): minutes and hundredths of minutes ■ Universal time, Greenwich Mean Time ■ inclination in degrees and hundredths of degrees. If the orbit inclination is negative (satellite fired west ward) group is preceded by NEGAT 3 always an X = sub-indicator for geographical longitude of northbound node west of Greenwich at reference time • longitude of northbound node in degrees and hundredths of degrees » 1 if plus: when the "prime sweep interval" is one day plus a certain number of minutes 2 if minus: when the "prime sweep interval" is one day minus a certain number of minutes This is equivalent to saying that the same portion of the orbit plane will reappear at the same location a certain number of minutes earlier each day. ■ number of minutes and hundredths of minutes by which "prime sweep interval" differs from one day or 1440 minutes. This is another way of expressing the relative "westward motion" of the orbit plane. = sub-indicator (argument of perigee) angular distance of perigee from node at reference time. For modified orbital elements, this is also the position of the satellite in the ellipse at reference time (mean anomaly at epoch is always equal to zero in this system) a angular distance of perigee and satellite from northbound node, measured in the direction of satellite travel in degrees and hundredths of degrees ■ 1 for plus, if perigee moves in the same direction as satellite travel 2 for minus, if perigee moves in the direction opposite to satellite travel = average decimal fraction of a degree which perigee moves per period, measured in thousandths of a degree = always an X ■ sub-indicator for perigee-to-perigee period (anomalistic period) 49 ooooo * perigee-to-perigee period (anomalistic period) in minutes and thousandths of a minute. If first two digits are less than 85 it should be understood that 100 should be added in order to arrive at the correct period (period cannot be less than about 88 minutes). Should the period be greater than 185 minutes a special no tation will be made in the message, ppppp = average per period change in perigee -to -perigee period, measured as a decimal fraction in one hundred thousandths of a minute ECCEN * sub-indicator for eccentricity ggggg = eccentricity, measured as a decimal fraction in one hundred thousandths PERRA « sub-indicator for radial distance of satellite from center of earth at perigee rrrrr = radial distance of satellite from center of earth at perigee, measured in miles and tenths of miles RAFRE ■ sub-indicator for radio frequencies currently being transmitted from satellite sssss ■ radio frequency in megacycles and hundredths of megacycles RADEG = sub-indicator for right ascension of the ascending node expressed in degrees and hundredths of degrees in order that this message may also serve the needs of those who prefer traditional orbital elements (Note that this sub-indicator and the following code group represent a revision of the code appearing in the Fifth Sup plement to the Draft Manual) ttttt > degrees and hundredths of degrees of right ascension (Note that right ascension is given in degrees and hundredths of degrees rather than hours and minutes) [ Since all of the above quantities have sub-indicators, a message need only include those quantities which have changed since the last reference time (epoch)] Example: (modified orbital elements used in example in booklet): SATOR 58051 80816 4916Z 5029X NO WES 19269 21809 ARPER 08545 0223X PERIOD 09887 00225 ECCEN 12678 PERRA 41236 RAFRE 10800 10803 RADEG XXXXX ***** It may sometimes be advantageous to up date a set of modified orbital elements by giving an estimated correction to crossing time, since the most perishable information is the satellite position in the ellipse at any given time. Code word : EST CO Symbolic form: ESTCO XuuvX EARLY or LATEX xyyzz ESTCO = sub-indicator for estimated correction to crossing times X ■ always an X; gives group distinctive appearance uu - minutes by which satellite is expected to early or late v = tenths of minutes by which satellite is expected to be early or late X - always an X EARLY * if satellite is estimated to be early LATEX = if satellite is estimated to be late x ■ time for which correction is computed: last digit of month yy = time for which correction is computed: date zz ■ time for which correction is computed: hour Example: SATOR 58051 80816 4916Z ESTCO X054X EARLY 81116 Translation: On the third day after reference time, satellite 58 epsilon is estimated to be 5.4 minutes earlier than the position computed on the basis of modified orbital elements having a reference time of August 8 at 1649. 16Z 50 C. CIVIL AIR PATROL. (CAP)— Radio broadcasts of modified orbital elements within the United States (including Alaska), Hawaii, Puerto Rico and adjacent portions of Canada and Mexico. A sample message form for modified orbital elements, and origins, frequencies and times of broadcasts are given below: MODIFIED ORBITAL ELEMENTS FOR IStyDUH-J. From S¥HW0A/t4Af /M>^/c4L 06t&f/*T**f Reference time OX O^t at ,2.3 hours YT, 3 3 minutes Zebra; Orbit inclination 6S" 3 3 degrees; Longitude of northbound node 3/ f, 2 3 degrees west of Greenwich; Prime sweep interval one dayAWM'W minutes; Perigee and satellite position 3 HX ,<£J degrees, Q.oiooX degrees per period; Perigee-to-perigee period lOl.bW minutes, minus o OolS'i minutes per period; Eccentricity 0.O9AV6; Radial distance of perigee statute miles; Radio frequencies XOfiOtfS". *f0. 00<i . megacycles; (Alt, position of node) Right Ascension ,209, #Z degrees. Regular broadcasts* are scheduled for Tuesday and Friday evenings as follows: Station Frequency VP0, Hq. CAP, Boiling AFB, Washington 25, D. C. 4275 Kc VP01, Box 105, Mitchell AFB, N. Y. VP02, Shaw AFB, Sumter, S. C. VP03, Old Adm. Bldg., DetroitWayne Metro. Airport, Inkster, Mich. VP04, Dept. of Commerce Bldg., Berry Field, Nashville 10, Term. VP05, Bldg. T384, Minn. -St. Paul International Airport, Minneapolis, Minn. VP06, 102 Walnut Hill Village, Dallas 20, Texas VP07, Bldg. 471, Lowry AFB, Colo. VP08, Bldg. T-235, Presidio of San Francisco, San Francisco, Calif. 2374 Kc or 4585 Kc 4467.5 Kc Time 1900 EST & 2000 EST 2030 EST 2030 EST 4507.5 Kc 2030 EST 4467.5 Kc 2030 CST 2374 Kc 2030 CST 4507.5 Kc 2030 CST 4507.5 Kc or 4585 Kc 4585 Kc 2030 MST 2030 PST ♦Special broadcasts will be made nightly (seven nights a week) on the above schedule in the event of a Satellite with rapidly changing elements. SI D. SPECIAL MAIL SERVICE TO PARTICIPATING VOLUNTEER OBSERVERS — When feasible, modified orbital elements are mailed to partici pating volunteer observers. Moonwatch (volunteer visual observer) teams re ceive modified orbital elements as part of a general information sheet. Inquiries from Moonwatch teams should be addressed to Smithsonian Astrophy sical Ob servatory, Moonwatch Headquarters, 60 Garden St., Cambridge 38, Mass. Moon beam (radio tracking) and Phototrack (photographic tracking) groups receive airmail announcement cards similar to the sample message form shown above in section C. Inquiries from the latter groups should be addressed to 826 Connecticut Avenue, Washington 6, D. C. E. RELATIONSHIP BETWEEN MODIFIED ORBITAL ELEMENTS AND MORE TRADITIONAL FORM. Modified Form More Traditional Form Used by NRL Relationship (1 ) Epoch (1) Identical (2) Inclination (2) Identical (3) Celestial longitude of (3) Equivalent but complex ascending node east of ver therefore both forms given nal equinox (in plane of ce lestial equator, not eliptic) (4) Prime sweep interval (4) Westward motion of nod e(4) Equivalent; one easily derivable from the other (5) Position of perigee (5) Identical (5) Argument of perigee (6) Position of satellite (6) Mean anomaly at epoch (6) Reference time always chosen to make mean anomaly = zero; i.e., when satellite is at perigee (7) Identical (7) Perigee-to-perigee (7) Anomalistic period period (8) Average change in (8) Given in different forms (8) period, per period or sometimes not at all (9) Eccentricity (9) Identical (9) Eccentricity (10) Perigee (measured (10) Differ only by mean (10) Radial distance of satellite from center of from mean surface of earth radius of earth earth at perigee (1) Reference time (2) Inclination (3) Geographic longitude of northbound node west of Greenwich 52 APPENDIX 3 - Computation Short-Cuts & other suggestions A. SHORTCUTS PERMITTING SLIDE-RULE DIVISION- Where a desk calcu lator is not available, the long divisions indicated in Schedule B, and in Sched ule C, Item 4 can be reduced to slide rule problems of sufficient accuracy as follows : 1. To find westward motion from prime sweep interval: Average westward motion due to earth's rotation T.cnO —TTT? — " 0?2500/min 1440 min Adjustment for precession of orbit plane and equation of time jg 5760 " 5760 "+ 0°0Q3 15/min* Westward motion 0?2532/min Where: A I is the amount, in minutes, by which the prime sweep interval differs from one day. Justification for ignoring the quadratic and higher terms in cases where AI does not exceed about 20 minutes can be found in the following : 360° 360° Westward motion = prime sweep interval = (1440 -Al)min 360 ri AI / AI \2 o. . 360 . , 1 1 +~[440 + {1440} +" -] /mln = 1440" [ 1 = AIl0. . 1440 1 1 ^ (where AI is small compared to 1440) = (0 . 2500+ 5^Q)°/min Note that for negative orbit inclinations, prime sweep interval will be equal to one day plus AI, and the adjustment must be subtracted. 2. To find time equivalent of longitude to be swept by orbit plane: Time required for earth to rotate 72 ?9 at 4 min/° 291.6 min LESS: Adjustment for precession of orbit plane and equation of time during above interval.. 291.6 min x 0 ? 0032/min* x 4 min/° - 3.7 min Time equivalent of longitude to be swept by orbit plane 287.9 min *0.0032 is the Adjustment found in Shortcut #1 (above). Justification: 072 ?9 _ 072 ?9 Equivalent time 0?2532 /min (0 92500 + 0°0032)/min = 4 x 72.9 tl - 4(0.0032)] = 291.6 - 291.6 x (4) x 0.0032 = 287.9 min. 53 B. PLOTS— If predictions are made quite reqularly, Dr. Erwin Schroader of Applied Physics Laboratory points out that it is worthwhile to construct plots of (1) westward motion as a function of AI (amount by which prime sweep in terval differs from one day); (2) time equivalent of longitude for various val ues of westward motions, and (3) current perigee-to-perigee period as a function of time elapsed since reference time, for various values of change in period per period. Also, the series of additions and subtractions in Schedule C can be computed graphically by means of a finely -divided clock face or compass rose and a pair of dividers. Finally, it is possible to devise extra polation formulas to eliminate part of the work involved in Part II, when pre dictions are being made for several successive days. C. CORRECTIONS FROM LOCAL OBSERVATIONS-An observer may use his own observations to correct already computed predictions. For example, if a satellite appears 3 minutes early and 2° of longitude east of predicted posi tion, this information may be entered in the appropriate boxes in Schedule F, item 13 or 15 and Schedule G, item 4 or 6. D. USE OF OVERLAYS — Tracing paper or clear plastic is useful for mark ing the observer's position on the plotting grids or for making computations in the event of a temporary shortage of computation forms. E. SUNSET TIMES AT 88 MILES FROM TABLE VI-Table V is used for de termining whether the sun is shining at satellite altitude for various satellite longitudes, latitudes and local times. Table VI is used for determining whether the sun is less than or more than 12° below the horizon at various observer longitudes, latitudes at various local times. However, Dr. R. H. Wilson of the Naval Research Laboratory points out that the information contained in Table VI essentially gives the sunrise and sunset times for a point 88 miles above the earth, and thus is useful for the critical satellite heights between 88 and 200 miles. When Table VI is used in this way, care must be taken to enter table with satellite latitude, longitude and local time rather than observer's latitude, longitude and local time. For latitudes greater than 50° interpolation between Tables V and VI is inconvenient since the latitude entries for the two tables are not identical. F. PREDICTIONS FROM INCOMPLETE LAUNCH DATA The pre diction system outlined in this booklet can be adapted to making predictions based on the type of information often given at the time of launching a new satellite. Since it is normal to launch a satellite with a velocity in excess of that needed for a circular orbit, the best guess is to assume that perigee is at the launching point, i.e. that there are no launching angle errors. With this assumption, and the time of satellite passage over any given geographic loca tion, it is possible to work backward with the aid of Tables II, III- A and I to construct modified orbital elements, provided inclination, approximate eccen tricity, perigee-to-perigee period and perigee distance are known. The prime sweep interval and change in perigee-to-perigee period may be inferred from previous experience. 54 II o(0° meridian relative nlonThis gis irteufder)e.nce SELECT sLOCATE station rof vrRelatitude rf'eused sin rPart eII. ncecentral Preliminary Preof Plotting pGrid aratio(for nwith useL Pass of any given Saatplotting Oebnear lgrid sa Sshowing eitrlatitude avetboth riof 'oosbn2. )eand 1. LOCATE Obsrelative erposition veplotting rgrid on 'using sstation latitude (given) and relative longitude (from Schedule F. Item 13 15) + horT-. + h?-■ + h?.+ h?■- 20. Sain tsunlight e(from lTable V) iYes tNo eYes No Yes No Yes No "8 uBjo iisaAV papou upeunjo soiqaioypadg prjqoiuSuoj -U38JQ jo isdcniresi(papn^uoq jo uoapu:H3I,N3 i}s ds.i}uiod amp -ye o.ws paisbxovHxaas Boipub paav ui aav (apmiSuoi PUBjsvd SS3T »09£) H™* daaMs sauip apou punjo osqapimJioSu cri point(s) of interest h9 h? hy h?—- shown above. EXTEND the resulting satrack(s) teboth lsides onof the irtepoint ference 5. DRAW straight line(s) through repoint feheading(s) ron en(cmelfrom aoNorth) scukrweidse Schedule H To Obtain Azimuth, Elevation, — Slant Range and Passage Times 3. ENTER Heading along satrack for tgiven eorbit linictand lerienlatitude fateiroen ce PART HI-OPTIONAL ADDITIONAL DETERMINATIONS 21. Sky Dark station at (from Table VI) Yes No and MARK sdait(s) rewith lecaitr(s). ieownhead + 4. ALSO ENTER: 180° less Item 3, above .. 16. SUBTRACT Time required forsato gee repoint to ference 17. lepoint over fie( + t) re+( n) c—18. eADD +( ) —when +( ?—) Time interval (s) between satel ite point ttravel from elperi ciutre ent position Time s—a9— te—passes l ite passage of (s) overandsaterpassage interest 19. Time(s) of satepassage loverite 0 0 (SF, Item ch10) edule relatitude overference (from Table IV) point. . + 0 0 i-l*-**•* 2 K HX -W2 _ft (fl M J « «*.ft * ft<— «! o « S u O TOS "«2 2 o a „u 'u*401^ v^,ft 3 .2 S 0c u *a id .«t C— SH 3 <i*JJ3 ^N ^cr 0) d U 0 4-> in o0 U a, o 4)o in l) ft c £ ^.-M*« o C O-<^ 0 f£t ^' Ii— c cr 4jV UM « v 00.ceS' ° 0-1 O' fCt ■H •O to .2? 3 *i ft> 00 ? V (X V 0 nj »< S| * P > ft uMm U ft O X) -H Longitudes A: To Find of NoSweep Node at rSpecific tTimes and hbCentral ound Angles Equator Between and ReLatitude ferenceSchedule Smile ; ktia=l1 1.609 ktom=0.621 U iaul5 mepile; oaretmiles er8 koitsxl;eormaet elrys o U South fetrietnucde STRIKE OUT ALL of line aob wchoiarcnhteavienrs Rleis faetrietnucde a.Rleais North lENTER: Minimum onof gnode owest irthubdoeundb. false statement: msweep of eat times rI) (from Table iand dian £ cw£m *^ > ~ point 0. sgiven of Table I howing iorbit nclination, SELECT rlecfato station eltroiaestnuecidsteudpart eFrom nnode ogat riettime fhuebrdouendce Orbit inclination (Station Rtime eGMT) f(Time e+ h) r=e19 n-).ce»(Rtime eGfrMean GMT, eTime Z) reUT orn19 =.wcie»ch Prime interval: Loof change Per perperiod in ige -to-perige Perperiod position and saat rtetime (measured degrees flin eof arcrifrom etnece sweep igeat r-etime tof-epreigneceChange perigee position in per period +( ) ! /period — Perigee eorbit ntricity period cso(not to tralways times given) imeacteidon Ec of fRadio treanqsumeinscioens Radial dof siafrom sperigee center tof earth at ealnciete Ecrossing nonode and rin dtof imotion) sharbteocluf tnidoten's 4-iCO2° /orLfo/dngfor/LrtandovmiOca,nRPrLtoOetglobinaHtngriwver GIVEN ON (date) BY (Compute ONLY given ONCE for station iand nclination) FOR EARTH SATELLITE 19 - .5 .3 00 MOORBITAL DELEMENTS IFIED .U <D C (1 day), or(1440-00 + f-) 5 z5 «J PRIME SWEEP 1 „M +ii—Nj 180 ?00 + 0?00 ^3■4-> 5 s (-) 0 f Wof Greste nwich D T3 rtTO■ U« J)•H O ^3 T3 EARLY stmiles atute (LATE) Mc Mc Mc RETURN SWEEP /period 0? — (" r— 0] ?00 180 360 ?00 4: ca u 0)H* N(S) •„.. ...ST - ..GMT - IGY Satellite Report Series Number 8 15 June 1959 IGY WORLD DATA CENTER A Rockets and Satellites NATIONAL ACADEMY OF SCIENCES EPHEMERIS OF SATELLITE 1957 ALPHA 2 and COLLECTED REPORTS ON SATELLITE OBSER NATIONAL ACADEMY OF SCIENCESNATIONAL RESEARCH COUNCIL Washington 25, D. C INTERNATIONAL GEOPHYSICAL YEAR WORLD DATA CENTER A National Academy of Sciences 2101 Constitution Avenue, N.W. • Washington 25, D. C, U.S.A. World Data Center A consists Airglow and Ionosphere: IGY World Data Center A: Airglow and Ionosphere Central Radio Propagation Laboratory National Bureau of Standards Boulder, Colorado, U.SA. the following eleven archives: Glaciology: IGY World Data Center A: Glaciology American Geographical Society Broadway at 156th Street New York 32, New York, U.S.A. Longitude and Latitude: Aurora (Instrumental): IGY World Data Center A: Aurora (Instrumental) Geophysical Institute University of Alaska College, Alaska Aurora (Visual): IGY World Data Center A: Aurora (Visual) Rockefeller Hall Cornell University Ithaca, New York, U.S.A. Cosmic Rays: IGY World Data Center A: Cosmic Rays School of Physics University of Minnesota Minneapolis 14, Minnesota, U.S.A. IGY World Data Center A: Longitude & Latitude U. S. Naval Observatory Washington 25, D. C, USA. Meteorology and Nuclear Radiation: IGY World Data Center A: Meteorology and Nuclear Radiation National Weather Records Center Asheville, North Carolina, U.S.A. Oceanography: IGY World Data Center A: Oceanography Department of Oceanography and Meteorology Agricultural & Mechanical College of Texas College Station, Texas, U.S.A. Rockets and Satellites: IGY World Data Center A: Rockets and Satellites National Academy of Sciences 2101 Constitution Avenue, N.W. Washington 25, D. C, U.S.A. Geomagnetism, Gravity, and Seismology: IGY World Data Center A: Geomagnetism, Gravity & Seismology Geophysics Division U. S. Coast and Geodetic Survey Washington 25, D. C, U.S.A. Solar Activity: IGY World Data Center A: Solar Activity High Altitude Observatory Boulder, Colorado, U.S.A. Note: fi) Communications regarding data interchange matters in general and World Data Center A as a whole should be addressed to: Director, World Data Center A, National Academy of Sciences, 2101 Constitution Avenue, N.W., Wash ington 25, D. C, U.S.A.; (ii) Inquiries and communications concerning data in specific disciplines should be addressed to the appropriate atchive listed above. IGY World Data Center A fvr^ (^►Rockets and Satellites. National Academy of Sciences Washington 25, D.C. I IGY Satellite Report Series Number 8 15 June 1959 EPHEMERIS OF SATELLITE 1957 ALPHA 2 * and COLLECTED REPORTS ON SATELLITE OBSERVATIONS t * Prepared by the Theoretical Division Office of Space Flight Development National Aeronautics and Space Administration Washington, D. C. fSpecial Reports Nos. 22 and 25 and excerpts from N Smithsonian Institution, Astrophysical Observatory Cambridge, Massachusetts Note 1. This report is issued in accord with international arrange ments on the responsibility of IGY Data Centers: (i) to provide a copy of data and results to each of the other IGY world data centers and (ii) to make copies avail able at cost to scientists upon their request. 2. These data and/or report contents are reproduced as received from the experimenter. 3. Recipients of these reports are advised to communicate with the authors prior to utilization of experimental data for further publication: aside from the matter of courtesy, results in some reports may be preliminary in nature. IGY World Data Center A Rockets and Satellites CONTENTS Page Part I EPHEMERIS OF SATELLITE 1957 ALPHA 2 by Ann Eckels, Ruth Koldan, Isadore Harris, and Robert Jastrow Section Section Section Section Part II A: B: C: D: October 5-12, 1957 October 12-17, 1957 October 17-21, 1957 October 21-25, 1957 1 4 24 37 49 COLLECTED REPORTS ON SATELLITE OBSERVATIONS Smithsonian Astrophysical Observatory Special Reports Nos. 22 and 25 and excerpts from Nos. 18-21 Technical Parameters of Satellites 1958 Delta and 1958 Epsilon by Janet B. Clarke (SAO Special Report No. 18, pp. 3-4, October 4, 1958) 65 Orbital Acceleration of Satellite 1958 Beta Two by L. G. Jacchia and R. E. Briggs (SAO Special Report No. 18, pp. 9-12, October 4, 1958) 67 The Diurnal Effect in the Orbital Acceleration of Satellite 1957 Beta One by L. G. Jacchia (SAO Special Report No. 20, pp. 5-8, January 5, 1959) 71 The Earth's Gravitational Potential as Derived from Satellites 1957 Beta One and 1958 Beta Two by L. G. Jacchia (SAO Special Report No. 19, pp 1-5, December 6, 1958) 75 The Earth's Gravitational Potential Derived from the Motion of Satellite 1958 Beta Two by Yoshihide Kozai (SAO Special Report No. 22, pp. 1-6, March 20, 1959) 79 On the Effects of the Sun and the Moon upon the Motion of a Close Earth Satellite by Yoshihide Kozai (SAO Special Report No. 22, pp. 7-10, March 20, 1959) 85 An Empirical Formula for Satellite Ephemerides near the End of their Lifetime by L. G. Jacchia (SAO Special Report No. 20, pp. 1-4, January 5, 1959) 89 Atmospheric Densities from Explorer IV by G. F. Schilling and C. A. Whitney (SAO Special Report No. 18, pp. 13-22, October 4, 1958) 93 The Structure of the High Atmosphere, I. Linear Models by C. A. Whitney (SAO Special Report No. 21, pp. 1-12, February 27, 1959) 103 The Structure of the High Atmosphere, II. A Conduction Model by C. A. Whitney (SAO Special Report No. 25, April 20, 1959) 115 Note on References to Smithsonian Astrophysical Observatory Special Reports 122 PART I EPHEMERIS OF SATELLITE 1957 ALPHA 2 by Ann Eckels, Ruth Koldan, Isadore Harris and Robert Jas trow Theoretical Division Office of Space Flight Development National Aeronautics and Space Administration Washington, D.C. EPHEMERIS OF SATELLITE 1957 ALPHA 2 Satellite 1957 Alpha 2 (Sputnik I) was launched by the USSR on October 4, 1957, and transmitted radio signals during most of the interval from October 4 to October 25, 1957. The Alpha 2 signals are exceptionally interesting for ionospheric investigations because they were transmitted at the relatively low frequencies of 20 and 40 megacycles. The present ephemeris has been prepared for use in these investigations at the request of the Working Group on Satellite and Ionospheric Measurements of the U.S. National Committee for the IGY, pending release of an official 1957 Alpha 2 ephemeris by the USSR. The ephemeris is based on a combination of minitrack observations and Illinois Uni versity interferometer data. Mr. J. T. Mengel of Project Vanguard provided the minitrack data, which were used for the determination of initial approximations to the eccentricity and the perigee altitude. The Illinois University interferometer observations were obtained from Prof. G. Swenson. These give the times of crossing of the 40° North latitude and the corresponding longitudes at those times, and were the basis for the deter mination of the orbital period and for minor improvements in the approximations to the remaining orbit elements. The period of the observations is divided into four sections represented by indepen dent sets of orbit elements. Each set of orbit elements has been adjusted to give optimum agreement with the Illinois observations for the corresponding interval. A list of the elements appears in Table 1. The variations in this table are a measure of the probable errors in the determination of the orbit elements. Tables 2 and 3 list the differences between the ephemeris and the observations with respect to the time of crossing the 40° North parallel of latitude, and the longitude at the time of latitude crossing. The residuals in crossing time have a mean value of 1 second, corresponding to an error of 8 kilometers along the satellite track. The mean residual in longitude is 0. 15°, corresponding to a displacement of 10 kilometers in satellite position at 40° North latitude. The perigee altitudes deduced from the minitrack data have a probable error of 10 km. The positional error in the ephemeris is therefore approxi mately 10 kilometers in all directions. We wish to thank Mr. Mengel and Prof. Swenson for their kindness in furnishing the records and data used on our calculations. We are also grateful to Mr. William F. Cahill for the preparation of the IBM 704 programs required in the construction of this ephemeris, to Mr. Joseph Wegstein for his collaboration in writing the earlier forms of these programs, to Mr. Clarence Wade, Jr., for his assistance in executing the machine calculations, and to the Applied Mathematics Division of the National Bureau of Standards for its cooperation in providing the operating staff and IBM 704 facilities. April 1, 1959 1 Table 1 Orbit Elements Used in the Generation of the Ephemeris Ephemeris Section Time: October 1957 5 13 30 01 12 13 34 48 17 01 49 19 21 01 29 38 Period: (Min.) 96.160 95.920 95.748 95.588 Inclination: 65°. 1 65°. 3 65°.2 65°.0 Perigee: (st. mi.) 151.5 145.5 143.6 140.3 Argument of Perigee: 50°. 5 48°.62 47°. 40 46°.33 Motion of Perigee: - 0 27/day - °. 27/day - °. 27/day - °. 27/day Motion of Node: -3°.19/day -3°.17/day -3°.16/day -3°.ll/day Table 2 Comparison of the Ephemeris with Observations: Southbound Passes Observed Time (October) d h m s 6 7 8 10 11 12 12 13 14 15 15 16 16 17 17 18 18 19 20 21 22 23 23 24 24 25 13 13 13 13 13 11 13 11 11 10 11 10 11 10 11 10 11 10 09 09 09 08 08 07 09 07 32 33 35 36 35 58 34 57 55 17 53 14 49 10 46 06 42 01 56 50 43 00 00 52 28 44 13 55 09 01 41 50 48 28 31 11 00 09 55 31 15 18 00 29 04 02 22 34 34 41 08 08 O - C o - c Seconds of Time Degrees of Longitude -1 -2 -1 0 +2 -1 0 -2 -3 -3 -3 -2 -2 0 0 0 0 0 0 +3 +2 +1 +1 +1 +1 +1 - .07 - .13 - .17 - .29 -1.83 -0.38 0 - .04 - .08 - .09 - .10 - .13 - .13 + .01 + .03 + .01 0 0 0 - .02 + .04 + .09 + .09 + .15 + .13 + .18 NOTE All times in Tables 1, 2 and 3, and in the ephemeris are in Universal Time. 2 Table 3 Comparison of the Ephemeris with Observations: Northbound Passes Observed Time O - C o - c (October) Seconds of Time Degrees of Longitude d h m s 7 10 11 12 13 13 14 14 15 15 16 17 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 05 03 03 03 01 03 01 03 01 03 01 01 01 01 23 01 23 01 23 01 23 01 23 01 23 01 23 10 37 37 36 59 35 57 33 55 31 52 49 45 40 59 35 54 29 47 23 40 16 32 08 24 00 15 56 33 25 44 38 32 54 46 36 26 45 19 18 40 50 28 03 38 38 11 36 06 55 23 36 01 37 -2 +1 +2 +1 +1 +1 0 0 -1 -1 0 0 0 0 +1 +1 +1 0 0 0 0 -1 0 0 +1 0 0 + + + + + + .54 .95 .44 .29 .13 .13 0 0 - .13 - .15 - .25 0 - .11 - .20 - .06 - .03 - .38 0 - .05 - .04 - .07 - .10 - .11 - .10 - .16 - .16 - .21 8 999 il*601 E9*E£I 10*191 Z£*£9IiZ*i*I- £I*Z*IZE'OEI- SZ*2 IEZ'ZOI- 96*69- S£*Zi- 95*6*- 9S*9Z- *S*9- 11** Oi*6I *o*sz S9*6Z 96*£ SI*£* £6"8* 15*95 ZE*i9 Bi'e i8*iOl SE'SEl 9Z*iSl SiMil i9*9il£1*98- iE'i - 98* 9- £6*9*- 9ft- i4*9I 4i*i£ E * * 19*6* 02**4 14*84 4i*i9 69*Iil69*Z9 09*Ei 0£M8 *£*Z6 49*i£I6* i l- *6*E4l2 *iI *0*£I *£*9E 6 *£Z86*8Z 20* £I- 6* 9ZI*9*01I64 EC I*' 96< 60 88 6£ 28 20 ¥9 ££ £> 90 i8 48 69 SI ¥i zs 6i 16 3-7 OS it 9t CO a es £0 E* £9 95 41 ET 60 91 01 60 *i' 9Z' IS 96 t8 6£ £9 bZ tZ CT 29 iZ 81 69 60 £8 9B t8" tZ' 11- 15- 85- £9- 49- 29- iS- 6*7- I*- •l£- IZ- 01- •0- •01 tz 'ZC £9 'ZS -9 '♦9 E9 34 04 •19 IE IZ ZI •z •i- 91- 5Z- 11- 15- 95- £9- 59- £9- iS- os- I*- I£- IZ- II- '0- '01 IZ •Z£ z» zs 04 ¥9 •79 h4 5S I* Z£ £*6Z 91 it 81 03 •*6*£6 £4•64* £8 4£•ii£ 98•££E 9Z•I6Z ZS•I5Z 9S *0 6Z •551♦I 56 ¥S ¥£ 9* It z„ it 46•SZE tl•59E ZI 95 62 61 EZ •ESS14 0£ 10 tz E6 to jr. 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Special Reports Nos. 19-25 are all entitled "Research in Space Science. TECHNICAL PARAMETERS OF SATELLITES 19S8 DELTA AND 1958 EPSILON Janet B. Clarke* Astrophysical Observatory, Smithsonian Institution The following table is presented as an extension of the chart which appeared in Special Report No. 12, entitled "Technical Parameters of the Artificial Earth Satellites. " That chart itemized the pertinent technical data for the nine objects then orbiting in outer space. Since the completion date of Report No. 12, however, three additional objects have been ejected Into orbit. Two of these are the components of the third Russian satellite launching, Sputnik III or 1958 Delta, and the third is the U. S. satellite, Explorer IV, or 1958 Epsllon. Pre liminary technical characteristics of these additional satellites have been gathered trom various sources and are summarized briefly below. It should be noted that the values of orbital elements are given only for the initial launching time. While these are interesting in that they illustrate the degree of success of the particular launching, they are inherently less accurate than orbital data computed for later time periods. Since the exact values of orbital elements can be derived only after several observations have been made, the initial values are extrapolated backwards and thus, are not based solely on immediate observations made the day of launching. Data given regarding the physical dimensions and payloads of the artificial earth satellites are based on releases by the U.S.S.R. and U.S.A. National IGY Committees, re spectively. As is evident, less information has been received for the Russian satellite, 1958 Delta, and consequently, the mass-area ratios have been inferred through rather speculative methods of numerical deduction. In conclusion, we should emphasize that the information presented in this table is by no means final or complete. Needless to say, we would be most interested in receiving aav additions or corrections which the recipients of this report might have to offer. Acknowledgements I am exceedingly grateful to Dr. D. Lautman, Mr. Jack Slowey, Mr. Raymond Woo, and Miss Marilyn Rane for their contributions to the tabular content of this report. * Secretary to the Special Assistant, Office of the Director. -65- TABLE OF ARTIFICIAL SATELLITE PARAMETERS SATELLITE 19S8 Si 1958 82 1958 & Parameters Carrier Rocket SPUTNIK III EXPLORER IV Launching Date (U.T. ) Launching Time (U.T. ) Injection Point: Time (U.T. ) Latitude (°) Longitude (•) 15 May 1958 09 00 7 7 7 ' 7 7 7 Initial Period (min) Initial Apogee (km ) Initial Perigee (km) Inclination (°) Initial Eccentricity 105.9 1,879.8 241.4 65.4* 0.111 105.9 1,879.8 241.4 65.4* 0.111 Length (cm) Diameter (cm) Weight (kg ) Payload Weight (kg ) 7 ? 7 Radio Transmission t Frequency (mc) Power (mw) Frequency (mc) Power (mw) Battery Lifetime (days) Satellite Lifetime (days) Effective Mass-Area Ratio (gm/cm2) Scientific Experiments Carried 26 July 1958 14:59 15 May 1958 09 00 7 15.07 33.96*N 285. 9*E 110.3* 2, 197 257 50.33* .127 357 173 (base) 1,327 968 204 15.9 16.7 8.3 20.005 108.00 10 108.03 30 about 60 365 (2) 7 7 583 (1) 203 (1) 6.42 (28-58) 7 (8-17) f geophysical - | geophysical * Nodal Period. (1) Prediction made by Mr. J. Slowey, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. (2) Prediction mode by Dr. D. Lautman, Optical Satellite Tracking Program, Smithsonian Astrophysical Observatory. -66- ORBITAL ACCELERATION OF SATELLITE 1958 BETA TWO L. G. Jacchla* and R. E. Briggs** Astrophysical The present study is based on an analysis of 1450 Minitxack observations of Satellite 1958 Beta Two made between March 17 and September 16, 1958. The observations, kindly made available by Project Vanguard at the Naval Research Laboratory, were reduced using the subsatellite -point program (1, 2), with the assumption of the following elements: i q « a. = JO ■ (t in 34*255 1. 1028 earth's equatorial radii 158*53 - 3*0126(t - 1958 March 16.0) 121*58 * 474027 (t - 1958 March 16.0 ) days, U.T. ) The resulting times of perigee passage, anomalistic period P , and orbital acceleration dP/dt, are given in the accompanying Table I j the last two quantities are shown graphically in Figure 1 . It appears that the acceleration varies rhythmically, with cycles of the duration of 24 to 37 days ; the mean period is dote to 30 days. During each of these cycles the acceleration varies over a range of 50 to 100 percent of its mean value; the mean value itself seems to be subject to slower fluctuations. Of particular interest is the sharp rise in the acceleration in the second half of August, when it increased by a factor of 4 in just over two weeks. A periodicity of about 25 days was barely discernible, according to E. C. Comford (3), in the acceleration of Satellite 1957 Beta One ; the author mentioned that "this had provoked speculation that the tide -raising force of the moon may play some part", although several other possible sources for the irregularities were envisaged. The acceleration curve published In Special Report No. 13 (2) does not bear out this periodicity and seems rather to point to 19 -day cycles or to double oscillations with a period of 37 days. The fluctuations in 1958 Beta Two appear to be too irregular to be explained by tidal phenomena, and seem to suggest, rather, semi-regular changes in the atmospheric density such as could be caused by variable solar radiation - for which one would expect to find occasional periodicities of the order of 27 days and possibly a correlation with geomagnetic activity. A preliminary comparison of the observed accelerations with geomagnetic planetary indices appeared rather Inconclusive - although the sharp acceleration maximum near Sept. 1 followed two weeks of strong geomagnetic activity. It must be emphasized that the accelerations determined from positional observations of artificial satellites cannot be compared, day by day, with geomagnetic or other phenomena, inasmuch as they are the second time derivatives of the observed function. At best, the computed accelerations will always be a smoothed-out version of the true accelerations, in which each individual value ii the average of a few days. We may add that the synodic period of precession of the line of apsides for 1958 Beta Two amounts to approximately 9000 revolutions, so that any effect arising from the motion of the perigee from night to day and vice-versa should give origin to fluctuations with a periodicity of * Astrophysicist, Division of Meteoritic Studies ** Mathematician, Division of Meteoritic Studies -67- this order. This is clearly not the present case ; in particular, the rapid rise of the acceleration during the second half of August occurred at a time when the perigee was not far from the subsolar point. In Special Report No. 12, a value log p = -15.45 (g/cm') for the atmospheric density at perigee height (656 km) was computed by one of the authors (4), under the assumption of an acceleration of -1 . 95 x 10 days per day. The present analysis shows that this value of the acceleration was quite close to the average acceleration in the interval from March to August 1958. Since, however, the acceleration has shown variations from -1. 1 x 10-7 to -5. 3 x 10"? days per day, the computed atmospheric density must be considered to be variable between log f> = -15.0 and log p = -15.7. References 1. Jacchia, L. C. : "Program for Determination of Geographic Sub-Satellite Points. " Chapter IV, Special Report No. 11, Smithsonian Astrophysical Observatory, Cambridge, February 21, 1958. 2. Jacchia, L. C. : "Orbital Results for Satellite 1957 Beta One. " Special Report No. 1 3 , Smithsonian Astrophysical Observatory, Cambridge, May 21, 1958. 3. Comford, £. C. : "A Comparison of Orbital Theory with Observations Made in the United Kingdom on the Russian Satellites. " Royal Aircraft Establishments (Famborough), July 1958. 4. Jacchia, L. C. : "The Secular Perturbations and the Orbital Acceleration of Satellite 1958 Beta Two." Chapter II, Special Report No. 12, Smithsonian Astrophysical Observatory, Cambridge, April 30, 1958. -68- TABLE I n 0 50 100 ISO 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 (days) \ (U. T. ) 1958 Mar. Apr. May June July Aug. Sept. 17.61053 22. 27335 26.93614 31.59889 5.26160 9.92425 14. 58685 19. 24941 23.91193 28. 57441 3. 23682 7.89917 12.56146 17. 22370 21.88590 26.54806 31.21017 4. 87222 9.53420 14. 19614 18.85805 23.S1993 28.18176 2.84355 7.50530 12.16702 16.82872 21.49038 26.15202 30.81362 4.47517 9.13666 13.79810 18.45950 23.12083 27. 78208 1.44322 6. 10424 10.76515 15.42597 0*0932561 554 546 536 525 516 508 500 489 476 464 453 444 436 427 416 403 392 385 379 371 362 354 347 342 336 330 324 315 304 293 284 273 258 239 216 193 173 0.0932157 -69- dP/dt (day/day) -1.7 x 10"' -1.6 -2.7 -2.1 -1.7 -1.7 -1.6 -3.1 -2.6 -2.6 -2.1 -1.7 -1.7 -2.1 -2.6 -3.1 -1.6 -1.3 -1.2 -2.2 -1.7 -1.7 -1.3 -0.8 -1.8 -0.8 -1.7 -2.1 -2.6 -2.1 -1.6 -3.1 -3.3 -4.8 -5.3 -4.7 -3.9 Figure 1 Time variation of iMOllHllMIl period and orbital acceleration of Satellite 1958 Beta Two -70- THE DIURNAL EFFECT IN THE ORBITAL ACCELERATION OF SATELLITE 19S7 BETA ONE by L. C. Jacchia* Astrophysical Observatory, Smithsonian Institution (Manuscript received December 15, 1958) A tabulation of the orbital acceleration of Satellite 1957 Beta One has been given in S. A. O. Special Report No. 13 (1 ). At the time the report was written, there was still some uncertainty - at least in this writer's mind - about the origin of the fluctuations in the observed accelerations. Since then observations (2} of the Vanguard Satellite 1958 Beta Two have made it clear that the fluctuations are not caused by a change in the effective presentation area of the satellite, but are of atmospheric origin. It seems appropriate, therefore, to re -appraise the results for 1957 Beta One in this light. In particular it may be of some interest to check the acceleration curve for the presence of a diurnal effect, which should manifest itself as the perigee changes its position with respect to the sun. Table I gives, at 10 -day intervals, the geocentric angular distance \f/ between the perigee and the sun, together with other basic quantities, i.e. i The argument of perigee CO , the right ascension of the ascending node On , the right ascension 0- and the declination S- of the perigee. The number of revolutions n corresponding to each date has the same origin as in Special Report No. 13. The observed accelerations are plotted inRgure'l, at the bottom of which the angle yr Is graphed for comparison. There seems to be little doubt about the presence of the diurnal effect. Apart from shorter, superimposed fluctuations, the departures of the observed acceleration from a smooth curve are very closely in phase with the \f/ curve. The effect is gradual, and there is no evidence of a discontinuity at the time when the perigee crosses from light into shadow or vice -versa. The observed semi -amplitude of the diurnal effect is roughly 10% of the acceleration. Since the corresponding semi -amplitude in yr was 60°, we can say that the magnitude d of the diurnal effect can be expressed as d= .0017 A ( -f-yo) where A is the undisturbed acceleration and \fr- >j/"0 is expressed in degrees. is a reference angle comprised between 90° and the zenith distance of the horizon at perigee height - depending on the assumption concerning the effective height at which the diurnal effect operates. During the time interval covered by Table I the height of the geometric horizon at perigee height decreased from 104°. 6 to 103°. 3. ♦Astrophysicist, Division of Meteoritic Studies -71- REFERENCES Jacchia, L. G. : "Orbital Results for Satellite 1957 Beta One. " Special Report No. 13, Smithsonian Astrophysical Observatory, Cambridge, May 21, 1958. Jacchia, L. G. and Briggs, R. E. : "Orbital Accelerations of Satellite 1958 Beta Two. " Special Report No. 18, pp. 9-12, Smithsonian Astrophysical Observatory, Cambridge, October 4, 1958. -72- Table I POSITION OF PERIGEE WITH RESPECT TO SUN FOR SATELLITE 1957 BETA ONE t(U.T. ) 1957 1958 Nov. 6.0 16.0 26.0 Dec. 6.0 16.0 26.0 Jon. 5.0 15.0 25.0 Feb. 4.0 14.0 24.0 Mar. 6.0 16.0 26.0 Apr. 5.0 n 22 162 302 442 583 725 867 1012 1157 1303 1450 1598 1747 1898 2051 2206 CO aA 59° 3 55.2 51.1 47.0 42.9 38.7 34.5 30.3 25.8 21.6 17.3 12.8 8.3 3.7 3S8.9 353.7 108° 3 81.7 54.9 28.0 0.7 333.1 305.1 276.7 247.9 218.7 189.0 158.8 128.0 96.5 64.0 30.4 -73- «, 143? 6 112.8 82.4 52.2 22.0 351.7 321.2 290.5 259.4 228. 1 196.5 164.3 131.5 98.1 C3.5 27.7 +51° 4 48.2 45.0 41.6 38.2 34.6 31.0 27.3 23.3 19.5 15.7 11.6 7.5 + 3.4 - 1.0 - 5. 7 94? 6 122.4 150.2 154.5 126.5 93.6 63.7 48.8 62.8 94.5 132.2 172.3 145.6 102.9 59.2 18.3 Number of revolutions 1S57 1958 Figure 1 . Orbital acceleration of Satellite 1957 Beta One, compared with the geocentric angular distance between the sun and perigee. A smooth curve has been drawn for reference through the jagged acceleration curve (top). When ^ is approximately 104° (bottom), perigee is at the divide between light and shadow. 74- THE EARTH'S GRAVITATIONAL POTENTIAL AS DERIVED FROM SATELLITES 1957 BETA ONE AND 1958 BETA TWO by Luigi G. Jacchia* Astrophysical Observatory, Smithsonian Institution ( Manuscript received November 1 , 195*8 ) An excellent set of 68 orbit determinations of Satellite 1957 Beta One (Sputnik II ) , covering the interval from November 9, 1957 to April 13, 1958, has been published by the Royal Aircraft Establishment, Farnborough, England (1 ). These data permit an accurate interpolation of all orbital elements during the lifetime of the satellite. Since the orbital inclination of this satellite differs by 31° from that of 1958 Beta Two (the Vanguard satellite) — which, thanks to its high perigee and continuous radio performance, yields highly reliable values for its secular perturbations --it was thought advisable to investigate the possibility of using the two satellites for the independent de termination of the second and fourth-order coefficients of the earth's gravitational potential. The secular precession of the right ascension of the ascending node, when all distances are expressed in units of the earth's equatorial radius, can be written as follows (1 ): • -3/2 2 SL = - n* a p" cos i (l) Here a is the major axis of the orbit ; n* is the mean motion of a satellite revolving around a point mess equal to the mass of the earth in an orbit with a = 1 ; p is the orbital parameter rp = a(l-e^)j i is the orbital inclination, J and K are, respectively, the coefficients of the second and fourth harmonics in the earth's gravitational potential. In the above expression all terms containing J , and higher powers of J and K, as well as their cross-products, have been neglected. We have used n* = 6135? 58/day. For Satellite 1958 Beta Two we have used the following mean elements, obtained by R. E. Briggs from Naval Research Laboratory orbital data and corrected on the basis of Minitrack obser vations. Epoch: t = 1958 June 18 .858 Anomalistic period = 0^09 32379 Eccentricity = 0. 19023 Inclination = 34°. 253 - 0°.00010(t-to) R.A. ofAsc. node = 259°.76-3°.0126(t-to) Arg. of perigee = 179°. 2 + 4°. 4027(t-to) ( t in days, U. T. ). No departure from linearity can be observed in the, motion of the node in the interval from 1958 March 17 to October 10. The estimated error in St is +0°.0002. From the anomalistic period, using first-order perturbation theory, we can compute a = 1. 361527. For Satellite 1957 Beta One we have interpolated at 10-day intervals, from the Royal Air craft Establishment data, the orbital elements in Table I. The nodal precession derived from the data in the last column is tabulated in Table II, together with the individual values of J computed from them, using K = 1.0 x 10"^. These values of J were computed only to test the inner con sistency of the data. ♦Astrophysicist, Division of Meteoritic Studies -75- A secular decrease is observed in the orbital inclinations of both satellites, and a prelimi nary computation, based on a theory developed by Sterne (2) shows that in both cases it is by far too large to be accounted for by the transverse drag caused by the rotation of the atmosphere; moreover such a drag would not yield a nearly constant rate of decrease. Whatever the force which causes this perturbation, it will presumably have some effect on the motion of the node. In the case of 1958 Beta Two the change in the inclination is <so slight, that no effect can be reasonably expected to result in the motion of the node. In 1957 Beta One, on the contrary, the possibility of such an effect cannot be discounted. To obtain mean values of ] and K over the observed interval for 1957 Beta One, we have integrated equation (1) timewise, between the limits tj and t2, and we thus obtain: <&2 - &j = AJ + BJ + CK (2) where ^ n* a"3/2p~2 cos i dt = ft2f ^ ij dt rt2 rt2 C=- 14 J-^(7sin2i-4)dt= ^ f3 dt Values of fj, f2 and f^ are given in Table II. Integrating from tj = 1957 Nov. 26.0 to t2 = 1958 March 16.0, we obtain (for 1957 Beta One ): -318°. 48 = -1°.9624 x 105 J - 4°. 91 x 104 J2 + 6°. 10 x 104 K . (3) For 1958 Beta Two, on the other hand, we have -3°, 0126= -1853°. 74 J + 536°J2 - 411°iK. (4) Solving (3) and (4) simultaneously, we obtain J = 0.0016244; K = 6.9xl0"6. (5) In the interval from t j to tj, the inclination of 1957 Beta One changed by -0°. 12. Assuming that the perturbing force which caused this change had an exactly equal effect on the node, i. e. caused an extra precession of the node £SL = -0°- 12, the result would be J =.0016241; K = 8.0xl0~6. -76 (6) The values of K which have been derived using gravity measurements and different hypotheses concerning the departures of the geoid from a rotational ellipsoid, vary between 9.0 x 10 and 11.4 x 10 if we wish to adopt the higher of these two values, then we must postulate an extra precession Aft -0°. 47 in the node of 1957 Beta One, and we obtain J = 0.0016234; K = 11.4xl0-6. (7) The fact that the rate of change of the orbital inclinations is negative shows that the force responsible for it must be acting in a transverse direction along the general eastward motion of the satellite. Such a force would, if anything, have caused a westward (negative) motion of the nodes ; it would seem then that the possibility of a positive excess in the nodal precession due to this cause can be excluded. We can thus consider the value of 6.9 x 10-6, obtained under the assumption of A& = 0 ac a lower limit for K. It is reasonable to assume that the actual value of K is somewhat smaller than 10 x 10 As to J, it is clear that, no matter what final value is adopted for K, it must be not far from 0.0016240, with an estimated error of + 10 x 10" . The coefficients J and K are related to the "flattening" a of the spheroid by the equations , = a " \P -\ a2 + if" fl/° + 7*< +0<fl3> K = 3a2 - ^ ap + ^ K. +0(a3). <8> (9) In these equations 0 = RIO 2/k 2 , where R is the equatorial radius of the earth, CD the earth's angular velocity of rotation and ke the "geocentric" gravitational constant; we have adopted p = 0.00346149. The parameter rC is associated with the depression of the spheroid. If we assume that the equipotential surface of the earth is an exact spheroid, we have K = 0 ; estimates of K vary from zero to 6. 8 x 10-7. For J = 0.0016240 we obtain a = 1/298. 26 under the assumption of K. = 0, and a = 1/298. 30 assuming K =6,8 x 10~7. The corresponding values of K are 8. 8 x 10"^ using K. m 0, and K = 11. 2 x 10-6 using K = 6. 8 x 10-7. Since, to first-order, d(jl) = - 1 dj and dK = 6a dj, we find that a change of + 10 x 10-7 in J will result in a change of 0. -.09 in .i- , but of only -2 x 10"^ in K (i. e. , K as derived from equation (9) in unaffected by any reasonable error in J ). We are thus led to the following most probable values with their estimated errors: J K 1/a K =0.001624 + .000001 =9(+2) x lO^ = 298.28 + .11 ■ 3(+3) x 10"7 The value of 1/a given above is in essential agreement with the values of 1/298.0 +0.3 and 1/298. 38 + .07 derived by the U. S. Army Map Service (3) from satellites 1958 Alpha and 1958 Beta Two. It should be noted, however, that this flattening derived from dynamic data does not necessarily have the same meaning as the flattening determined from geodetic measurements on the earth's surface. As pointed out by G. Veis (4), the "dynamic" flattening is the flattening of a fictitious, equipotential spheroid containing all the earth'* mass, which will give rise to the observed gravitational potential. This fictitious spheroid does not necessarily coincide with the spheroids obtained from geodetic observations, which need special assumptions to correct for the effect of masses left outside the geoid. -77- Table I Orbital Elements for 1957 Beta One Interpolated from K. A. E. Data . t (OnU.T. ) Nov. Dec. Jan. Feb. Mar. Apr. 6 16 26 6 16 26 5 IS 25 4 14 24 6 16 26 5 a e i u> 1.14601 1.14236 1.13869 1.13494 1.13106 1.12694 1.12238 1.11721 1.11193 1.10676 1.10138 1.09547 1.08877 1.08085 1.07113 1.05750 0.0981 0.0953 0.0926 0.0897 0.0867 0.0835 0.0800 0.0759 0.0719 0.0678 0.0635 0.0588 0.0534 0.0470 0.0392 0.0284 65? 37 .36 .34 .33 .32 .31 .30 .29 .28 .27 .26 .25 .24 .22 .a 65.20 SSP.Z 55.2 51.1 47.0 42.9 38.7 34.5 30.3 25.8 21.6 17.3 12.8 8.3 3.7 358.9 353.7 ft (108? 3) 81.69 54.93 27.95 0.69 333.09 305.11 276. 72 247.91 218.67 188.97 158.76 127.96 96.45 64.03 30.41 Table II Satellite 1957 Beta One Observed Values of Nodal Precession (from R. A. E. data) and individual values of J t (0hU.T. ) Nov. 26 Deo. 6 16 26 Jan. 5 15 25 Feb. 4 14 24 6 16 fl ft (degrees per day) (degrees) h (degrees) -2.686 -2.711 -2. 742 -2. 778 -2.818 -2. 860 -2.902 -2.946 -2.994 -3.049 -3.113 -3.191 -1652. 8 -1670.9 -1690.0 -1710.5 -1733.7 -1760.5 -1788.5 -1816.6 -1846.6 -1880.3 -1919.6 -1967.6 -399 -405 -412 -420 -428 -438 -448 -458 -469 -482 -497 -516 f3 (degrees) +495 503 512 521 531 544 556 569 583 599 618 641 io3j (K = 1.0 x 10"5 1.6275 1.6248 1.6249 1.6265 1.6278 1.6270 1.6250 1.6242 1.6238 1.6240 1.6242 1.6243 References Cornford, E. C. , "A Comparison of Orbital Theory with Observations Made in the United Kingdom on the Russian Satellites. " Royal Aircraft Establishment (Farnborough), July, 1958. Sterne, T. E. , "The Effect of the Rotation of a Planetary Atmosphere upon the Orbit of a Close Satellite. " (Unpublished). O'Keefe, ^. , H. G. Hertz and M. Marchant, "Oblateness of the Earth by Artificial Satellites. " Harvard College Observatory Announcement Card 1408. June 24, 1958. Veis, G. Private communication. -78 THE EARTH'S GRAVITATIONAL POTENTIAL DERIVED FROM THE MOTION OF SATELLITE 1958 BETA TWO Yoshihide Kozai* Astrophysical Observatory, Smithsonian Institution J. A. O'Keefe and Miss Eckels have recently reported flj that the long-period (80 days) variations in the eccentricity of the orbit of Satellite 195802, the Vanguard satellite, can be explained by a north-south asymmetry in the gravitational potential of the earth. That is, the axial symmetry of the field is retained, but the third harmonic in latitude is added. Explicitly, it is assumed that the potential of the earth is + 7* {W + J ,in2 5 " i za> + } • (1) at a point whose declination is $ and whose geocentric distance is r_. In this expression, A|, Aj, and A^ are constant, C is the constant of gravitation and M is the mass of the earth. Expressing U», the part of the third harmonic, in terms of the conventional orbital elements, rather than declination and radius vector, and eliminating terms depending on mean longitude, I find the long-period part of U> , accurate to the third degree in the eccentricity, e, to be as followst <U3fc.P. " GM y ^ »in 1 (4 Jin2 i - l)e(l + |- e2 ) tin (2) where i is the inclination of the orbital plane to the equator, a is the semimajor axis and W is the argument of perigee. We note that no secular variations of the orbital elements are produced by this odd harmonic in the potential and that the coefficient of cor Vu is xero. The equations of variation of elements due to the third harmonic are the following; ♦Astronomer, Satellite Tracking Program -79- d&a = 0 , dt dge dt = dgl _ dt dt dSuJ dt V 1-e2 3U3 naV ' cos i 3U3 na* Vl-e^ sin i na2 -Vl-e2 sin i 3i cos i nor V 1 -e* sin i + dti- ' di dI -Jl-e2 na*e de &U33 3e ^tT where n is the mean motion, n is the longitude of the ascending node, and fi = A, 3- n cos i , 40 2 P = o(l-e2) Integrating these equations we have the following results S3 A3 e = -— 4 A2a S3 A3 i = - — -j 4 A2p p ' A3 blO = : 4 Ajp pA 3 Oil = A3 A2p sin i sin (J, e cos i sin U> , sin2 i - e2 cos2 i :—: sin i cos i sin i 1 cos CO , e e cos CO • -80- To confirm the suggestion of O'Keefeand Eckels, I analyzed the orbital elements of 195802 furnished by the Vanguard Computing Center from June 19, 1958, to Jan. 29, 1959. At first I subtracted the effect of air-drag as given by the following formulae* under the assumption that the perigee height is not changed through this period: a A A = - -~|- cos i *-5»"2' AM , \LzS\ah, (6) A M = J&n dt , where Aa> An and Ae are deviations from the values for Oct. 16 L2*1 27m (UT) 1958. Then I also subtracted solar and lunar perturbations** as follows: §e x 104 = -1.7 cos 2(Q+a-X&) + 0.5 cos (2U)+2A-3X0+iro) +0.1 coi 2(CJ+n-X(j). Si = 0°003 cos ft, (7) 8(U= 0?011 sin 2(cu+/l-\0) - 0?062 sin (20*2*1-3X0+* ) + 0?003 sin (20H/V2XQ) + 0?005 sin O + 0°055 sin , 80 = -O°001 sin 2X^ + 0?028 sin Z((ji+ft-\^ + 0°001 sin 2(X0-O) + 0?032 sin ( 2 UH 2 £1-3X^+1^) - 0?005 sin ft - 0?039 sin N<j , where \q, Hq, and are, respectively, mean longitude, longitude of perigee of the sun, mean longitude of the moon, ana the longitude of the ascending node of the lunar path referred to the ecliptic. * K. Squires, private communications to Dr. C. A. Whitney. ** Y. Kozai, unpublished. -81- Then assuming that the periodic inequalities are due to the third harmonics we obtain Ihe variations given in Table 1 . Table 1 Inequality Se Si Sa Observed Computed (0.43 +0.02) x 10"3 sin U3 0.42 x 10"3 -(0?007 + 0?001) sin 0> -07007 (0?106+0°010) cos CJ 07122 (0?01 8 +07003) cos to 07012 The diagram on, page 5 shows the observed values plotted against theoretical values for this same period, June 19, 1958, to Jan. 29, 1959. Assigning to each observed amplitude the weight that is reciprocally proportional to the square of the probable error, we have as the coefficient of the third harmonic, = (2.20+0.08) x 10~* The predicted amplitudes from this value are also shown in Table 1 . Table 2 SECULAR MOTIONS A Observed (per day) -37015 07 + 4 47404 62+10 Solar part -0.000 13 0.000 18 Lunar part -0.000 28 0.000 39 Corrected -3.014 66 4.404 05 The values of the secular motions of the node and the perigee, given in Table 2, correspond to the following quantities: n = 38627640 , anomalistic mean motion per day , e = i = 0.190 00, 34*250. 82- 150 175 —i— 200 225 250 —i— 275 300 325 350 375 195802 +.00040 Se .00000 -.00040 +°.20 So) +.10 .00 -"10 -.20 . . . j +°040 +°020 Sn .oo -1020 -1040 +°020 +!oio .00 -.010 -°020 150 175 200 225 250 275 300 325 X 350 Epoch (number of days after January 0.0, 1958) The dots represent the observed values for each seven days, and lines represent the theoretical values from =2.20 xlO-6 -83- 375 To compare with my results* , fl = - -^§n |l - ^| ( -i- - -|- sin2 i)J cos i -^n a »n2 i) (l + -£e2) cos i , W-^J. ,4-5 A,2 i,^.£(1.2i.„„J„} + ^4(16-62 sin2 i+49 sin4 i) (8) + e2( 328 -1244 sin2 i + 973 sin4 we must subtract solar and lunar perturbation from the observed values. The solar and lunar part have been derived from the following equations , 4 n* 3 2 n -|-fC|-i i (9) Vl-e' where 1 2 2 2 2 — sin J ( 1 + cos € ) + sin £ cos J . Here mj, J and £ are, respectively, the mass ratio of the moon to the earth, the inclination of lunar path to the ecliptic, and the obliquity. If we set njj a n^, m* » 1 and J = 0 , we may also derive the solar secular perturbation from these equations. m Then from CI and Co I derived the following: 1.6208 x 10 3 , 2.1 x 10"5. I am grateful to Drs. C. A. Whitney, L. G. Jacchia and G. Veis for their valuable discussions. References £lj Harvard Announcement Card No. 1420, Dec. 29, 1958. * Y. Kozai, unpublished. -84- ON THE EFFECTS OF THE SUN AND THE MOON UPON THE MOTION OF A CLOSE EARTH SATELLITE »»y Yoshihide Kozoi * Astrophysical Observatory, Smithsonian Institution In the present paper I will treat the lunar and solar perturbations of a close earth satellite whose radius is very small compared with that of the moon. Since the disturbing functions of the sun and the moon both have similar forms, only the method of deriving the perturbation for the moon will be described here. If we denote the geocentric radius vector of the satellite and of the moon by **r and rt r, respectively, and expand the disturbing function R into a power series of r/r1 , a small quantity, we obtain the expression, where G is the constant of gravity, m1 is the mass ratio of the moon with respect to the earth, and Sj it the Legendre polynomial of the i-th order; that is, S = t rVrr' . (2) We can omit the first term, which does not depend on the orbital elements of the satellite. We cannot expect any secular contributions from the odd-order terms, so I will derive the perturbation produced from the second-order term. Adopting geocentric coordinates, with x-axis directed towards the equinox and x-axls towards the north pole, we have the following three components of r (by using the conventional orbital elements): = cos (L+Xl) + 2 sin2 2 sin L sin CI, i = sin (L + ri) - 2 sin sin L cos A, (3) Y = sin i sin L, where L is the argument of latitude. We derive similar expressions for the moon, using primed letters to represent elements referred to the equator. Then, s has the following expression) * Astronomer, Satellite Tracking Program -85- » cot (L + A-L' -A') + 2 sin2 i- sin L sin (L' + A-A) + 2 sin2 sin L' sin (L + fl-A) (4) + 4 sin 2 i- tin 2 ^i tin L sin L' cos (A-A') + tin i sin i' sin L sin L' . It it convenient to express the disturbing function by mean longitudes, X and X' , and other orbital elements. Dropping all terms depending on the mean longitude of the satellite, which have little effect on the satellite's motion, we have as the principal terms of the disturbing functic R - n'2 m' a2({l+S«' cos (X' - (J -Jl')j |(1 + ^e2) A+ -j- eh j - 4.' tin (X- - U)< -ni) {(1 + \ •*) A- + J£ eS'}] , where A ■ 4 (* " 4 4 2 *) (1 - 4 «*«>2 '') 2 ' + X tin 2i sin 2i' cos (A-A') 16 + -2- dn2 i fln2 |i cot 2(/l-A') 16 + -| tin2 i'(l 8 tin2 i) cot 2(X' -A') Z + -2. sin2 i cot4 4r«* 2(X' -A) 8 2 - 4sin 21 8ln lIeo«2 v 008 (2X* -A-A') 8 Z + 4 «n2 1 ri°4 4 001 2(X' -2ft+A) 8 2 + |- sin 2i tin i' tin2 ^- cot (2X* +A- 3fl«> , 8 Z -86- (S) B - cot4 1 cos4 £ cos 2(X« -0>-il) + i- fin2 I (l-i- rtn2 2 '2 + cot4 co* 2 CO ' sin2 i' cos *2(0)+A-A'> + fin4 i cot4 -jr cot 2(u)-A+V) 2 2 + cot4 |. sin4 £ cot 2(u)+fl+X'-2il') + tin4 ^ tin4 ~ cot 2(X» - ZCl> -W+A) + -| tin2 i tin2 i' cot 2(V -JV- w) + |- tin2 i tin2 i' cot 2(X, + UKfl!) + tin i cot2 ~. sin i' cot2 cot (2X' -A' - iu>-fL) - i- tin i cot2 \ sin 2i< cos (2u*iViT) t£ <+ sin4 4j- sin2 i' cos Z{l»-£l+CV) + i- tin i sin2 i- sin 2i' cos ( 2 cu-il +/}.') + tin i sin2 i- sin i' cos2 j cos (2V + 2C0-1W11) - sin i cos2 i- sin i« sin2 ^- cot (^^^/l-SiT) + sin i sin2 i sin i' sin2 ^ cos ( 2X' - 3/1? - 2«»£) . By selecting all terms depending on X1 and by replacing cot by tin , we can alto derive expressions for A1 and B\ from A and B, respectively. The variations of e and i are obtained from the equations de _ Vl -e2 3R naZe . —- "» ' naa -/l -e* sin i _ 3 to -87- __Lna« -/l - ea sin i £R 3" (6, By using the variations $e and Si , Shi and $11 can be derived from the T cos i dt i2 VT-e2 sin i 3i na 2e 3e + 4?- Se + 4M«. de di (7) AO. di na2VTe^ sin i where fc) = A2„ 4-5 sin2 i P 2 fl = - n cos i . P4 It is remarkable that these disturbing functions do not affect the semimajor axis. In the righthand sides of the equations, i' , the inclination of the lunar path to the equator, Is gradually, but we may regard it as constant during one year or so. As for the secular terms of Ci and Oj, we have ^ dt 4 n —1— <2--| sin2 l4e2) (l--|iin2 V) , VT? 2 2 2 (•) where tin 1* = y sin2 Jtl+cos* €) + sin4 € cos J JL sin 2* sin 2J cos N - -i" "n* J sin 2 2 6 cos 2N. Here ] and N are the lunar inclination and the longitude of the ascending node referred to ecliptic, and C is the obliquity. "We can find the values of ] , N and V in the American Ephemeris. If we set m1 = 1 and J = 0 , we can derive the solar perturbations from the same equations . -88 AN EMPIRICAL FORMULA FOR SATELLITE EPHEMERIDES NEAR THE END OF THEIR LIFETIME by L. G. Jacchia* Astrophysical Observatory, Smithsonian Institution (Manuscript received December 15, 1958) In a post-mortem analysis of Satellite 1957 Beta One, searching for a simple function that would represent the period variations of the satellite during its last few hundred revolutions, the author found a relation between the period and the number of remaining revolutions. This turned out to be extremely useful in making predictions during the last week of the lifetime of Satellite 1958 Delta One. Since some interest has been expressed concerning prediction techniques at the end of a satellite's lifetime, we think we are justified in presenting a brief discussion of this formula, in spite of its purely empirical character. Let n be the number of revolutions of a satellite, counted from an arbitrary origin, and n* be the number of the last revolution In such count. Moreover, let P be the orbital period of the satellite at the n^> revolution and P* a critical period, constant for each satellite. For Satellite 1957 Beta One it was found that, during the last 100 revolutions the relation 3 constant =, k d log (** - n) (1) ' ' was almost rigorously satisfied when P* was put equal to 0&6030. For 1958 Delta One the same relation held true, equally well, with P* again equal to 0^06030. Since the area/mass ratio was very similar for the two satellites, k itself was nearly identical in the two cases (0.406 for 1957 Beta One and 0.403 for 1958 Delta One). A plot of log (P - P*) against log (n* - n) for both satellites is shown in Figure . 1 . It will be noticed that the critical period P* = 05*0603 = 86.8 minutes is just about the value of the period that a satellite reaches in the course of the last revolution, when it starts in its final descent arc; the corresponding height in a circular orbit is 120 km above the equator. This critical height should not be too different from one satellite to the other, so its stands to reason that P* can always be taken equal to 0^0603, thus eliminating one unknown parameter in equation (1). From equation (1 ) we have, by integration log (P - P*) = log b + k log (n* - n), (2) P = P* + b (n - n*)k, (3) or where b is a constant. Integrating again, we obtain ♦Astrophysicist, Division of Meteoritic Studies 89- T = a + P*(n*-n) - J±- . n)k+l {4) where T is the time of ascending -node crossing (or any other crossing from which the period P is determined), and a is another constant. A comparison of the observed instants of ascending -node crossings with instants computed by equation (4) with suitable parameters is given in Table I, both for 1957 Beta One and 1958 Delta One. It will be seen that the residuals in both cases amount to only a moderate number of seconds. The equations used are: For 1957 Beta One : T= 1958Apr. 8.02102 + 0.0603 (ng-2250) - 0.0003275 ( 2350-nB)1,406 (5) For 1958 Delta One : 1.403 T= 1958 Nov. 27.16316 + 0.0603 (nD-2790) - 0.00032894 (2897-nD) (6) njj and n_ represent the number of revolutions for each of the two satellites, respectively, counted from an arbitrary origin. The quantity An tabulated for 1958 Delta One is the difference between Bjj and the value of n— for which the first satellite had the same period. As can be seen, the two satellites were out of phase by 544 revolutions at the start of the tabulation, but the difference increased slowly, at a nearly constant rate. This circumstance made it possible to have an independent estimate of n* - i.e., of the time of demise - for 1958 Delta One. A similar procedure could have been used, presumably, even if the area/mass ratio of the second satellite had been widely different; in that case, however, a scaling factor in n would have been advisable before computing An. It should be clear that for a determination of the parameters k and n* it is simpler to use the observed periods P, rather than the crossing times T. If we write log (n*-n) = x, and log (P-P*) = y, and select three corresponding sets of x and y (subscripts 1, 2, 3), the procedure is to find by trial and error, a value of n* which will satisfy the relation x2 -xi _ y2 - vi x3 " x2 v3 ' y2 which derives from equation (1 ). Once n* is found, we have x3 " Xl k= , (8) y3-yi after which a and b can be determined from two observed values of T. It should be obvious that equation (1 ) cannot be expected to hold throughout the lifetime of a satellite, especially in the case of highly eccentric orbits, so that the formula does not appear suitable for the computation of long-range life expectancies of satellites. It appears, however, that toward the end of a satellite's lifetime, when formulae based on the orbital eccentricity are bound to fail, this empirical formula may offer a distinct advantage. 90- 0 Figure 1. Plot of log (P-P*) against log (n-n*) for Satellite 1957 Beta One (open circles) and Satellite 1958 Delta One (dots). -91- Table I The Last Revolutions of 1957 Beta One and 1958 Delta One Comparison with Ephemerides Using Equations ^4) Satellite 1957 Beta One "B 2250 2275 2300 2310 2320 2330 2340 2345 2347 2348 2349 2350 Tftobs. Apr. O-C P log(n*-nB) (n*= 2350) 7. 80859 .00000 ?063296 9. 38686 +.00010 .062957 10.95582 -.00004 .062547 11.58032 -.00013 .062355 12. 20281 -.00012 .062136 12. 82285 -.00007 .061859 13.43970 +.00002 .061477 13. 74637 .00000 .06117 13.86853 -.00006 .06099 13.92947 -.00008 .06088 13.99028 -.00011 .06072 14.05088 -.00014 .06050) \og(P-P*) (P* = .0603) 2.0000 7.4765 -10 1.8751 7.4244 1.6989 7.3516 1.6021 7.3128 7.2639 1.4771 7. 1928 1.3010 1.0000 7.0708 6.940 0.6990 0.4771 6.839 0.3010 6.763 6.623_ 0.0000 L last revolution J Satellite 1958 Delta One A-' T 4tOM. 2790 2800 2810 2820 2830 2840 2850 2860 2870 2880 2890 2895 2896 2897 Nov. 26.93177 27.56463 28.19623 28.82651 29.45533 30.08256 30.70811 Dec. 1.33186 1.95348 2.57255 3.18814 3.49371 3.55456 3.61530 O-C P .00000 fo63347 +.00010 .063224 +.00016 .063096 +.00019 .062957 +.00015 .062804 +.00003 .062641 -.00009 .062472 -.00013 .062272 -.00016 .062046 -.00009 .061756 +.00003 .061304 -.00007 .06090 -.00007 .06080 +.00005 (.06067) -92- log (n*-nD) (n* = 2897 ) log(P-P*) (P*= .0603) 2.0294 7.4839 -10 7.4660 1.9868 1.9395 7.4465 7.4244 1.8865 1.8261 7.3986 1.7559 7.3694 1.6721 7.3369 1.5682 7.2949 7.2420 1.4314 1.2304 7.1632 0.8451 7.0017 6.778 0.3010 0.0000 6.690 t~ last revolution -J An 544 545 545 545 546 546 546 546.0 546.4 546.8 547.0 547.2 547.4 ATMOSPHERIC DENSITIES FROM EXPLORER IV by G. F. Schilling* and C. A. Whitney** Astrophysical Observatory, Smithsonian Institution Abstract Orbital changes of Satellite 1958 Epsilon have been analyzed to derive upper atmosphere densities in the altitude interval of 257 km to 270 km between latitudes 50° north and 31° south. Uncertainties and possible errors in the calculations are discussed in detail. At an altitude of 262. 5 km, the most probable value of mean density is 1.3 + 0.5 x 10~13 gm/cm . The results show a high degree of in ternal consistency, but give no evidence of an appreciable variation of density with latitude. Introduction A summary and review of average density values, derived by various investigators from the satellites that had been launched prior to May, 1958, can be found in two publications (1, 2). Mean densities inferred from Sputnik III by B. M. Folkatt and us (3 ) agree generally with the earlier findings, but since they are based on speculative assumptions about the shape and weight of the Soviet satellites, they cannot be considered reliable. The variations of the orbital elements for Satellite 1958 Epsilon have been used to determine a number of values of upper atmosphere density between 257 km and 270 km above the earth's surface, and latitudes 50° north to 31° south. The initial orbit calculations were based on re ductions of photographs made with the Baker-Nunn satellite cameras, radio observations by Minitrack and Microlock stations, visual sightings by Moonwatch teams, and radar observations. The basic ephemeris and elements, distributed at roughly weekly intervals by the Smithsonian Astrophysical Observatory, were computed by Dr. D. A. Lautman. A number of complex phenomena can affect the reliability and accuracy of upper atmos phere densities inferred from satellite observations (1, 4, 5). Since all satellite density values obtained to date appear to be about an order of magnitude greater than most of those measured or extrapolated from rocket experiments (6), we consider it important to detail here the basic assumptions as well as the computational techniques that we used to obtain density values from the orbital behavior of Satellite 1958 Epsilon (Explorer IV). Satellite Parameters and Orbital Data From published descriptions of the technical characteristics of Explorer IV (7), we derived the following parameters for our calculations: Total superficial area: a = 10, 400 an Area of longitudinal cross-section: A, = 3; 220 cm2 * Special Assistant to the Director ** Astrophysicist, Division of Solar Radiation Studies -93- Effective cross-sectional area tommmig completely random orientation: q q A = T = 2, 600 cm Minimum effective cross-sectional area, assuming random orientation about a transverse axis: A' = 2, 170 cm 2 Area of transverse cross-section: A^. = Effective mass-area ratio, assuming completely random orientation: 196 m/S =6.42 gm/cm 2 In our conclusions, we shall refer to the numerical values of these additional parameters: Maximum possible mass-area ratio: m/Aj = 85. 2 gm/cm 2 Maximum probable mass-area ratjo: m/A' = 7. 68 gm/cm 2 Minimum possible mass-area ratio: m/A. a 5.18 gm/cm 2 The minimum possible cross -sectional area, Af, is the area of a circular cross-section of the cylindrical satellite. However, to obtain a minimum probable cross-sectional area for Explorer IV we consider the question of angular rotation of the satellite. MOONWATCH reports and precision photographs taken with the Baker-Nunn satellite tracking cameras have been analyzed to obtain data concerning the photometric behavior of Explorer IV. Numerous visual observers have noted considerable variation in brightness, and have con sistently reported periods of about 3 seconds from one maximum to the succeeding one. Five photographic images taken with exposure times of .8 and 1.6 seconds (width short timing -breaks superposed ) all show significant variations of brightness consistent with the periodicity reported by the MOONWATCH teams. For the cylindrical shape of Explorer IV, these data indicate a rotational period of approxi mately 6 seconds. This period is consistent with angular momentum considerations if the rotation has changed from the initial longitudinal spin imparted during launching to a transverse tumble. Therefore, we have calculated a minimum probable cross-sectional area, A1, on the assumption that the satellite tumbles with a period which is small relative to the time of appreci able drag near perigee. In this case, the minimum effective value is attained when the cylinder flies through perigee with its axis of tumble perpendicular to the flight trajectory. For any other angle between the axis of tumble and the flight trajectory, the effective area will be larger. For a right circular cylinder, this effective minimum has the value A' = -2 (AL + AT) = 2, 170 cm^ This argument considerably reduces the range of uncertainty in densities caused by the geometry of the satellite. In Table I, we list the orbital elements that formed the basis of our calculations. In addition to these variable quantities, we took a constant orbit inclination of 50. 33°, and a perigee distance of 1.0403 earth's equatorial radii, measured from the center of the earth. -94 Table I. Variable Orbital Elements Epoch Aug. 1958) Anomalistic Period (days) Argument of Perigee 7.021655 11.21821 15.40983 23.78067 30.47689 40.84007 47.03737 55.93850 0.0763475 0.0762501 0.0761712 0.07601620 0.0758786 0.07563587 0.07551520 0.0753660 81.073° 93.102° 105. 236° 129.470° 145.961° 178.857° 196.944° 222.971° Right Ascension of Ascending Node 22. 282° 7. 231° 352.300° 322.483° 302.017° 260. 877° 238.494° 205.906° Table II gives the quantities derived from the basic orbital elements under the following assumptions: Between the individual epochs, the anomalistic period is assumed to change linearly with time, resulting in an average period change for the epoch intervals, and a mean period for a reference iGatm halfway between the epochs. The perigee altitudes for the reference dates are computed from the international ellipsoid and are given in kilometers above the mean sea level. Note that the perigee distance remains constant, while this perigee altitude decreases when the sub-perigee point approaches the earth's equator, solely because of the flattening of the earth. Table II also lists the solar time at the sub-perigee point, computed from the difference between the right ascension of perigee and the right ascension of the sun. Table II. Orbital Characteristics Reference Date ( Datum ) Aug. Aug. Aug. Aug. Sept. Sept. Sept. 9.12 13.31 19.59 27.13 4.66 12.94 20.49 Mean Period (days) Period Change ( sec/ day ) Sub-Perigee Point Geocentric Latitude (degrees) Perigee Altitude (km-MSL) Solar Time at Sub-Perigee Point 0.0762988 0.0762106 0.0760937 0.0759474 0.0757572 0.0755755 0.0754406 -2.00 -1.63 -1.60 -1.78 -2.02 -1.68 -1.45 50.2°N 49,S°N 43.1°N 30.2°N 14.5°N 6.1°S 22.6°S 269.7 269.4 267.1 262.5 258.4 257.3 260.2 9:38 a.m. 9:38 a.m. 9:22 a.m. 8:34 a.m. 7:18 a.m. 5:41 a. m. 4:22 a.m. Computations Sterne's simplified formula (8) was used to calculate upper atmosphere densities for the reference dates and perigee altitudes given in Table II. His formula relates the atmospheric density near perigee to the aerodynamic drag coefficient, Cp, an effective satellite mass-area ratio, m/A, and the orbital acceleration P, in the following way : -95- where F(a, e) is a slowly -varying function of the orbital parameters (semi-major axis and eccen tricity). The factor of proportionality depends on an assumed gradient of density at the perigee altitude. We adopted the gradient given by the Smithsonian Interim Atmosphere No. 2 (9 ). Since the resulting numerical values of absolute density are insensitive to reasonable variations ol the density gradient, no appreciable error would be introduced, if the a priori assumed gradient were to be based on other model atmospheres. The value of Cjj ■ 2 was used for the aerodynamic drag coefficient. A discussion of possible errors introduced by a number of independent effects is given in the subsequent sections. Numerical Results The numerical results obtained are shown in Table III below. Table III. Values of Atmospheric Density Atmospheric Density Range of Perigee Altitudes Range of Geographic Latitudes Most Probable Probable Minimum ? Ki^cg^eters Degrees ftmin gm/cm3 gm/cm3 Probable Maximum Possible Maximum />' /max gra/ cm3 gm/cm 269.7-269.6 50.3oN-50°N 1.52 x lO"13 1.23 x lO"13 1.82 x 10~13 20.2 x 10-13 269.6-268.9 50°N-48°N 1.24 x 10"13 1.00 x 10"13 1.48 x 10-13 16.5 x 10"13 268.9-264.6 48°N-36«N 1.21 x 10"13 0.98 x 10"13 1.45 x 10"13 16.1 x 10"13 264.5-260.5 36°N-24°N 1.35 x lO"13 1.09 x 10"13 1.61 x 10"13 17.9 x 10"13 260.5-257.1 24°N- 2°N 1.53 x 10"13 1.23 x 10"13 1.83 x 10"13 20.3 x 10"13 1.27 x 10"13 1.05 x lO"13 1.52 x 10"13 16.9 x 10"13 1.09 xlO-13 0.88 x 10"13 1.30 x 10-13 14.5 x 10-13 257.1-258.0 258.0-262.5 130S-31»S _ The column labelled "Most Probable" is based on the use of an effective mass-area ratio m/A = 6.42 gm/cm , and assumes that orientation was completely random during the passages of the satellite through the perigee. The other columns assume that the above condition has not been fulfilled and give the possible extreme values of density which would result under non —ranctom orientation. If the satellite had passed the perigee in a broad-side position on each revolution, the use of the minimum possible mats-area ratio, m/A|_ = 5.18 gm/cm^, would indicate a probable minimum density /^_m- Conversely, if the long axis of the satellite had been aligned, An every passage through perigee, parallel to the flight trajectory, the maximum possible -96- mass-area ratio, m/Ar = 85. 2 gm/cm , would be applicable, resulting in a high density, /max* The P*0000!' maximum density, 0', based on m/A', is considerably below this value, however. For a satellite whose axis is not aligned in inertial space by rotational momentum, aero dynamic torques during perigee passage may cause an alignment of the body axis, leading to systematic deviations from completely random orientation. For example, if the center of mass is sufficiently far from the center of volume, the assumption of completely random orientation at perigee may result in an over-estimate of the average presentation area and lead to under estimates of density. However, this argument does not apply to Explorer IV. The photometric evidence cited above shows that Explorer IV tumbles about a transverse axis. Therefore, we do not admit the applicability of the possible maximum, and we believe that reasonable limits are given by the probable maximum and probable minimum values of density listed in Table III. We have thus estimated the range of densities introduced by uncertainties in the effective presentation area of the non-spherical Explorer IV. Numerically, this range covers a factor of 1.48, the ratio Al/A'. Uncertainties in the Density Derivation Three types of criticisms can be levelled at the direct application of Sterne's formula to the data for Explorer IV. The first, that the orientation of the object at perigee cannot be precisely specified, has been shown above to introduce uncertainties of +2SK in the geometrical effective cross-sectional area. Second, an important uncertainty is introduced by the variation of the drag coefficient with altitude (10 ). Recently a study group at the RAND Corporation thoroughly investigated this phenomenon. On the basis of all available knowledge and evidence (11 ), both experi mental and theoretical, we conclude that a probable value of the drag coefficient, for the alti tude of our present concern, and for the shape and surface characteristics of Explorer IV, is Crj = 2. 3, with probable limits of 2. 0 and 2. 5 depending primarily on the degree of dissociation of nitrogen. Since the values listed in Table III are based on the use of Crj = 2, multiplication of all entries in the second and third columns by factors of 0. 87 and 0. 80, respectively, will give reasonable corrections due to deviations of Gq from the value used. Finally, while electrostatic (12) and electrohydrodynamic (13) drag effects must not be neglected as additional sources of possible error, we can safely neglect the known effects, for the perigee altitudes of Explorer IV. Re -evaluations (1, 14) of the early theoretical considerations by Jastrow and Pearse (12), and experimental data on charge accumulation obtained by Soviet scientists with Sputnik III (IS), make it appear extremely unlikely that such additional drag effects would alter our derived densities by more than five percent. We have neglected all additional drag effects due to the presence of the earth's magnetic field and ionization of the atmospheric gases, for the perigee altitude and configuration of Explorer IV. While such effects may become appreciable at portions of the orbit near apogee, theoretical arguments suggest that they would be negligible in comparison with the atmospheric drag force acting near perigee. Further, there is an empirical justification for ruling out the possibility of severe drag effects not included in our discussion above. Warwick (16) has derived an atmospheric density from the observed damping of the rotation of Satellite 1957 a2, on the assumption that aerodynamic drag on the antennae produced the damping. The density thus derived agrees very well with those -97- derived from changes of orbital period of Satellite 1957 a2 (1 ). Since completely different regimes are involved, non -aerodynamic effects changing the orbital period would not effect rotational motions to the same degree. Therefore, the agreement in densities strongly suggests that aerodynamic drag is, indeed, the only force acting to dissipate energy. Our calculations did not consider rotational velocity of the earth's atmosphere. For the orbital characteristics of Explorer TV, this neglect leads to an underestimate of density by per haps as much as 10 percent, depending on the latitude of the sub-perigee point. We now consider possible errors due to inaccuracies in the orbital elements. We have re produced, in Tables I and II, the orbital data to the precision with which they were known or could be reasonably calculated. Uncertainties in these data cannot affect the density results by more than one or two percent. However, the perigee altitudes are probably accurate only to +5 kilometers above the geoid, and hence the absolute altitudes to which these densities refer are uncertain by the same amount. The relative altitudes or altitude differences, on the other hand, are accurate to several tenths of a kilometer. Numerical Estimates of Probable Errors By assuming that all effects discussed above can introduce possible, although not probable, accumulative errors, we can derive the numerical limits of accuracy. We have chosen the alti tude of 262.5 km for this purpose, but the analogous calculations can, of course, be carried out for all values of density listed in Table III. In the following Table IV, possible values of density for different presentation creas and drag coefficients at perigee are shown. All density values are given in grn/an', Cp is dimensionless, and m/A is in gm/cm^. Table IV . Possible Density Values at 262. 5 km Altitude as a Function of Mass-Area Ratio and Aerodynamic Drag Coefficient 35. 2 7.68 6.42 5.18 2.0 17.9 x 10~n 1.61 x 10"13* 1.35 x 10"13 1.09 x 10"13 2.3 15.6 x 10"13 1.40 x 10"13 1.17 x 10"13 0.94 x 10"13 2.5 14.3 x 10"13 1.29 x 10"13 1.08 x 10"13 0.87 x 10"13** * highest probable value ** lowest probable value A quantitative evaluation of the various other effects which can contribute possible errors is attempted in Table V. Correction factors are listed which represent maximum probable deviations from the computed density values shown in Table IV. -98 Table V. Estimates of Probable Error Corrections in Addition to Uncertainties in Mass-Area Ratio and Drag Coefficient Possible Effect Decrease p by Increase p by Electrostatic and electrohydrodynamic drag : 5* - Rotation of atmosphere : - 10* Inaccuracies of orbital elements: 2* 2* Uncertainty in perigee height: 14* 14* Accumulative effect: 22* 28* If we now take the highest and lowest probable density values shown in Table IV, and multiply with the appropriate total correction factor, we can place limits on the true value of upper atmosphere density inferred from Satellite 1958 Epsilon at a perigee altitude of 262. 5 km c above geographic latitudes 24°-36° North, as follows: 0.68 xlO"13 gm/cm3< p^ 5 < 2. 1 x 10"13 gm/cm3. While we think that this procedure takes into account all possible accumulative errors, it is, of course, rather arbitrary and has little real value. It does, however, illustrate and place reasonable limits on the errors which lack of knowledge could introduce Into derivations of density from satellite observations. We feel Inclined to believe, however, that the most probable limits for the accuracy of our average density point at 262. S km would read in accordance with Table IV: /?262 5=1'3± .5 x 10"13 gm/cm3. It will be noted that all densities, derived with any one set of assumptions, show a re markable consistency with each other. A similar analysis, averaging orbital data over smaller time intervals, will show the extent to which this consistency was produced by using weekly intervals of about 100 revolutions each. Conclusions The variation of atmospheric density with altitude between 250 km and 275 km (geometric) is shown in Figure 1 . The most probable values of density derived from Explorer IV are plotted for the reference dates and altitudes given in Table II . We have indicated the range of probable accuracy as estimated in the preceding section. In addition, the figure contains portions of model atmospheres (9, 17, 18). It will be noted that all points in Figure 1 fall so close to the Smithsonian Interim Atmos phere (9), that it was not necessary to fit another curve to the determined values. Taking into account the calculations which we performed with regard to probable errors and uncertainties, we conclude that satellite observations provide a consistent means of deriving the ambient density of the upper atmosphere. -99- Figure 1. Variation of Atmospheric Density with Altitude above Earth's Surface -100- Examination of Figure 1 and the corresponding latitudes in Table III shows no evidence for a consistent variation of the derived density values with latitude, other than produced by ellipticity of the geoid. Although a slight diurnal variation of density might be inferred from the corresponding solar time at the sub-perigee points listed in Table D, the data are insufficient to warrant any conclusion, because all deviations fall within the limits of uncertainty. With the simultaneous existence of a number of satellites in different orbits, extension of the present method of analysis may soon result in a wealth of information on the variations of upper atmosphere density with latitude, season, and time of day. Acknowledgements We wish to express our appreciation to the many members of photographic, radio, and visual satellite tracking stations, whose efforts furnished the basic observational data. We were stimulated to undertake our calculations as the result of an informal conference on satellite drag phenomena at the RAND Corporation, arranged by Drs. C. Gazley, Jr. , H. K. KallmannB1J1, D. J. Masson, and others. Special thanks are due Drs. A. F. Charwat, University of California at Los Angeles ; F. C. Hurlbut and S. A. Schaaf, University of California at Berkeley ; H. W. Liepmann, California Institute of Technology; L. Kraus, Convair; H. C. Chang, M. C. Smith, and E. H. Vestine, RAND Corporation, for valuable thoughts and ideas freely given during many fruitful discussions. For the present interpretations and use, right or wrong, of some of the results of these discussions, we are solely responsible, of course. Dr. Max Krook has provided us with helpful criticism of our manuscript. References 1. Steme, T. E. : "High^Altitude Atmospheric Density. " Physics of Fluids, JL, 165-170, 1958. ~ 2. Schilling, C. F. and T. E. Steme: "Densities and Temperatures of the Upper Atmos phere Inferred from Satellite Observations. " Journal Geophys. Res. , (in press), January 1959. 3. Schilling, G. F., C. A. Whitney, and B. M. Folkart: "Preliminary Note on the MassArea Ratios of Satellites 1958 Delta 1 and 1958 Delta 2. 11 Special Report No. 14, pp. 32-34, Smithsonian Astrophysical Observatory, July 15, 1958. 4. Harris, I. and R. Jastrow: "Upper Atmosphere Densities from Minitrack Observations on Sputnik I." Science, 127, 471, February 28, 1958. 5. Jastrow, R. and I. Harris: "Upper Atmosphere Properties from Minitrack Observations on 1957 a2." Transactions, AGU, 3j>, 519-520, (abstract), 1958. 6. La Gow, H. E. , R. Horowitz and J. Ainsworth: "Arctic Atmospheric Structure to 250 Km." IGY Rocket Report Series No. 1, pp. 38-46, ICY World Data Center A, National Academy of Sciences, July 30, 1958. 7.. Boehm, J. : "Physical Properties - Explorer IV. " Orbital Data Series, Issue 1, p. 2, Army Ballistics Missile Agency and Smithsonian Astrophysical Observatory, August 11, 1958. 8. Sterne, T. E. : "Formula for Inferring Atmospheric Density from the Motion of Artificial Earth Satellites. " Science, 127, 1245, May 23, 1958. 9. Steme, T. E. , B. M. Folkart, and G. F. Schilling: "An Interim Model Atmos phere Fitted to Preliminary Densities Inferred from USSR Satellites. " Special Report No. 7, Smithsonian Astrophysical Observatory, December 1957. (Re-printed in Smithsonian Contrib. Astrophys. ,2. 275-279, 1958.) rlOl- 10. Baker, R. M. L. , Jr., and A. F. Charwat: "Transitional Correction to the Drag of a Sphere in Free Molecule Flow." Physics of Fluids, 1, 73-81, 1958. 11. Schaaf, S. A., A. F. Charwat, and F. C. Hurlbut: Personal Communication. 12. Jastrow, R. andC. A. Pearse: "Atmospheric Drag on the Satellite. " Joum. Geophysical Research, 62, 413-423, 1957. 13. Kraus, L. and K. M. Watson: "Plasma Motions Induced by Satellites in the Ionosphere. " Report ZPh-016, Physics Section, Convair, San Diego, 1958. 14. Naval Research Laboratory: "Interaction of Satellites with the Ionosphere. " Conference Proceedings, Naval Research Laboratory, March 28, 1958. 15. Krassovsky, V. I. : "The Soviet Exploration of the Ionosphere by Means of Rockets and Sputniks. " Presented at the General Assembly of CSAGI, Moscow, August 1-9, 1958. 16. Warwick, J. S. : "Satellite Research. " Scientific Report No. 10 , ARDC Contract AF19( 604) -1491, High Altitude Observatory, University of Colorado, April 30, 1958. 17. Minzner, R. A., and W. S. Ripley: "The ARDC Model Atmosphere, 1956." Air Force Surveys in Geophysics, No. 86, Geophysics Research Directorate, AFCRC, ARDC, December, 1956. 18. Grimminger, G. : "Analysis of Temperature, Pressure, and Density of the Atmosphere to Extreme Altitudes. " RAND Report No. R-105, 1948. -102- THE STRUCTURE OF THE HIGH ATMOSPHERE I. LINEAR MODELS by Charles A. Whitney * Astrophysical Observatory, Smithsonian Institution and Harvard College Observatory 1. Introductory Remarks This paper is the first of a projected series on the structure of the terrestrial atmosphere above 100 km as Inferred from data on artificial satellites. Orbital accelerations derived by analyses performed at the Smithsonian Astrophysical Observatory will be employed to infer atmospheric densities near the perigee heights of the satellites. Despite remaining uncertainties in charge-accumulation effects on the drag parameters (1 ), computations neglecting these effects give the most reliable data available on densities above 100 km. The principal aim of this first paper is the presentation of a homogeneous set of mean satel lite data and the fitting of three simple models to the inferred densities. These models, being based on sectionally-linear distributions of molecular temperature, must not be considered as more than smoothing operators for the satellite data. On the other hand, these models provide an excellent basis for a study of the range of models which will fit the satellite data. They allow a rather convincing demonstration of the uncertainties inherent in the derivation of a temperature distribution from data on the density distribution. 2. Preliminary Comments on the Nature of the High Atmosphere Although I shell defer detailed discussions of the physical nature of the high atmosphere to later papers, several outstanding features must be mentioned at the outset. The reader is referred to the literature (2, 3) for more detailed discussions and further references. First, the chemical composition of the atmosphere above 80 km is not well known. Molecu lar oxygen undergoes dissociation somewhere between 90 and 200 km, and the details of the transition evidently undergo significant temporal and geographic variations. Auroral spectra indi cate the presence of molecular nitrogen to at least 500 km, and although it must be partially dissociated at such heights, the working approximation that nitrogen is molecular is sufficient in discussing mean molecular weight. Also, diffusional separation of species of differing molecular weights is significant above 120-150 km. The variation of molecular weight resulting from these effects makes it convenient to employ a molecular temperature rather than true temperature in establishing preliminary models. A molecular temperature, T , may be defined as ♦Physicist, Division of Solar Radiation Studies, Smithsonian Astrophysical Observatory, and Research Associate, Harvard College Observatory. -103- Tm = T (1) M where M and T are the true molecular weight and temperature and M_ is a reference molecular weight. MQ is conveniently taken as the molecular weight at the ground or at the greatest height for which it is well known. Although radiative effects are important at lower levels, it seems fairly certain that conduction plays the major role in heat balance above 300 km (4). This statement may not be valid during times of large ultra-violet excess in solar radiation. Chapman's suggestion (5 ) that the high atmosphere is heated by conduction from the solar corona is clearly of basic importance in this regard. Finally, the concept of an exosphere has been rediscussed by Spitzer (4). The base of the exosphere, or the critical level, is defined as that level at which "a fraction 1/e of a group of very fast particles moving upward . . . will experience no collision as they go to infinitely greater heights. " The atmosphere above the critical level is essentially isothermal and diffusional sepa ration must take place. For neutral particles the number density at the critical level is given by nc= where a is the typical atomic radius (1.5 x 10 \ <2> cm) and }( is the scale height. 3. Comments on the Satellite Data Orbital accelerations employed in this paper for deriving densities have been obtained from second differences of the times of perigee passage. In practice it has been found necessary to employ intervals of at least 30 to SO orbital revolutions in deriving accelerations, so the data are averaged over several days. The accelerations thus derived have shown, for all satellites, semi -periodic fluctuation with mean periods around 28 to 30 days. Although I suggested (6) that this could be explained, for 1958 Alpha, by systematic variations in geometric effective cross-section, this interpretation is no longer valid. Jacchia (7) has shown a remarkable correlation between the variations experi enced by 1958 Beta Two (Vanguard ) and 1958 Delta One (the rocket of Sputnik in ). Further examination removes all doubt that this correlation is ubiquitous, all satellites showing virtually simultaneous maxima and minima of acceleration. Although these variations are only semi regular, they show mean semi-amplitudes of 15% to SOU with 1958 Beta Two, the highest satel lite, showing the greatest amplitude. W. Priester (8) has recently discovered a surprisingly-close positive correlation between the daily averages of 20 cm solar radiation and the variable acceleration of 1957 Beta Two as derived by Jacchia for the interval November 1, 1957, to February 10, 1958. Priester notes that G. Elwert's work (9) indicates that these atmospheric fluctuations may be produced by 6A to 30A radiation from coronal condensations. The satellite data show an increase with perigee height of the amplitude of the acceleration variations. In discussion with Jacchia we noted that this indicates a change of density gradient over a rather large depth-interval in the atmosphere, since the mean density gradient probably -104- decreases with increasing height. Jacchia's and Priester's discoveries will be of tremendous importance in studying the high atmosphere, since they imply the existence of world-wide and synchronous variations of density. Jacchia has also shown that there is a term in the acceleration of 1958 Delta One which can be correlated with the zenith distance of the sun at die sub-perigee point. At this time it seems best to proceed by averaging out these periodic fluctuations and derive densities from mean accelerations over several months. I have taken the data, insofar as possible, from the spring and early summer of 1958 in order to eliminate possible difficulties from longer-period terms. Also, there is evidence in rocket data for rather considerable latitudinal and short-period or irregular fluctuations of atmospheric density at high elevations. However, an earlier analysis has shown that there is no evidence in the data for 1958 Epsilon of any severe latitudinal changes of mean density at 2 = 260 km. Therefore I have combined data from different latitudes in the present study. It is hoped that the mean models thus obtained will provide a basis for a "differential cor rections" study of the fluctuations observed. 4. The Satellite Data I have derived atmosphere densities from accelerations using T. E. Sterne's formula (10), applying also the major portion of his correction for the assumed solid-body rotation of the atmosphere. (I am indebted to Dr. Sterne for providing me with this correction prior to publi cation. ) The data pertinent to the use of these formulae are assembled in Table I. For two reasons, I have taken all geometric perigee -heights, I_, as measured from a sphere of radius 6378 km. First, the motions of the lines of apsides were, m most cases, rather large in the intervals covered, and second, the mean accelerations could not be defined so well that a few kilometers is significant. The quantity Hp is the geopotential height of perigee derived from H = Z(1+ I)"1, R = 6357. (3) The geopotential height, like molecular temperature, is an artifice used to facilitate the integration of the equation of hydrostatic equilibrium. -105- Table I SATELLITE DATA Satellite a e 0 P ( sec/ day ) (km) (km) 1957 al 220 213 1.086 .0482 - 2.4 1958 a 360 341 1.2276 .139 1958 02 656 594 1.3619 1958 y 185 180 1958 € 257 247 m/A (gm/cm^) Length (cm) 24.1 58 - 0.455 5.5 200 .190 - 0.017 3.97 15 1.211 .153 -12.6* 5.6 200 1.1883 .125 - 1.72 6.4 200 ♦Derived from curve communicated by J. Siry. , r , / where X is the scale-height just above perigee, it is necessary to have an approximate: ^ model before densities can be derived. I have, therefore, proceeded by successive approximations and in Table II give the densities as derived from scale heights given by models 4 and 5, described below. The densities derived from the scale -heights of model 4 are the values used in constructing models 4 and 5, and represent the results of iteration. Actually the process had converged after one adjustment, since the densities are insensitive to the model employed. Thus, although model 5 is not rigorously self-consistent, further adjustment would produce only a trivial change. Table II also includes the drag -coefficient, Cq , used in deriving the densities. These values are consistent with the densities of model 4 and their derivation is discussed in Section 9. In order to speed further the convergence of such an iteration it would be possible to make use of a fact apparently first noticed at the Naval Research Laboratory. The satellite accelerations determine, essentially independently of the adopted }\ , the density at some distance above the perigee height. The following simple analysis shows that this must be so. At a height Ah above perigee the density is />pexp(^L). For a given set of orbital data, Sterne's formula shows ^ oc H"1/2. Therefore /3(Hp+ Ah). OC H-1/2exp (- The relation leads to the condition -106- Thus the density is well determined for a point one-half scale height above the perigee point. For this reason it would be convenient to modify Sterne's equation writing -1/2 /MHp + f ) = />* e where fp* Is the density of perigee as given by Sterne's formula and fl (Hp + density one-half scale height above perigee. is the 2 Table II ATMOSPHERIC DENSITIES FROM SATELLITE ACCELERATIONS log10 P (9m/«n3) Satellite CD Model 4 Model 5 1958 y 180 1.2 -11.86 -11.91 1957 o2 213 1.9 -12.37 -12.40 1958 < 247 1.9 -13.00 -13.02 1958 a 341 2.0 -13.74 -13.75 1958 02 594 2.0 -15.47 -15.45 5. An Earlier Linear Model - T. E. Steme, Barbara FoUcart, and G. F. Schilling derived (11) three tentative model atmospheres from a density at Z = 200 km evaluated from the acceleration of 1957 Alpha Two. They adopted 220) = 4.5 x 10~13 gm cm-3 and forced the temperatures and densities of these models to fit the A.R.D.C. model (12) at Z' = 80, 90, and 100 km, respectively, by adjustment of the constant temperature gradient aobve Z' . These models were designated Interim Atmospheres Nos. 1 , 2, and 3 respectively. The defining relations for Model 2 are Model 2: Tm=! -603.3 + 9.0167 H log p = 2. 588 - 4. 79 log Tm. -107- In these relations, and these to follow, logarithms are to the base ten , densities are in gm/cm^ and heights are in kilometers. The molecular temperature for this model is defined by equation (1 ) and MQ = 28. 966. The densities given by this model are plotted against geometric height in Figure 1. Con sidering the fact that this model, for which the authors stated a preference over Models 1 and 3, was based on data from a single satellite, it is remarkably good even at 500 km. However, since the later data seems to deviate systematically, I have considered it worthwhile to construct further models. 6. Models Number 4 and 5 I have extended the calculations of Sterne et al (11 ) by adjusting the height, Z', at which the A.R.D.C. model is fitted and L the temperature gradient above Z', to produce a fit to the satel lite data of Table II, at heights of 260 and 656 km. Explicitly the model fits, by construction, the following data at V = 88.4: log = -8.29, Tn ■ 196.9. The defining relations are, Model 4: T = -465.6 + 7.641 H log f> = 4. 311 - 5.4712 log Tm. The densities given by this model are plotted in Figure 1 , and they seem to give a significant improvement over Model 2. Furthermore, the excellence of the overall fit of Model 4 to the data indicate that the assumption of a constant temperature gradient above 100 km is adequate. In order to estimate the range in models permitted by satellite data, I have constructed a fifth linear model based on rather different assumptions. Models 4 and 5 are in no way limiting cases on acceptable models. However, being based on independent boundary conditions at the bottom and rather different temperature assumptions, they might be considered as independent samples of acceptable models. In this sense, the differences between them give a reasonable, rather than extreme, estimate of the remaining uncertainties. I have constructed this fifth model by forcing the density through three points and the temperature through one. For the lowest point I took T = 150° K, M = 28. 57, log /°= -8. 66 at H = 90 km. These values are nearly those given by Nicolet's tabulation (13 ). The height of 90 km was chosen as the maximum height at which uncertainties in the dissociation and diffusion are insignificant. The atmosphere was assumed to have constant, but different, temperature gradients above and below 150 km. The breaking point of 150 km was chosen arbitrarily as representing, roughly, an elevation at which the nature of the atmosphere changes significantly (vis a vis diffusion and 02 dissociation). Also it is a convenient round number near the lowest satellite perigee. The model is described by the following formulae, whose derivation is Standard (cf. (11 )), -108 T - 150 + L' (H - 90), 90 < H <150 (H) \ log /> =log O (90) -(1+ ^iffi) log [ — ] 1 f L \Jml*>)J T_ = 150 + 60 L' + L" (H - 150), H >150. ft-. (") log j> = log j) (150) -(1 + iL-Ti?) log In these relations L' and L" are the temperature gradients (°K/km) below and above 150 km and Tm is related to the true temperature through equation ( 1 ) with MQ = 28. 57. After several trials, a pair of L' and L" was found which fit the required densities. These lead to the defining relations. Model 5; T„ = -966 + 12.4 H log j> = -0.56 - 3.723 log T T = -111+ 6.70 H m H >150. log f> =6. 275 - 6.039 log As a measure of the uncertainties within the framework of this particular model, I have evaluated the following partial derivatives for heights of 260 and 656 km. = 0.12, |_2i°aZf) =0.19, V 3h /656 .0..,, (LzA 260 =0.a. Taking A log — +0.1 as a reasonable upper limit on the uncertainty in the basic data, we see that the temperature gradients for this particular modal are reliable only to + 0.5°K/km, or so. The discussion in Section 7, however, shows that the actual -109- 7. The Temperature Gradient above 300 Km (Model 6) Considerable interest is attached to the temperature gradient above 300-400 km. Bates has shown that absorption of ultraviolet solar radiation appears insufficient to maintain a significant positive temperature gradient above the F layer. If such a gradient indeed exists, it will probably be explained by conduction from above, as outlined by Chapman (5 ). Unfortunately, the satellite data give only two mean-density values above 300 km, so this question probably remains an open one. As an experiment I have constructed Model 6 in the following manner. From Model 4.1 derived densities at Z = 300 and 600 km. The assumption of a constant scale height above Z = 300 km leads to Tm = 2527°K, (MQ = 28.966) above this height. The model was fitted to lower levels by assuming a constant temperature gradient and forcing temperature to T = 150°K at H = 90 km. ( 13 ). It was not necessary to assume a density at heights other than Z = 300 and 600 km. The resulting model is described by the following equations. Model 6: T = -751?44 + 10.016 H 90 < H < 287 log p = 1.274 - 4.411 log Tm T = 2123°K m H > 287. log p = 11.404 - .0069591 H The densities given by this model are graphed in Figure 1 and they are seen to fit the data quite well. Also, at H = 90 km, this model gives log = -8.32, in excellent accord with log p =-8.31, given by the A.R.D.C. model. Table III compares the densities and molecular-scale temperatures given by Models 4 and 6. Table III COMPARISON OF LINEAR MODELS Model 6 Model 4 Tm Z(km) Tm 200 1017 -12.14 1192 -12.30 300 1727 -13.40 2123 -13.40 400 2407 -14. 19 2123 -14.02 500 3080 -14.78 2123 -14.63 600 3722 -15.22 2123 -15.22 log/) -110- log p The remits of this comparison are neither surprising nor encouraging. Although the temperatures agree well at low heights and near 350 km, as they must, they differ considerably at heights greater than 400 km. I would not say that it is possible at present to choose between these two nonphysical models. 8. The Base of the Exosphere Equation (2) above has been used to evaluate Zc, the geometric height of the critical level, or base of the exosphere. The results are Zc (Model 2) ■ 630 km, Zc (Model 4) = 500 km. Assuming that the numerical coefficients of equation (2) are correct, the value of Zc as given by Model 4 is probably accurate to 20 km for the mean atmosphere during the early summer of 1958. At Z = 500 km, Models 4 and 6 give Tm = 3080° K and 2123°K, respectively. If, as seems likely from Nicolet's discussion (13) and further results to be presented in Paper II, we may assume the gas at this level to be pure oxygen, these molecular temperatures lead to true temperatures of 1700° K and 1200°K, respectively. These values are lower than 2250° K, the lower limit derived by Nicolet for the required escape of helium, but the discrepancy may not be serious. Further, the present data do not exclude the possibility of a rise to 2000° K somewhat below 500 km, since these data determine the mean temperature and not its detailed distribution. 9. Evaluation of the Drag Coefficient Dr. R. M. L. Baker, Jr. , of Aaronutronic Systems, Inc. , Glendale, California, has kindly made available, prior to publication, his formula for Cq in the transition region. The expression is of the form CD = CD0 where CT~ is a dimensionless atmospheric density, Cp = Cp ( (J"= 1 ), and C is related to the ratio of mean free path to body size. Employing Baker's formula and the atmospheric densities of Model 4, I have computed for the transition region. I have adopted v = 8 km/sec for the satellites, and M T = 8000°K, where Mc is the dimensionless molecular weight of the particles "emitted" from the satellite and Ts is the surface temperature of the satellite. Table IV gives representative values of Cq. Z is the geometric height of the satellite and d is its "typical" linear dimension. -Ill- Table IV TRANSITIONAL DRAG -COEFFICIENT, C d( meters) 3 10 0.92 0.92 Z(km) 160 1 0.99 30 0.92 180 1.30 .96 .92 .92 200 1.60 1.21 .92 .92 220 1.79 1.48 1.04 .92 240 1.89 1.68 1.26 .95 260 1.93 1.81 1.48 1.06 280 1.96 1.88 1.65 1.24 300 1.98 1.92 1.77 1.43 320 1.99 1.95 1.75 1.59 340 2.0 1.97 1.90 1.69 Since the algebraic representation of Cn is a rather arbitrary one, the details of the transi tional Cq are not too reliable. However, the heights of the transition regions of various satel lite sizes are probably fairly accurate. Baker's formula leaves little doubt that variations of Cp from the conventional value of two, employed heretofore in deriving satellite densities, are significant. There may, of course, be an increase of Cq due to plasma effects. The implications of Baker's results for analyses of satellite data are manifest. I shall defer a discussion of some of these possibilities to later papers, and merely state that I have used these values in computing the densities for Table HI. The changes introduced by Cjj^. 2 are important only for the two lowest satellites in the present analysis. 112- i 1 1 1 1 Geometric Height (km) -113- 1 r References (1) Schilling, G. F. and C. A. Whitney, "Atmospheric Densities from Explorer IV. " Special Report No. 18 , Smithsonian Astrophysical Observatory, Cambridge, October 4, 1958. (2) The Atmospheres of the Earth and Planets , Ed., G. Kuiper, University of Chicago Press, 1952. (3) The Earth as a Planet , Ed., G. Kuiper, University of Chicago Press, 1954. (4) Spitzer, L,, The Atmospheres of the Earth and Planets , Ed., G. Kuiper, University of Chicago Press, 1952. (5) Chapman, S, , "Notes on the Solar Corona and Terrestrial Ionosphere, " Smithsonian Contributions to Astrophysics, Vol. II, No. 1, 1957. (6) Whitney, C. A. , "Tht- Orbit and Variable Acceleration of Satellite 1958 Alpha, " Special Report No. 11, Smithsonian Astrophysical Observatory, Cambridge, March 31, 1958. (7) Jacchia, L. G. , Nature , in press. (8) Priester, W. , Communication from University Observatory, Bonn, Germany, dated December 18, 1958. (9) Elwert, G., Zs. f. Ap. , 41, 67, 1956. (10) Steme, T. E. , The Physics of Fluids, 1, 165, 1958. (11) Steme, T. E. , B. Folkart and G. F. Schilling, "An Interim Model Atmosphere Fitted to Preliminary Densities Inferred from USSR Satellites. " Special Report No. 7, Smithsonian Astrophysical Observatory, Cambridge, December 1957. (12) Geophysics Research Directorate, A.F.C.R.C., Air Force Survey No. 86, 1957. (13) Nicolet, M. , Pennsylvania State University, Ionosphere Research Laboratory, Scientific Report No. 102, April 1958. -114- THE STRUCTURE OF THE HIGH ATMOSPHERE II. A CONDUCTION MODEL by Charles A. Whitney* Astrophysical Observatory, Smithsonian Institution 1. Introduction In Paper I of this scries (Whitney, 1959 ), I summarized atmospheric densities as derived from satellite accelerations. In an attempt to smooth the data, 1 constructed three models with scctionally-constant temperature gradients. Such models, although fitting the data quite well and providing a useful basis for discussion (to be presented in a later paper), are admittedly nonphysical. Nicolct (1958) has outlined several aspects of physical models for the high atmosphere. In this paper 1 shall construct a conduction model based on his discussion. 2. Algebraic Description of the Conduction Model The total heat flux, F, carried downward by conduction across a geocentric sphere of radius r is given by the equation *»2 BT*/2 « , („ where BT*^ is the coefficient of conduction. On the assumption that radiative losses may be neglected, F « constant, and equation (1) may be integrated directly. It is convenient to measure heights from a reference level whose geocentric distance is r . Let z be the geometric height measured from this level and Te be the temperature at z = 0. If is the temperature at z ■ h, then the temperature, T, at the level is given by the equation T3/2 3/2 2 T 3/2 . T 3/2 *h *o a JL _2 h r +, o . (2) 1 ' Also, if r ■ r_ *■ z, the flux per unit area, E, follows from the relation 3/2 E(r) oSS— h T2 _B (3) * Physicist, Division of Solar Radiation Studies, Smithsonian Astrophysical Observatory, and Research Associate, Harvard College Observatory. -115- If diffusive equilibrium holds above z = 0 , and NQ(M) and N(M) are the number densities of particles of molecular weight M(gm) at heights z = 0 and the general level, respec tively, we find the following approximate relation, valid to within several per cent in N(M): logiiW ^ NQ(M) ^TQ K o o * r ' a + 3 (4) * ' where Also g = 980. 7 cm sec -2 , R is the radius of the earth, and all distances are measured in centimeters. Logarithms arc to the base 10. The density at any level is then derived from the sum of the partial densities: /0 = £mN(M), (S) and the mean molecular-weight M follows from the relation M = —L . (6) 3. Construction of the Model I have assumed, following Nicolet's suggestion, that the important atmospheric • are N£ and O. Also I have adopted TQ ■ 560s at z = 0 , where z is measured from a geo metric height of 140 km, and n= JlIOL= N<N2> 5.60 IP" 4.15 1010 The values of Tfc (h = 360 km) and NQ(0) were adjusted to fit the satellite data, and the results were the following! At z =0: NQ(0) = 1. 39 x lO11^ NQ(N2) » 1.03 x 10* *. These concentrations are 2.48 times those suggested by Nicolet. At h = 360 km (a real height of 500 km above the earth ) , Th = 1465 °K , E = 0. 27 ergs cm4 sec-1 , and F = 1 . 609 x 1018 erg/sec. Table 1 lists some physical properties of this atmosphere as functions of height, Z, from the earth's surface. -116- Tabic 1 ATMOSPHERIC PROPERTIES (MODEL NO. 7) Geometric height (km) T (°K) N(O) . -3 (cm ) N(N2) .3 (cm ) log/0 R (gm cm _3 ) F- 1.03 x 1011 -11.07 21.10 2. 29 x 10~7 1.39 x 10U (erg cm sec ) 140 560 175 677 4.01 x 1010 1.40 x 1010 -11.76 19.11 6.62 x 10"8 200 754 1.94 x 1010 4. 26 x 109 -12.15 18.16 3.20 x 10"8 250 898 5.58 x 109 5.47 x 108 -12.76 17.07 9.21 x 10"9 300 1026 1.94 x 109 9.54 x 107 -13.25 16.56 3.21 x 10 "9 350 1146 7.80 x 108 2. 10 x 107 -13.66 16.31 1.29 x 10 "9 400 1258 3.44 x 108 5.36 x 106 -14.03 16.18 5.67 x 10"10 450 1364 1.85 x 108 1.92 x 106 -14.30 16.12 2.71 x 10"10 500 1465 8. 30 x 107 5.00 x 105 -14.65 16.07 1.37 x 10"10 600 1653 2. 47 x 107 6.55 x 104 -15.18 16.03 4.08 x 10"11 — -24 The mean molecular weight, JUL, is defined by /t=M/1.673 10 . The column headed "R" gives the rate of radiation (erg cm~3 sec-*) from atomic oxygen according to Nicolet (1958): R = 1.65 x 10"18 N(O). (7) The densities of Model 7 are plotted against geometric height in figure 1 for comparison with the satellite data. The overall fit to the data is quite adequate, and I conclude that the form of the density profile predicted by the conductive atmosphere is not inconsistent with present data. The temperature of Model 7 is plotted as the solid smooth curve in figure 2. The tempera tures given by Models 4 and 6 of Paper I, included for comparison, were derived from the molecularscale temperature by use of the mean molecular weights of Model 7 (table 1). The spread of temper ature above 250 km is rather large, considering how well these models fit the satellite data, and arises from the coarseness of the data and the nature of the equation of hydrostatic equilibrium. 4. Domain of Failure of the Conductive Atmosphere The temperature equation (2) is based on the assumption that the global conductive flux, F, is independent of height. If there are radiative sources and sinks of energy, the transfer equation may be written: -117- -118- -^-F(r) = 4tr2(R-A), (8) where R and A are the rates of emission and absorption per unit volume per second. In general, the forms of A and R will require numerical integration of equation (8). Introducing the explicit form for F and performing the indicated differentiation, we see that equation (8) becomes 1 + -J- -31 + (£L. -1 £t_ „ 4rr2(R-A) r 2T dr K dr ' dr7^ F(r) (0v 11 It it convenient to put this equation into dimensionless form by expressing the temperature in terms of the temperature, T. at a reference level of geocentric distance rQ, Writing r-xr0, (10a) T-TTC, (10b) and introducing <»•> (lib) I find the following pair of first-order equations in y, z and xi o y - o • (13) This pair can be integrated downward from the following At .x- 1 (r-ro)» x2 = T>l, y-y0. The value of yQ follows from the physical conditions at rQ through the following relation, F0-4fr^T03/2yol (14) FQ is the assumed global flux at the reference level. Alternatively, yQ may be evaluated -119- from the value T and an assumed temperature gradient, with the use of equation (11a). If the value of R-A is known from an initial model as a function of height, equations (10) to (14) suffice to determine T(r) in the presence of conductive and radiative heat transfer. As a simple test of the region of failure of the conductive model, I have performed a numer ical integration of these equations, setting A = 0 and adopting equation ( 7) for the radiative loss due to oxygen. Of course, in reality the radiative absorption, A, is finite, and will to a large extent compensate the radiative loss. For this reason, the present test should give a sure indication of the level below which the conductive model fails. The results of this test are shown in table 2, which compares the temperatures and global fluxes obtained with and without the radiative -loss term. Table 2 EFFECT OF RADIATIVE LOSS R-A = 0 A=0, R=*R(Oz) Height (km) T(°K) T(°K) F/F o 500 1465 1465 1.000 400 1258 1259 0.982 300 1026 1046 0.880 200 754 851 .446 150 595 859 .400 The tabulation indicated quite clearly that, within the framework of Model 7, radiative emission terms are not significant above 200 km. It should be bome in mind, however, that radiative -absorption terms may significantly perturb the temperature distribution below 300 km. The temperatures computed with radiative losses are plotted in figure 2 as the dashed branch of Model 7. 5. Conclusions In summary, it appears that through adjustment of parameters, the conductive model can be made consistent with present satellite data. The total flux required, 1.61 x 10*® erg sec-* , or E = 0. 27 erg cm -2 sec -1 , is comfortably below 2.4 x 10 19 erg sec--1 , the amount of solar coronal heat estimated by Chapman (1957) to be available for such conduction in the earth's upper atmosphere. As indicated by figure 2, the temperature distribution above 250 km is still open to consider able uncertainty insofar as direct evidence from satellite data is concerned. However, the data are of such a quality that within the framework of a particular theoretical or semitheoretical model the temperature distribution can be determined with a fairly small uncertainty. 120 I shall repeat two comments made in Paper I. First, the satellite data show a definite correlation with solar activity. For this reason considerable care must be exercised in combining data from different epochs. The present data represent an average over several months during 1958, with the exception of the data from 1957a 2. Second, although satellite data give no evidence for a considerable latitude -dependence of density, the nature of the data tends to obscure such a dependence. Evidently the present type of data derived from the acceleration of dense satellites is of principal value in deriving a global picture of the density structure, and not for fine structure of either a temporal or a spatial nature. It is to be anticipated that baloon satellites of small mass-area ratio will offer an improved picture of the more rapid variations. References CHAPMAN, S. 1957. Notes on the solar corona and terrestrial ionosphere. Smithsonian Contr. to Astrophys. , vol. 2, p. 1. NICOLET, M. 1958. Science, vol. 127, p. 1317. WHITNEY, C. A. 1959; The structure of the high atmosphere. I. Linear models. Special Rep. No. 21. Smithsonian Inst. Astrophys. Obs. , p. 1 . -121- NOTE ON REFERENCES Co SMITHSONIAN ASTROPHYSICAL OBSERVATORY SPECIAL REPORTS Most of the Smithsonian Aatrophysical Observatory Special Reports which are referenced in the preceding papers have been reprinted, in their entirety or in part, in the IGY World Data Center A Satellite Report Series. Below are listed those issues of the IGY WDC-A Satellite Report Series in which the Special Reports can be found. Smithsonian Special Astrophysical Report Observatory Reprinted in Satellite IGY World Report Data Center SeriesA No. Date No. Date 10 March 1, 1958 all 1 March 1, 1958 11 March 31, 1958 all 2 April 30, 1958 12 13 April 30, 1958 May 21, 1958 16-45 all 4 July 15, 1958 14 15 16 July 15, 1958 July 20, 1958 July 25, 1958 1-21, 32-34 all all 6 August 15, 1958 18 19 20 21 22 25 October 4, 1958 December 6, 1958 January 5, 1958 February 27, 1959 March 20, 1959 April 20, 1959 3-4, 9-12, 13-22 1-5 1-4, 5-8 1-12 all all 8 June 15, 1959 Passes -122- IONAL ACADEMIES LIBRA iiiiiiniiiiiiwi