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Although these data may be superceded by subsequent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.
Cape Canaveral also reports time to units and gives
positions to OfOl.
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-106-
5.
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
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- 14 -
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^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
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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
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H
H
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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°
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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.
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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
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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
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apnjpiV -0Byf
• i *
9+
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»Pn»T»HY
£090
0090
,jtfv a
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«6I Zt SS
'61 «2» S"9S
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wanxooM
£090
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06
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8S6T Si
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'•WW 02
'TI SS ZO
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'»H 92
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6ZT 9£
081
61 80
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62- 81
s*z+
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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
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•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
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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
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•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
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.66 ,98 18 .21 39 47 73 24
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•23 •71 70• •63 02• 79• 86• 86• 83• 66• 11• 87• 4i
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-63.
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-4.
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22* 41. 37, 65, 59, 43. 30,
S3.
•17,
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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.
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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.
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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
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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
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IGY Satellite Report Series
Number 7
1 January 1959
IGY
WORLD
DATA
CENTER
A
Rockets and Satellites
NATIONAL ACADEMY OF SCIENCES
SIMPLIFIED SATELLITE PREDICTION FROM
MODIFIED ORBITAL ELEMENTS
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.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. The resulting in
formation was entered in Item 14.
15
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TABLE V - 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
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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.
TO CENTER
OF EARTH
45
OF SATELLITE
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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
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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
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PART II
COLLECTED REPORTS ON SATELLITE OBSERVATIONS
Special Reports Numbers 22 and 25
and excerpts from
Special Reports Numbers 18-21
of the
Smithsonian Institution, Astrophysical Observatory
Cambridge, Massachusetts
(Special Report No. 18 is entitled "Satellite Data and Analyses."
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