the orbit of satellite 1958 alpha explorer i during the first 10500 revolutions 1963042046

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SPECIAL R E P O R T

Number 50

October 3 , 1960

C A M B R I D G E 3 8 , M A S S A C H U S E T T S



TABLE OF CONTENTS

The Orbit of Satellite 1958 Alpha (Explorer I) During the First

10500 Revolutions

-- by Pedro E. Zadunaisky . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1



THE ORBIT OF SATELLITE 1958 ALPHA (EXPLORER I)

DURING THE FIRST 10500 REVOLUTIONS

Pedro E. Zadunaisky 1

This paper presents the results of a computation of mean orbit al elem ents of Sat elli te

1958 Alpha, the first Ame rican sat ell ite, at two-day intervals during the entire period from

February 6, 1958 (5 days after launching tim e), until April 30, 1960. An analysis of these

results is being prepared for lat er publication. Th e computations have been made by use of a

ma chi ne progmm of differential corrections designed by G.Veis and C. Moore at the Smith-

sonian Observatory (Ve is, 1960).

The observations used cam e from three main sources; Min itmc k, Smithsonian Baker-Nunn

photogmphic trucking, and Moonwatch stations. T o these three types of observations we assigned

relative accumci es of, respectively, 660, 184, an d 3300 seconds of arc . In the d iffere ntial cor-

rection process, ma de according to th e method of l east squares, the weights assigned to the corres-

ponding equations of condition were the reciprocals of the squares of these numbers.

The mdio tmnsmitters contained on the satellite operated for nearly four months and

during that early period they were almo st the only source of observations.

mitters stopped opem ting on May 23, 1958, observations of other types were very scarce until

July 6, 1958, when it was possible to resume the computation on th e basis of rel iable observa-

tions. This and other minor gaps in our computations are due to a simi lar lac k of observations.

Th e word "mea n" referring to the orbital eleme nts presented here must be understood in

When the m dio tmns-

two senses.

oblateness of the Earth have been computed analyti cally (Kozai, 1960) and sub tmct ed from the

observations before the differential correction of the elements was performed.

elements are mean in the sense that they represent observations distributed over a period of

seveml days.

stants but by polynomial, sine, and eventually exponential functions of the ti me .

tions were chosen, for convenience, to represent in an- emp iric al way the secul ar and long-

period perturbations resulting from th e non-spherical form of th e Earth and from atmosph eric

drag. Th e numeric al values of the coefficients involved in these functions were refined by a

process of successive approximations a s follows.

First, the word indicat es that the first-order short-period perturbations due to the

Secondly, the

It is true, however, tha t the elements of such an orbit are not represented by con-

These func-

At th e beginning it was found (Tesk e, 1958) tha t the o rbita l elements could be most

simply represented by breaking the first three months of the life of the satellite into segmentsof about a week , and fitting polynomial expressions for th e perturbed eleme nts to each of th e

1 Astronomer, Research and Analysis Division.

-1 -



segments. Th e coefficien ts of these polynomial s were found mostly by combining theory and

successive emp iric al corrections of the eleme nts already known at the ti me the satellite went

into orbit. In this way the argum ent of peri gee (a),he right ascension of the ascending node

( hd), and the m ean anoma ly were represented by quadrati c polynomials; the eccentr icity (e ) was

represented by a line ar expression, and the inclinat ion ( i ) by a single constant ter m. Using these

expressions as input for the m achine program, we correc ted only the first coefficient of each

polynomial at each two-day interval, but we kept th e other elements constant for periods of one

to two weeks. In the me an anomaly we corrected, also every two days, the three coefficients

of th e quadratic polynomial in order to take into account the rapid and unpredictable changes in

the atmospheric drag.

Those corrections were made in order to mak e the elem ents consistent with the observa-tions of the satelli te during a particular period of 6 days, 3 days before and 3 days after the epoch

of th e elements. Since any two successive epochs are s eparate d by an interval of 2 days, the cor-

responding periods of 6 days overlap on 4 days; this method assures a better continuity in our re -

sults. The period of 6 days to be represented by a single set of eleme nts (expressed as polynomial

plus sine functions of time) proved to be optimum in this computation. A period of 8 days

yielde d results that were to o much smoothed; a period of 4 days was too short to accumula te

enough observations and the results were rathe r unstable. Using this method of correcting the

first coefficient of the polynomial representing eac h elem ent, every two days, we covered the

f i r s t three months of the life of the satellite. The compu tation continued by the procedure des-

cribed above, which used as a first approximation for each epoch the results corresponding t o an

epoch two days before. Step by step, we computed the orbital ele men ts every tw o days for the

entire life of the sate lli te through April 30, 1960.

Next we started a new stage of th e computation, considering 7 successive periods ofabout 5 months each. For each period we represented the elements by quadratic polynomials

obtained by a least squares fit to the coefficients already corrected. This ti me we also added

to each polynomial a sine (or cosine) term corresponding t o the effects of t he third harmonics

term in the gravitational poten tial of the Earth, computed theoretically ( K a a i , 1959a).

eac h el ement was represented by a n expression of t he form

Thus

E = Eo + E1(T - To) + Ez(T - To)2+ E4 {:&] cu ,

CU being th e argument of perigee. We then repeated th e whole process of correction of the coef -

ficents Eo of all the elements, and of the linear and quadratic coefficients Mi and M2 i n the

mean anomaly. This tim e the positions computed with the new elemen ts agreed much better,

in general, with th e observations; in certa in periods the compu tation was repeated once more,to obtain a better fit to the observations.

The final results ar e shown in T able 1, which coven successive periods of two months

each. The first column gives the Modified Julian Date (MJD) of th e epoch of the elements;

this is mer ely the act ual Julian Date from which, to avoid repetition, the number 2400000.5

has been subtracted. The following four columns give the argume nt of peri gee (a),he right

ascension of the ascending node ( ba ), the inclination (i), and the eccent ricity (e). The single

digit placed at the right of ea ch valu e represents the standard error and affects th e last digit

given. The mean anomaly (M) and the anomali stic mean motion (n) have been computed from

th e corresponding polyno mial plus a sine expression, as given in equation ( l ) , or the epoch T,whereas n1 is the va lue of t he third coeffic ient !M2) of that polynomial at the same epoch. The

following three columns contain the geocent ric distance of the perigee (q) in megameters, the

number of observations used (N), and th e number of days (D) along which thes e observations were

distributed. The last column gives the standard deviation ( Q ) or mean quadratic error of asingle observation whose wei ght is unity.

-2-



The funda menta l system of referen ce of these elements is that defined in Smithsonian

Special Report No . WR ) , page 2. The reference plane is the true equator of date, and the

origin of right ascension is a line shifted from the mean equinox of the date by an amount

equal t o the precession in right ascension between 1950.0 an d the da te. Therefore the right

ascension of the ascending node ($2 ) given in Table 1 may be transformed into a right ascen-

sion referre d to th e mean equinox of da te ( Q ) by means of th e simple formula,

Q 1 = + 3?508 x lo” x (MJD -33281).

In Table 2 we give some data that are especially related to the perturbing effects of

atmos pheric drug. The column heads have the following meanings: MJD is the actual Julian

Date minus 2400000.5; fi is th e ra te of change in period in days per day; 2 is the perigee height

(i n km) above the international ellipsoid; @ is the latitude of perigee; D. R.A. is the right as-

cension of perigee minus the right ascension of the sun; and @ is the geocentric angular d$-

tan ce between perigee and the sun. We have computed the rate of change of the period, P, by

using for the m ean anomaly th e expression,

M = Mo + M l ( t - to) + MZ(t - to)’ ,

thus neglecting the sine term whose effect is small.

by the relation,

Then the mean anom alistic motion is given

n = dM/dt = M1 + 2M2(t - to) ;

the period is P = 1/n and the rate of change of the period is fi = -2MZ/n2. The other data,

whic h refer to the recently discovered correlation between solar activity and v ariati on of the

atmospher ic density (Jacch ia, 1959; 1960) were computed as explained in Zadunaisky (1960).

We also give a graphical representation of our results as functions of time. In all cases

except that of the mte of change of the period, we have plotted the residuals of the given el e-

ment against a quadratic or linear equation obtained by a least squares f i t which contains the

secular part of t he variation of the element. On the axis of tim e we have marked the zero day

of ea ch month, and the Modified Julian Da te at 10-day intervals.

As is well known, the atmospheric drag effect on an object such as Satellite 1958 Alpha

The magnitude of th e dmg de-s practically concentrated on a narrow region around perigee.

pends mainly on the atmospheric density at that point and its variations will be reflected in

variati ons of the mea n motion of the satellite. Figure 1 shows clearly th e correl ation existing

between th e geocentric angular distance from the Sun to the perigee of the sate llite orbit and

th e me an motion of the satellite. Between the two curves there is a lag due probably t o th e

diurna l rotation of the atmosphere (see Jacchia, 1959; 1960). On he graph corresponding to

the rate of change of t he period the fluctuations are erratic, but some periodic oscillations,

with a period of about a month, are visible, especially during the times in which the perigee

was in sunlight. A careful analysis is required to separa te the purely gmvit ationa l effects from

those due to variations in atmosphe ric drug and, possibly, solar radiation pressure.

of the tumbling of this non-spherical sate llit e seems to be in general small, except during the

first few weeks after launching time.

The effect

-3 -



In Figure 2, the graphs corresponding to t he arg ument of perige e and the right ascension

of the ascending node show their residuals against the quadratic expressions,

with th e following numerical values for th e coef ficient s obtained by means of a least squares

f i t :

cu0 = 163t682 62 = 314748

031 = 643179jday 621 = -402343jday

W 2 = 4518 x 10-3/day2 66 2 = 0346 x 10’3/dayz

When only secu lar perturbations of the first order are taken into account the an alytical

expressions of a1 an d 4 are, respectively (Kozai , 1959b),

A2 n ( 2 - S s i n 2 i ) t ,2

P

a,=-- 2 n t c o s i ,

P2

where A2 is the coef ficient of the second harmonics term in the gravitati onal potentia l of the

Earth, an d p is the parameter of the el liptic orbit of the satelli te, which con be written in theform,

q being the distance from perigee to the cen ter of the Earth. From our tables we can see that,

from satellite launching to the present time, q diminished by an amoun t of a few thousandthsof a n ea rth radius and i had a maximum variation of a few hundredths of a degree. Then con-

sidering q and i as constants and putting 02 = h 1 / 2 and 622 = & 112, we find it is not too

difficult to obtain, afte r some transformations:

6 9

- - -7 - e

2 - 6 l + e

n2=--- e ; s a , .6 l + e

Theref ore we should have, approxi matel y,

-4-



If we use for i th e value of 3392, we obtain

5 22 - 2 sin i

= -1.493,cos i

whereas

in good accordan ce with the theory.

The effects of th e variations of n uponu and a , although somewhat smoothed, ar e

clearly visible on the curves of Figure 2. The graph of the argument of perigee (W) shows a

period ic perturbation, with a period of about two months, which is probably due to the ef fects

of the asymmetry of the Earth with respect to its equato rial plane. The same effects can be

noticed on he graphs corresponding to the eccentricity (Fig. 3) an d to th e distance between th e

perige e a nd the cente r of the Earth (Fig. 4).

Finally we computed the lifetime of this satellite by using the approximate formula

(s ee Kornford: 1958, p. 13),

e x ( 6 + 7 e ) x n

t L = 2 9 2 o x i l9

which gives the results in years when n is measured in revolutions per day. We computed th e

values of n and e for April 30, 1960, using the formulas given in Figures 1 and 3, by which we

obtain t L = 2.19 years. This result means that the demise of the satelli te, Explorer I, should

occur around th e month of July, 1962.

Most of the material work of handling the computing machine programs and making the

graphi cal representation was done with m e nd diligence by Mr. Jay C. Tapp and MIS. Beatrice

Miller, to whom I express my thanks.

References

pKCHIA, L. s.1959. Solar effects on the acceleration of arti fici al satellites. Smithsonian Astrophys.

Obs., Specia l Report No. 29, 15 pp.

1960. A variab le atmospheric-density mod el from sate llit e accele ration s. Smithsonian

Astrophys. Obs., Specia l Report No. 39, 15 pp.

KORNFORD, E. C.1958. A comparison of o rb iM theory with observations made in th e United Kingdom of

the Russian satellites.

of Supply, London. July.

Royal Air cmf t Establishment (Farnborough), Ministry

-5-



KOZAI, Y.1959a. T he earth's gravit ational potential derived from the motion of Sa tell ite 1958 82 .

Smithsonian Astrophys. Obs., Special Report NO . 22, pp. 1-6.

1959b. The motion of a close earth satellit e. Astron. Journ., vol. 64 , pp. 367-377.

1960. Osculating elements. Smithsonian Astrophys. Obs., Specia l Report No. 31, pp. 8-9.

TESKE, R. G.

1958. Positions of Satellite 1958 Alpha during the first 1400 revolutions. Smithsonian

Astrophys. Obs., Special Report No. 17, 173 pp.

VEIS, G.1960. Geo det ic uses of artificial satellites. Smithsonian Contr. Astrophys., vol. 3,

pp. 95-161.

ZADUNAISKY, P. E.1960. Relati ve positions of th e sun and per igee of an artificial satellite. Smithsonian

Astrophys. Obs., Special Report No. q R ) , pp. 24-25.

-6-



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m m d mo o m 9N O S d

m ~ m i t

m m m mI l l 1w w w wo m w mN I n V I Nl n l n m l n. . . .9 9 a i

4

N N N N0 0 . .

d 4 4 H

m m m m

4 4

. . . .i t 9

~ N + N

m m i t a

0 . 0 .

o d m l nm m m mm m m m

N N d N

a o m mr - W r - 90 0 0 0

r ( d d r (

. . . .9 m 9 m

m a i t l nd N N dN N N N. . . .

m m mm m m m

m N N N

S N t i t

m N N dI - w 0 - 0N N N mm m m mI l l 1

m m i t m. . . .

t *m a

0 9

I n n . 0 0 - 0

w m 9 . 4w m i t 9I n l n l n l n

l n l n l n m

. e . .

0 0 0 0

0 . 0 .

W O N 4m i t i t i t0 0 0 0

f - r - P r -m m m m

mNmN+9b

m

mIWit4

In

b

0,

m9

m9

r-lu

m.dm

mitN

OD.mm

N

m9

0d

.d

0

N

mm

.

N

itit.d

mmI

it

ODm.r-In

m

0

9it0

P-

m

.

m m m l nQ P D Nd m d o

m m c u mr - b c l c r -

9 9 9 9. . . .m i t

m mm m i II I W WW W Q 1~ r - m ol n 1 i t i t

d N

. . . .

d 9 I l r no o m l n- I m i t 9m w c o s ,N N N N

. . . .m m md 4 4 d

m r - m w

. . . .W m d Nm m * *m m m m

OD m m

d m wO l H - 4 9. . . .

o o m

N

m it titm m m mm m m mI l l 1

r-N m d

Nr - C n 0 . t. . . .

Q W Nw o - mm a 9 9m ' n m l n

n O O D

W O N *i t l n l n l n

0 0 0 0

P - r - r - C I cm m m m

0 . 0 .

-19-



TABLE 2

MJD

36240.3624236244

3624636248.

3625036252

36254.

36256.36258.

36260.36262

36264.

36266.36268

36270.36272.

36274

36276-36278.

36280.36282

36284.

36286.36288

36290.36292.

36294

36296.36298.

36300.36302

36304.

3630636308.

36310.

363 12

363 14-

36316.363 18

36320.

Data r e l a t e d t o t h e s o l a r e f f e c t s on t h e

a c c e l e r a t i o n of S a t e l l i t e 1958 Alpha

-P Z cp

PERIGEE I N EARTH SHADOW

00548E-050 558E-050.569E-05

0. 535E-050 0420E-05

0 365E-050.547E-05

0 0456E-05

0.459E-050 444E-05

0 466E-050.454E-05

0 462 E-C5

00484E-050.5366-(35

0.451E-0500478E-0500509E-05

O m 548E-050.496E-05

0. 556E-05

0 564E-05

0. 581E-05

0.604E-050.665E-05

0.577E-050. 652E-05

0. 835E-05

0.670E-050.708E-05

0.668E-0500553E-05

0.465E-05

0.453E-05004836-05

0. 606E-05

0. 57%-05

0. 579E-05

0. 579E-050 635E-05

0. 633E-05

355.357.357.

358.358.

3 613 6 1362.

365.367.

366.365.

364.

36 2360.

358.357.356.

356.356.

356.357.

357.

359.361.

360.360.

356.

356.351

349.355.

358.

359.360.

363

364.

366.

366.365.

364.

15.408.841.98

-4.96-11.73

-18 06-23 57-28 023

-31.55-33.13

-32 087-30.82

-27 19

-22 e34-16.44

-9.95-3.11

3.81

10.6217 006

22.83

27 60

31.06

32.9233.00

31.2827 09 5

23.29

17.5211.12

4.32-2.65

-9 049

-16 05-22 000

-26.97-30.69

-32 082

-33

.4

-31.60

-28 036

D.R.A.

158.65159.27

159.53

159.74160 22

161 14162.57

165.44

169.49174. 11

178.91183.32

186.90

189.46191.05

191.93192.35

192.57

193.04193.98

195.71198.35

201.98

206.47211.33

215.81219.52

222.06

223.80224.87

225.57225.84

226.25

227.12228.81

231.27

234.85

239.26

244.11248.76

252 68

Y

159.44158 76156 18

152 r42148.23

144.15140.66138 16

136.81136 79

138 14140.81

144 70

149 50155 009

160.77165 056167 046

164.88159064

153.56147 064142.30

137.77134.24

A31.90130.66

130.59

U1.24132025

133.23

134.12134.30

133.51131.62

128. 9

125.65

122 OO

118 a27114 72

111.49

-20-



M JD

36322.36324.

36326.

36328.36330.

36332.36334.

36336.

36340

36342.36344.

36346

36390.36392.

36394.36396

36398.

36400.36402.

36404.36406.

36408

36412.36414.

36416.

36418.36420.

36422.36424.

36426.

3642 836430.

36432.36434.

3643636438

36440.

3644236444

36446.36448

36450.

36452.36454.

36456.36458.

36460

3646236464.

36466

36338.

-P Z Q

PERIGEE I N SUMLIGHT

0.664E-050 0636E-050 0501E-05

0.508E-050.517E-05

0. 512E-05

0.489E-OS0 5 13E-05

0 522E-050 . 519E-05

0 544E-05O e 515E-05

0. 539E-05

0.569E-050 659E-05

00649E-050.311E-05

0.274E-05

Om470E-050.482E-05

0 489 E- 05

0. 523E-05

Om 548E-05

0.64OE-050e709E-05

0 724E-05

0 695E-05

00721E-05

0. 589E-050.601E-05

0r600E-05

0. 598E-050.609E-05

0.649E-050 666E-05

0 683E-050 808E-05

0. 667E-05

0 . 102E-0400977E-05

0.920E-050. 985E-05

0 e 103E-04

0 . 1OOE-040 926E-05

Om 9ME-050 995E-05

Oe101E-04

0.107E-040.1 WE-04

00897E-05

36 23600358.

356.355.

355.

355.356.

356.35 7.358.358.

357.

356.358.

361355.

357.

356.3600

360.

360.

355.

355.

356.

358

3590

363.363.

650

36 6 0

366.

365.363 e

362

360.

3590

357.

355.355.

3560357.

356.

358.359.

361e

3590

360.

355.67.

355.

-23.37

-18.07

- L i e 6 6

-4.812.18

9.10

15.692 1068

26 07430.51

32 7 433016

3 1e74

15.632 1070

26 8230.51

32.72

33.133 1 6 2

28.3623068

18.81

4.86

-2.21

-9 022

-13.96-22.20

-2 7 08-30.78

-32.87

-33 008-31 040-27.96-23.15

-17.25

-10.66

-3 72

3.4010e 4 5

17.0522 092

27 e83

31.2933.05

%? 95

30.94

27.28

22 2216 19

9.53

D.R.A.

2!55051257.33

258.33

258.90259.05

259.30

260.022 6 1 4 3

263.80267.11

271e30215695

200.37

321 55322.91

325.28328.16

332 74

337elO341.97

345 80

348 63

M e 2351.37

351057

35A 0 92352.85

354.92

357.040.54

5.09

1 0 e 0 1

140 6

A806921.50

23.40

24.41

24.86

25.2126.01

26.8328 e 5631.43

35a2839085

44.70

49.51

53.28

56eQ157.70

50.40

cy

108 e73

106.33

104.17

101e9899.85

97.38

94 e4990092

86.9782 078

78.5074e40

70.91

36.9034 28

31.7929.65

26.46

23.37

19.20

14.9511.02

1 O . U16.59

22.49

28e57

34.4939.69

43 8046.05

18060

48.924? e 8 1

$503941 9 5

37.5632.99

28.80

25 09525 062

27.3531.11

%a92

4ke 106!5.&3

490%

5 3047

55 95

570%54.46

58*a2

-21-



MJD

36468.

36470.

36472.

36474.

36476

36478.

36480.

3648236484.

36486

36488.

36490.

36492.36494

36516.

36518.

36520.36574.

36576.

36578

36580.

36582

36584.

36586.

36588 a36606.

36608.

36610.

36612

36614.

3661636618.

36620.

36622.

36624.

3662636628

36630.

36632.

36634.

36636.

36638.

36640.36642

36644

36646

36648.

3665 0

36652

.-P

0 861E-05

0 a 862 E-05

0.953E-05

00958E-05

0.919E-05

0.937E-05

0a883E-05

0. 895E-65

0 772E-05

0 a 749E-05

0. 792E-05

0 793E-05

0 885E-050 906E-LJ5

z

355.

355.

356

359.

360.

363.

366.

370.364.

360.

355.

361 a

353.354.

P

2 046-4.70

-11.71

-18.18

-24 08

-28.50

-31.98

-33.20

-32.60

-30.02

-25.70

-20.54

-13.90-7 02 4

PERIGEE I N E A R T H SHADOW

0.682E-05

00690E-05

00620E-050.519E-05

0.600E-05

0 a626E-05

0 520E-U50 0462E -05

0 42 1E-05

0.425E-05

00410E-050a465E-05

0. 47 1E-05

00473E-05

0 465 E-0 5

0 4786-05

0 486E- 050 50%-05

0.600 E-05

0.408E-05

0 492 E-05

0 560 E - 0 5

0 a 508E-05

0.474E-05

0a433E-05

339.

350.

354.336.

341.

353.

354.356.

359.

360.

360.352.

351.

352 a

353.353.353.353.

347.

353.380.

393.356.

351

346 a

PERIGEE I N

0a440E-05 358.

00440E-05 357.

0a412E-05 357.

0.433E-05 360.0a431E-05 363.

0.444E-05 364.

00450E-05 361.

0.463E-05 362.

0. 508E-05 358.

0.514E-05 356.

24.34

18 047

11.9611.90

5 006

-2 14-9 042

-16.33

-22 a48

-27.57

-31.236.53

13.60

20.07

25 64

29.92

32.5333.21

32.19

28.60

23.67

17 5611.12

3.99

-3.28

SUNLIGHT

-19.75

-17.51

-23 047

-28.35-31.71

-33.18

-32.60

-30.02

-25 a 7 2

-20.06

D.R.A.

59.1059.50

60.1661. 12

63.53

65 87

71.60

75.42

80.64

85.5789.53

91.22

93.2593.56

122.23

124.65

125.67186.45

186.20

186.02

186.3 1187.08

191.24

194.93217.87

218.49

219.76

222.01

225.37

229 a 7 9234.66

237.48

243 88

247.44

249.52250.07

250.51

250.79

188.67

2 5 1 7 4

252.80

254.66

257.74262.00

267006

272.43

277.08

280.72

283.30

Y

59.1159.6060.63

62 009

64.89

67.29

72.27

75.17

7 9 11

83.00

86.50

88 a38

91.0692.31

125.71

127.51

127.33

167 e65

161.68

155 00 6

148 a 17141e57

135.59

130.49

126.49141.81

142 72

141068

138 86

134.87

130.28125.75

123.20

117.72

114.36

112.04110.98

109.81

108.66

1 0 6 7 4

104.80

102.34

99a

1695 a 4 6

9 1052

87 e45

83.80

80.64

78 e03

-22-



MJD

36872.

36874.

36876.

36878.

36880.36888.

36890.

36892.36894.

36896.36898

36900.

36902.36904.

36906.

36908.36910.

3691236914.

36916.

36918.

36920.

36922

36924.

36926.

36928.

36930.

36932

36934.

36936.

36938.36940

36948.

36950.

36952

36954.36956.

36958.36960.

36962.

36964.36966.

36968.36970.

36972.36974.

36976.

36978.3698 0 e

36982

-P Z

0.408E-05 347.

0.424E-05 349.

0e423E-05 351.0.389E-05 351.

0.382E-05 351.00324E-05 389.

00324E-05 413.

0e330E-05 351.0e333E-05 353.

0.345E-05 352.00356E-05 355.

0e38lE-05 354.

PERI GEE I N

0.374E-050.378E-05

0.384E-05

0. 378E-050. 344E-05

0 e 31 2E-0500329E-05

0.336E-35

0 323 E-05

0 e 30 5 E-05

0.254E-05

0e236E-05

0 35 2 E-05

0.3545-05

0.344E-OS

00329E-05

0.35 7E-05

0.438E-35

0. % i E - 0 5

0.507E-05

0 405E-050e397E-05

Oe394E:-OS

0. 414E-050.454E-05

0e498E-050e572E-05

0 627E-05

0 0666E-050.721E-05

0.746E-050.694E-US

0. W9E-050 495 E-05

0 0471E-05

0 43 9 E-05

0e419E-05

0 464E-05

354.

355.

359.

358.355.

37'3,349.

350.

352

352

425.

348.

351

354.

347.

348

360.

345.

336.348

353.355.

356.

358.358.

360.355.

354.

352352

350.351

349.349.350.

350.

350.

352

cp

16.67

22.97

28 e 1431.67

33.1819.07

11.90

5.08-2.57

-10.06-17.15

-23.43

SUNL I GHT

-28 49-31.85

-33.21

-32.32-29.34

-24 r53-18.38

-11.43

-3 09 6

3.71

12.90

18.16

24.30

29 13

32 14

33.22

32.15

28.89

23.8017.61

-12 13-19.04

-25 03

-29.45-32.53

-33.17-31.59

-28.01

-22 77-16.23

-9 02-1 e24

6.3513.75

20.51

26.25

30.48

3 2 0 8 4

D.R.A.

201.34

203.19

206.32

2 1 0 0 6 4

215.76231 053

233.18

232.74233.04

233.37234.28

236.11

239.11243.19

248.52

253.54257.88

261.07

263.43

264.35

264.63

264.03

267.30

266.04

267.98

271.08

274.81

279.92

285.26

289.28

292.51294.21

296.08

291.17

299.30

302.62307.65

312 92317.79

321.91

324.86326.90

327.79328.50

328.73329.49

330097

333.58

337.37

342 3 9

(u

139. 2

156 48

152 36

147 e 88

143e65131 39

128044

l.26.73123 32

119.34114.66

109.50

104.1999 18

94.46

91 e0288 088

88 18

88 e67

90.62

93.35

96.21

97 e52

100.62

101.14

190.26

98.37

94.80

90.22

85.53

80.38

75.80

6 1e52

58 e 6 7

55.48

52s3948.2.2

4 4 0 0 740.01

36.20

33.273 1 e 6 8

32.2634 36

37.8341.51

44.85

47 2748.40

47.94

-25-



MJD

36984.

36986

36988.

36990.

36992.36994.

36996.

36998.

37000.37002.

37004.

37006.

37008.

37010.

37012.

37014.

37016.

37018.

37020.

37022.

37Ci24e

37026.

37028.

37030.

37032.37034.

37036.

37038.37040.

37042.37044.

37046.

37048.

37050.

37052.37054.

-P

0e456E-05

0e452E-05

00W4E-05

0 48 1E- 05

0.594E-05Oe555E-05

0.54OE-05

0e571E-05

0e

57 1E-050e503E-050.577E-05

0 502E-05

0 466E- 05

0.527E-U5

0a520E-05

0e529E-05

0 e 55 5E- 05

0e614E-05

0 e663E- 0 5

0 70 1E-05

Oe764E-05

0.767E-05

0e570E-05

0 604E-05

0e585E-050e58OE-05

0e574E-05

0 e 591E-050 628 E- 05

0 626E-050a593E-05

0e583E-05

0.590E-050.533E-05

0e496E-050a458E-05

Z

352.

352

351.

3 5 0 .

348350.

350.

350.

351.355.

356.

356.

358

358.

357.

356.

355.

351

348.

348

349.

349.

348

350.

351 e

351.

350.

349.345.

348.349.

351.

354.

36 1 e

351.356.

cp

32 e99

30.94

26.92

21.35

14.687.32

-0.33

-8.01

-15.35-2 2 e 03

-27.49

-31.34

-3 3 e 12

-32 67

-30.00

-25.43

-19.49

-12 a 4 4

-4.85

2.87

10.46

17.65

23.92

28.89

32.11

33.20

32.05

28.78

23.38

17.4110.24

2.53

-5.30

-13.06

-19.70-2 5 73

D.R.A.

347. 7 5

352 7 5

3 5 6 r 8 0

359.68

10.442.35

2.83

3.42

4.486.51

9.48

13.88

19.32

24.99

29.94

33.95

36.51

38.19

39.08

39.62

40.27

41.65

4 3 8 9

47.35

52.04

57.51

62.75

67.35

71066

72.987 4 0 2 1

74.99

7 5 0 6 5

77011

77.6980.46

Y45 e 8 5

42.14

3 6 0 9 530.51

25.3115.17

7.15

3.88

10.9218 e56

25.36

31.21

35.82

39 e09

4 0 e 89

41.58

41.22

40 a48

39.74

39.56

40.42

4 2 68

45 e96

49.9754.35

58 e 6 6

62.41

6 5 7 269.29

70.727 2 0 6 7

74.89

77 e28

80.86

83.538 8 e 0 4

-26-



4

tl

I

hN

I

rl



I I

N

wwIaw4.

LL0

..

.-

.-a

I I

* .

I

.-

I



9n

a

8E

t

1

W

_1-.IwI-

4

: -

. '

' .* .

..



1111

W..

+ ..'

w0zi5innww(3a

n0

F

szw

w(3I

.-

t

.

1 . 1 I I

I



NOTICE

T h i s se ri es of Special Reports w a s insti tuted under thesupervision of Dr. F. L. n i p p l e , Director of th e AstrophysicalObservatory of t h e Smithsonian Institution, shortly af te r th e

launching of th e f i rst ar t i f i c i a l ear th s a t e l l i t e on October 4,1957.Firs t issued t o ensure the immediate dissemination of data f o rsa t e l l i t e tracking, the Reports have continued t o provide a

rapih dbtr ib ut io n of ca talogues of s a t e l l i t e observations,

or bi ta l information, and preliminary results of data analyses

pr ior to formal pbl ica t ion in the appropriate journals.

Contributions come from the S ta f f of th e Observatory.

Edited and produced under t h e supervision of M r 8 . L. (3.

Boyd and Mr. E. N. Hayes, the Reports are indexed by the Scienceand Technology Division of t h e Library of Congress, and are

regularly distr ibuted t o all ins t i t u t ions pa r t ic ipa ting in the

U. S. space research program and t o individual s ci en ti st s whorequest them from the Administrative Officer, Technical Infor-mation, Smithsonian Astrophysical Observatory, Cambridge 38,Massachusetts.

The work repo rted i n t h i s s e r i e s i s supported, i n part,through grants from the National Science Foundation and theNational Aeronautics and Space Administration, and contractswith the Army Ballistic Missile Agency.

the orbit of satellite 1958 alpha explorer i during the first 10500 revolutions 1963042046

Documents