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NASA T M X-1201

PRIME MINITRACK AND BAKER-NUNN

ORBITS OF SATELLITE 1 9 5 9 ~ ~ 1 (VANGUARD 11)

By Hans G. Hertz

Goddard Space Flight C e n t e r Greenbel t , Md.

N A T I O N A L AERONAUTICS AND SPACE ADMINISTRATION

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ABSTRACT 2 I [ 0 0 Concurrent data necessary for making a comparison

study of the accuracies of Prime Minitrack and Baker-Nunn observations of Satellite 1959 nl (Vanguard 11) are presented in this report. In all, 244 Prime Minitrack and 187 Baker- Nunn observations a re available which were made over a 26-day period while the satellite's transmitter w a s oper- ating. Prime Minitrack observations were possible only during transmitter operation. Data included here a re com- prised of Prime Minitrack and Baker-Nunn observations made concurrently. .

ii

CONTENTS

ii

1

1

2

3

3

41

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . DISCUSSION OF D A T A . . . . . . . . . . . . . . . . . . . .

CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . .

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix A-List of Symbols . . . . . . . . . . . . . . . .

iii

.

PRIME MINITRACK AND BAKER-NUNN ORBITS OF SATELLITE 1959a, (VANGUARD II)

by Hans G . Her tz

Goddard Space Flight Center

INTRODUCTION

Satellite 1959a, (Vanguard 11) was launched 17 February 1959. The transmitter w a s operating for 26 days through 15 March 1959. Therefore Prime Minitrack observations could be obtained during this period. It was suggested to the author that a comparison of the accuracies of Prime Minitrack and Baker-Nunn observations of a satellite would be interesting. In the present report the data necessary for such a study a re presented. The observations used a re those made in the period where both types of observations were possible. There were 244 Prime Minitrack and 187 Baker-Nunn observations available which were made during this 26-day period.

DISCUSSION OF DATA

For each of the two types, twelve orbits were determined. Their epochs were at 2-day in- tervals from 19 February 1959 through 13 March 1959 inclusive. For each orbit, the values of the parameters s,, s2, . . . s, , s,, were determined by differential corrections. Here s, , s,, . . . s, are the values of the constant te rms in the expressions for the osculating elements a , e , I , 0, O, M

as given by Brouwer (Reference 1). The quantity SI, is the coefficient of the term SI, / 2 , T in units of 100 hours from the epoch, added to Brouwer's expression for the mean anomaly. In each differential correction all observations within 72 hours of the epoch have been used provided they generated residuals, C O S b la and A s , not larger than 020.

The earth parameters used in these solutions a re shown in Table 1. The parameters a re the equatorial radius R of the earth and the constants k , k 2 , A30, k , , As0 . The last four constants occur in the expression,

1

Several iterations were made. The orbits finally adopted as those based on the Prime Minitrack observations a re called briefly Prime Minitrack orbits (PM orbits) and received the numbers 603 through 614. The numbers for the Baker-Nunn orbits (BN orbits) a r e 631, 616 through 625, and 632. The relationship between these numbers and the epochs is shown in Table 2.

The resulting values for the parameters sl, s2, . . . s6, s,, are shown in Table 3. There a re twelve p a i r s of lines, one pair each belonging to one of the twelve epochs. The first line in each pair gives the results for the P M orbit, the second for the BN orbit. The orbit numbers given serve to identify the epochs.

Table 4 gives the probable e r rors for the SI obtained. They are arranged in eight pairs of columns. The first column of each pair belongs to PM orbits, the second to BN orbits. One line corresponds to a PM and the corresponding BN orbit for the same epoch. The numbers Of this PM and BN orbit are given in the first two columns of the table.

The residuals for the P M observations a r e shown in Table 5 and those for the BN observations in Table 6. Except for the observations near the beginning and end of the 26-day period every P M or every BN observation appears in three orbits. The P M observations have received serial numbers starting with 1. The numbers of the BN observations a re those assigned by the Smith- sonian Astrophysical Observatory, without the designation of the year. The observations being precision-reduced observations, all numbers begin with a "7'.

Table 7 gives information as to the accuracy of the representation of the observations by the adopted parameters. The weights given are those found in an iterative process in such a way that they a re consistent with the probable e r rors computed from the residuals. This table shows that the rejection limit of 030 referred to on page 1 was too large. Better results would be achieved if it were lowered or if the rejection limit were made dependent on the distribution of e r rors .

By making additional runs the condition that no observations with residuals of more than 3 times the probable error be included was approximately met.

Table 8 shows the differences A s , of the values of the si obtained for a P M orbit and the corresponding BN orbit belonging to the same epoch. The differences a re given in the sense PM-BN.

The si a re plotted versus the time in Figures la -g for the Prime Minitrack orbits and in Figures 2a-g for the Baker-Nunn orbits. If no drag or other non-gravitational forces were pres- ent S I , s,, s, would be constant, s4 , s,, s, would be linear functions of the time, and s,, would be zero. The probable e r rors in Table 4 and Figures la-f, 2a-f, and the non-vanishing of S,, indicate that there are deviations from gravitational behavior.

CONCLUSION

Additional aspects of this problem a re of interest and will be investigated if sufficient time and resources are available. For instance, the dependence of the si on the time could be investigated.

2

. I

' An examination of the A S i as to significance could be made. It would also be interesting to examine the residuals of the Prime Minitrack observations with respect to the Baker-Nunn orbits and the residuals of the Baker-Nunn observations with respect to the Prime Minitrack orbits. Finally, the data provide information on the relative accuracy of the two types of observations.

ACKNOWLEDGMENTS

The computations on which the results of this report are based were carried out with a Dif- ferential Correction Program System and some additional programs. The original package was based on the satellite theory by H.G.L. Krause (Reference 2) and was programmed by Miss Elise R. Fisher of the Theoretical Division. Gratitude is also expressed to Mr. Cahill of the same division. The IBM Corporation under Dr. K. Deahl was utilized to substitute Brouwer's theory. Additional work was carried out under the supervision of Mr. A. Shapiro of GSFC. I thank Messrs. H. Bremer and R. Bryant of the Theoretical Division, Messers. R. Danek and J. Weld of the Data Systems Division, and others for help and advice received. Acknowledgement is also due the Smithsonian Astrophysical Observatory for providing the observations prior to publication.

REFERENCES

1. Brouwer, Dirk, "Solution of the Problem of Artificial Satellite Theory Without Drag," Astro- nomical Journal, Vol. 64, no. 378, 1959.

2. Krause, H. G. L., "Die siikularen und periodischen Storungen der Bahn eines kiinstlichen Erdsatelliten," Proceedings of the 7th International Astronautical Congress, (1956) p. 523.

3

Table 1

Earth Parameters Used in Solutions.

6.378165

4118.0870

0.0220145 1

0.00059678

0.001 117 09

0.00000000

Epoch Oh AT

1959 February 19

21

23

25

27

March 1

3

5

7

9

11

13

megameters

degrees megameters 3/2 hour -

megameters*

megameters

megameters

megameters5

Table 2

Pr ime Minitrack and Baker-Nunn Orbits.

J.D.

2436618.5

6620.5

6622.5

6624.5

6626.5

6628.5

6630.5

6632.5

6634.5

6636.5

6638.5

6640.5

P M Orbit

603

604

605

606

607

608

6 09

610

611

612

6 13

614

BN Orbit

63 1

616

617

618

619

620

621

622

623

624

625

632

4

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c 0 c 0 C' c3 0 0 0 I> 0 0 1 1 1 1 1 1 1 1 1 1 1 1

. . . . . . . . . . . .

H Z z z z z z z T Z z z a m a m a m a m a m a m

24

Figure l a through lg-Si versus time for Prime Mini t rack Orbits.

25

I I I I

8.3228 i

1 I i I

8.3226 t 1 I I 1

8.3224 + I I I I

8.3222 +

I I

rn I 9) 1 8 8.3220 +

I I I I

8.3218 + I I I I

8.3216 t I I I I

8.3214 + I I I I

8.3212 + 1 I 1

*

3 - ; m

* *

*

*

1 I I I

1 I 1 I

1 I I I

I I 1 I

I I I I

I I 1 I

I I 1 1

1 I 1 I

I 1 I 1

I I I I

4

4

4

4

4

4

4

4

4

*

26

1 I I

~

~

, 0.16578

0.16576 4

I I I , I , 0.16574 t

I I I I

I I 0.16572 4 I I

1 I

I

I 0.165704

I I I I

0.16568 4 I I I I

0.16566 4

I 1 I I

0.16564 4 I I I 1

0.16562 4 I I I

*

*

*

*

* *

*

*

*

4 I I I I

I I I I

I I I I

1 I I I

I I I I

+

+

4 * I I I

I I I I

1 I I I

4

4

4

Figure 1 b-Values of Sz

27

I 32.8765 4

I I I I

32.8760 + I I 1 I

32.8755 4 I I 1 I

32.8750 +

I I

(1 1 1

32.8745 4 I 1 I I

32.8740 4

I I I I

32.8735 + I I I 1

32.8730 + I I I I

32.8725 + 1 I I I

1959 Feb..l7

rn

32.8720 +--

* *

*

*

* *

*

Figure lc-Values of S , (degrees)

28

1 1 I I

*

170.0 + I I I I

160.0 4

1 I I I

150.0 + 1 I 1 I

* 140.0t I I I

rn

1

130.0 + I I 1 1

120.0 + I I I I

110.0+

I

100.0 t--- 1959 Feb. 1'7

*

1

*

*

*

*

*

*

*

I 1 I I

I I I I

I I I 1

+

t

t

t

t

Figure Id-Values of S , (degrees)

29

.

260.0 4 I I I I

240.0 + I I I I

220.0 4

I 1 I I

I I 1 I

180.0 + 1 I I I

160.0 + I 1 1 I

140.0 + I I I I

120.0 + I I I

2 200.0 4

* *

*

* *

*

* I

I + I I 1 I

1 I I I

+

+

I +

+ 1 I I

Figure le-Values of S , (degrees)

30

*

*

*

*

I I I

100.0 t I I I I 1

50.0 + I I I I

*

* *

* *

I I I

I I 1 I I

I I 1 1

t

t

Figure If-Values of 56 (degrees)

31

I +O. 36 +

I I I 1

+O. 34 + 1 1 1 I

+O. 32 +

* * *

* *

1 $ +0.30+

1 1 I I

+0.28+ 1 I 1 I

+O. 26 + I I I I

+0.24 + 1 I I I

+0.22 + I I 1 I

+0.20 *- 1959 Feb.17

* *

* * *

I

I I I I

I I I I

1 I I I

1 I I I

I I I I

+

+

+

+

+

I 1 1 1

I I I I

1 1 I I

.------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ 19 21 23 25 27 Mar. 1 3 5 7 9 11 13

+

+

Figure 19-Values of S I B (degrees)

32

Figure 2a through 29--5, versus time for Baker-Nunn Orbits.

33

* *

*

* *

* *

* *

34

Figure 2a-Values of SI (megameters)

I I I I

0.16588+

0.16586; I I I I

0.16584 t I I 1 I

0.16582 + I I I I

0.16580t I I I I

0.16578 + I I I I

0.16576* 1 1 I I

0.16574 t I I 1 I

0.16572+ 1 I I

*

*

*

*

I I I I

I I I I

1 I I I

I 1 I I

I 1 I I

I I I I

I I I I

I 1 I I

I I I I

I I I

t

+

+

+

t

t

*

t

t

Figure 2b-Values of S2

35

I I I

32.8790 t I I I I

32.8780 + 1 I I I

* *

* *

*

*

*

*

*

* * I I

1 I 1 I

I 1 I I

+

+

+ 1 32.8770 +

I 1 I I I I I

m I I 1 1 I I I I

32.8750 4 + 1 I I 1 I I 1 I

32.8740 + + I I 1 I I I 1 I

32.8730 + + I I I * 1 I 1 I I

32.8720 +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------t-------+ 1959 Feb. 17 19 21 23 25 27 Mar. 1 3 5 7 9 11 13

o 32.8760 t +

Figure 2c-Values of S, (degrees)

36

.

180:O

110.0

I 160.0 +

I I I I

150.0 + 1 I I I

U; 140.0 + I I I I

130.0 + I I 1 I

I I I I

110.0 + I I I

120.0 t

.

*

*

*

*

*

*

*

*

*

+ ------- + I I I I

I I I 1

I I 1 I

I I I I

I 1 I I

I I 1 I

I I I I

I 1 I

t

+

+

+

*

Figure 2d-Values of S , (degrees)

37

I I 1 I

280.0 + I 1 I I

260.0 + 1 I I I

240.0 I I I I

220.0 + I I 1 I

200.0 + I I I I

180.0 + I I I I

160.0 + I I I I

140.0 + I I I 1

120.0 + I I I

* *

* *

* *

*

* *

* I

* 1 I 1 + I I

1959 Feb. 17 19 21 23 25 27 Mar. 1 3 5 7 9 11 13

I I

I I I I

I I I I

I I I I + I I I I

I I 1 I

I I I 1

+

+

Figure 2e-Values of S s (degrees)

38

.

I I I 1 I

350.0 + 1 I I 1 I

300.0 + I I 1 I 1

250.0 + I I 1 I I

r2 200.0 t 1 I 1 I I

150.0 + I I I I I

100.0 t I I I 1 I

50.0 t 1 I I I

*

*

*

* *

*

* I 1 I 1

1 I 1 I I

1 I I I I

I I I I I

I 1 1 I 1

I I I I I

I I * I I I

t

t

t

t

t

t

39

.

* * *

* I

*

*

* *

*

4040 t-------t-------+-------t------+---------t-------+-------t-------4-------t-------+------t-------+ 1 I I I

I I I I

1 1 1 I

+0.38* I I 1 I

+O. 36 + I 1 1 1

+O. 34 + I 1 1 1

+O. 32 t 1 1

m I 1

+O. 30 t I I 1 1

+0.28+ I I I I

+0.26+ 1 I I I

+O. 24 + I I I I

+0.22+ 1 I 1 I

+

+ * I I 1

I I I I

1 I I I

I I I 1

I I I I

I I I I

1 I I I

I I 1 I

19 21 23 25 27 Mar. 1 3 5 7 9 11 13

t

+

rn +

4

t

t

t

+0.2o,-------t-------+-------+-------t-------t-------t-------4-------4-------t-------4-------4-------4

1959 Feb. 17

Figure 29-Values of S,, (degrees)

*

40

Symbol

* 3 0

A5 0

I

M

R

a

e

k

k2

k4

A b

n .I

a

3

8

P

7

5,

cos 5 ' In

Appendix A

List o f Symbols

Meaning

Constant for earth's potential (megameters3)

Constant for earth's potential (megameters5)

Inclination of orbital plane to equator (degrees)

Mean anomaly

Earth equatorial radius (megameters)

Semimajor axis (megameters)

Eccentricity (non-dimensional)

Gravitational constant (degrees megameters 3'2 hour - I )

Constant for earth's potential (megameters 2,

Constant for earth's potential (megameters 4,

Residual in declination

Longitude of ascending node

Right ascension

Declination of point for which potential is considered

Declination

k * (degrees2 megameters hours -2)

Time in units of one-hundred hours

Argument of perigee

Residual in right ascension

NASA-Langley, 1966 G-628 41