these these these these these this

THE USE OF THE EARTH-MOON LIBRATION POINTS AS TERMINALS FOR SPACE STATIONS

George A . E l l i s and Anthony C. Diana Rome A i r Development Center G r i f f i s s A i r Force B a s e , New York

A b s t r a c t

The motion of a space s t a t i o n i n the neighborhood of the Earth-Moon l i b r a t i o n p o i n t s should be analogous w i t h the motion of the a s t e r o i d s of the Trojan Group i n the S u n - J u p i t e r -

a s t e r o i d system.

Lagrangian s o l u t i o n s o f t h i s phenomena have been provided by s e v e r a l r e s e a r c h e r s by c o n f i n i n g t h e i r mathematical t r e a t ­ ment to an i d e a l i z e d problem, namely, the r e s t r i c t e d t h r e e - body c a s e . U n f o r t u n a t e l y , these s o l u t i o n s n e g l e c t the a c t u a l conditions p r e v a i l i n g i n our s o l a r system and, a t b e s t , can only be considered a s f i r s t approximations. I n f a c t , one must conclude that these p o i n t s have not been defined i n the r e a l sense but t h a t the d e f i n i t i o n i s d i c t a t e d by mathematical expediency. T h e r e f o r e , a study t o determine the f e a s i b i l i t y of p l a c i n g and maintaining space v e h i c l e s i n the neighborhood of these l i b r a t i o n p o i n t s has been undertaken which considers the r e a l i t i e s of Earth-Moon space such as oblateness of the e a r t h , e c c e n t r i c i t y of the moon^fs o r b i t , s o l a r p r e s s u r e s , e f f e c t of N - b o d i e s , e t c . Other f a c t o r s that have been c o n s i d ­ ered a r e v e h i c l e guidance to these r e g i o n s and the r e a c t i v e t h r u s t necessary to maintain a r t i f i c i a l s t a b i l i t y .

Plans have been formulated f o r the p l a c i n g of instrumented space packages w i t h i n these r e g i o n s to supplement the study and p r o v i d e the e s s e n t i a l data f o r f u t u r e space v e n t u r e s .

A p p l i c a t i o n s , m i l i t a r y and o t h e r w i s e , a r e a l s o d i s c u s s e d . Section I

LIBRATION POINTS I N EARTH-MOON SYSTEM AND REQUISITE VEHICLE GUIDANCE

George A . E l l i s A. I n t r o d u c t i o n

427

those f o r s p e c i a l cases of Lagrange and a r e known as the f i v e l i b r a t i o n c e n t e r s .

The l i b r a t i o n centers form a constant c o n f i g u r a t i o n i n r e l a t i o n t o the Earth and Moon. The constancy of t h i s c o n f i g ­ u r a t i o n , shown i n F i g u r e 1, e x i s t s only i n a r o t a t i n g coordinate system with o r i g i n a t the Earth-Moon b a r y c e n t e r . The d i f f e r e n t i a l equations of motion of the r e s t r i c t e d problem are shownin

F i g u r e 2. L e t μ denote the mass of one f i n i t e body, (ι-μ) the mass of the other f i n i t e body, t h e i r constant d i s t a n c e b e i n g one l u n a r u n i t and p i , p 2 the distance of the i n f i n i t e s i m a l mass from ΐ - / ν μ , , r e s p e c t i v e l y . I n the plane of motion of the two f i n i t e masses, there a r e f i v e p o i n t s d i s t i n g u i s h e d by the c h a r a c t e r i s t i c that ^^x = ^^y = ο . A n i n f i n i t e s i m a l mass placed a t one of these points with zero r e l a t i v e v e l o c i t y , χ = y = o , w i l l remain a t t h i s p o i n t .

An a n a l y t i c a l a n a l y s i s to determine the s t a b i l i t y of these l i b r a t i o n points i n v o l v e d a s o l u t i o n of the f i r s t approx­

imation to the d i f f e r e n t i a l equations ( v a r i a t i o n a l e q u a t i o n s ) . The method employed and the r e s u l t s , as shown by s e v e r a l a u t h o r s , i n d i c a t e that the e q u i l a t e r a l points a r e the most s t a b l e of the group. I f ξ, η and ξ⁹ ή represent a small displacement i n p o s i t i o n and v e l o c i t y of the i n f i n i t e s i m a l body, the g e n e r a l s o l u t i o n t o the v a r i a t i o n a l equations w i t h constant c o e f f i c i e n t s can be w r i t t e n i n the form

1 = 1 ι- ι

where Kt's a r e constants of i n t e g r a t i o n and Lî(Kî) - In the s t r a i g h t l i n e s o l u t i o n s , i t was found that the two roots (χι) of the b i q u a d r a t i c were r e a l , i n d i c a t i n g t h a t the i n i t i a l displacements w i l l i n c r e a s e without l i m i t w i t h time.

I f the constants of i n t e g r a t i o n K t , s a s s o c i a t e d w i t h these roots are zero the motion of the i n f i n i t e s i m a l body ( w i t h only imaginary r o o t s ) w i l l then be p e r i o d i c . C o r r e c t i v e methods of inducing a r t i f i c i a l s t a b i l i t y can be c o n s i d e r e d . I f λ/,8

a r e pure imaginary numbers, then ξ, η a r e e x p r e s s i b l e as p e r i o d i c functions and the s o l u t i o n i s s a i d to be s t a b l e . The e x i s t e n c e of unstable motion i n the v i c i n i t y of the e q u i l a t ­ e r a l points can be made p o s s i b l e w i t h the proper s e l e c t i o n of i n i t i a l c o n d i t i o n s . This was found to be true a t the e q u i l a t ­ e r a l p o i n t s , where

428

Figur e 1 . Earth-Moo n Lihratio n Points .

429

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7- l - ν ΐ " 2 7 μ ( 1 - μ ) M + V 1 - 2 7 μ ( 1 - μ )

2

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Note i t s dependence on the mass product.

Since μ « 1/82 f o r the earth-moon system, the motion i s s t a b l e and has two o s c i l l a t o r y modes w i t h p e r i o d s of 28.6 days and 91·7 d a y s .

Since the s t a b i l i t y c r i t e r i o n , a t l e a s t to a f i r s t approx­

imation, i s s a t i s f i e d a t the two e q u i l a t e r a l p o i n t s , a compre­

hensive i n v e s t i g a t i o n was made of the motion of the v e h i c l e when perturbed from i t s nominal p o s i t i o n and v e l o c i t y .

A numerical i n t e g r a t i o n of the exact d i f f e r e n t i a l equations of motion, shown i n F i g u r e 3* was performed on the Bendix D i f f e r ­ e n t i a l A n a l y z e r D-12. A domain of p o s i t i o n s and a domain of v e l o c i t i e s were determined such that i f the v e h i c l e i s assigned these boundary c o n d i t i o n s , the t r a j e c t o r y remains f o r a

s p e c i f i e d time i n t e r v a l w i t h i n a given minimum and maximum d i s t a n c e from the e q u i l a t e r a l p o i n t . S e v e r a l examples o f the r e s u l t a n t motion of a v e h i c l e a r e shown i n F i g u r e s 4, 5* and

The Lagrangian s o l u t i o n s have been i n v e s t i g a t e d by many a u t h o r s . The r e s u l t s obtained can, a t b e s t , be considered a s f i r s t approximations i n regard to space systems u t i l i z i n g these l i b r a t i o n p o i n t s .

A study has been i n i t i a t e d to determine the d e s c r i p t i o n of l i b r a t i o n p o i n t ( s ) or r e g i o n ( s ) i n the r e a l i s t i c Earth and Moon system, the v e h i c l e guidance t o and w i t h i n the r e g i o n ( s ) .

In the s p r i n g of 196l, two c l o u d l i k e o b j e c t s i n the v i c i n i t y of L5 climaxed a t e n - y e a r t e l e s c o p i c r e s e a r c h by a P o l i s h astronomer, D r . Kordylewski. The Smithsonian A s t r o - p h y s i c a l Observatory i s planning to make photographic o b s e r v a ­ t i o n s w i t h i t s network of Baker-Nunn t r a c k i n g cameras when the time i s r i g h t .

B. L i b r a t i o n Points i n an Ν-body Problem

When an attempt i s made to remove the l i m i t a t i o n s imposed by the r e s t r i c t e d three-body problem, the d i f f i c u l t i e s a r e encountered. A number of s t u d i e s e x i s t i n which the problem of more than three b o d i e s i s t r e a t e d . The imposed r e s t r i c t i o n s r e s u l t e d i n a c o n d i t i o n that d e v i a t e d too d r a s t i c a l l y from the a c t u a l conditions p r e v a i l i n g i n the s o l a r system. Hence, the s o l u t i o n s of the r e s t r i c t e d problem a r e not a p p r o p r i a t e f o r the p r e c i s i o n t r a j e c t o r i e s r e q u i r e d f o r the space systems.

451

/ \

ι- μ Figur e 4 . / *

434

BOUNDARY CONDITIONS: (AT t*0) 04 ( IN LUNAR UNITS ) W LUNAR ζ = 0 °·?- UNITS ^=+0.01 ς = ο / \ τ?=-Ο.ΟΙ / \

/ \

4?5

BOUNDARY CONDITIONS : ίΑτ t = 0) (IN LUNAR UNITS ) i-o ^ = 0.005 £ = 0.005 ζ=0 *?= 0.0075 £=0.0075

ζ=A = ê = ο

c = o

LUNAR UNITS EARTH Figure 6.

approaches r e a l i t y j Hence an a n a l y t i c a l and numerical a n a l y s i s i s b e i n g conducted to search f o r these points or r e g i o n s whose p r o p e r t i e s a r e s i m i l a r to the l i b r a t i o n p o i n t s discussed e a r l i e r . The procedure i s i l l u s t r a t e d i n F i g u r e ?.

This a n a l y s i s has e n t a i l e d an i n v e s t i g a t i o n of the p o s s i b l e methods of p r o v i d i n g boundary conditions f o r a r e a l i s t i c program. I n i t i a l l y , a p a r t i c u l a r s o l u t i o n of the r e s t r i c t e d three-body problem was used to p r o v i d e the boundary conditions f o r a s o l u t i o n r ( t ) of an ensemble p î , s a t i s f y i n g the condition

1 ^ ( 0

- ^ ( 0

conditions that provided a Lagrangian s o l u t i o n of the l e a d i n g t r i a n g u l a r point ( ) were used i n a model that represented the e a r t h¹s o b l a t e n e s s , the e c c e n t r i c i t y of the moon¹s o r b i t , the sun, Mars, Venus and J u p i t e r . The i n i t i a l c o n f i g u r a t i o n of these bodies corresponds to 6 Oct I960. For 60 d a y s , the motion of the v e h i c l e r e l a t i v e to L / j , , ( i l l u s t r a t e d i n F i g u r e 9) was confined to a sphere of r a d i u s kO χ 1θ3 m i l e s . A d d i t i o n a l a n a l y s i s i n d i c a t e d that the problem can be t r e a t e d as a f o u r - body ( s u n - e a r t h - m o o n - v e h i c l e ) problem without a p p r e c i a b l e degradation i n p r e c i s i o n . I n F i g u r e 10, the motion of a v e h i c l e , r e l a t i v e to L ^ , f o r 180 days i s shown. Hence the concept of the l i b r a t i o n p o i n t s i s non-existent i n t h i s p a r t i c u l a r model. I l l u s t r a t i o n of a very p r e l i m i n a r y a n a l y s i s g i v e s an example of what may be expected. Should the i n v e s t i ­ g a t i o n r e v e a l e x i s t e n c e of r e g i o n s w i t h the d e s i r e d p r o p e r t i e s , the s t a b i l i t y of motion w i l l be c o n s i d e r e d .

C. S t a b i l i t y of Motion

An i n v e s t i g a t i o n of the p o s s i b l e methods of p r o v i d i n g boundary conditions of p e r i o d i c s o l u t i o n s about these l i b r a t i o n points f o r the r e a l i s t i c Earth and Moon space has been conducted.

The study of s t a b i l i t y of motions i s an extremely complicated problem. P r i o r to f u r t h e r d i s c u s s i o n s , the d e f i n i t i o n of s t a b i l i t y i s r e q u i r e d . Hence the motion of a v e h i c l e i n the neighborhood of a l i b r a t i o n point i s s t a b l e i f i t moves i n a r e g i o n bound by s p e c i f i e d minimum and maximum d i s t a n c e s from the point f o r a s p e c i f i e d l e n g t h of time.

This a n a l y s i s would r e q u i r e the numerical computation of s p e c i f i c o r b i t s . However, t h i s may cause s e r i o u s d i f f i c u l t i e s . I f the computation proceeds long enough, round-off and t r u n c a ­ t i o n e r r o r s become a p p r e c i a b l e and when i n s t a b i l i t y i s

4J6

MATHEMATICAL MODEL

INITIAL CONDITIONS IMPROVE MODEL STOP

COMPUTER PROGRAM SOLUTION T(t) DOES V REMAIN IN REGION THAT IS FIXED RELATIVE TO THE EARTH-MOON SYSTEM ?

Figur e 7 · Procedur e fo r Determinin g Fixe d Regio n in Actua l Earth-Moo n System .

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Figur e 9 . Motio n o f a Vehicl e Abou t Leadin g Lagrangia n Poin t , wit h o n a Rigi d Equilatera l Triangl e Rotatin g Abou t th e Earth , wit h th e Angula r Velocit y [ ω (t) ] o f th e Moon .

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Figur e 10 . Motio n o f Vehicl e W.B.T . Lagrangia n Libratio n Point , (S,E,M t = 7/9/63 ^ Mea n Moon , Apoge e Earth .

i n d i c a t e d , one may not be sure of the r e a l cause. The motion may be u n s t a b l e i f the computational e r r o r s could mask the r e a l motion.

To avoid t h i s d i f f i c u l t y , an a n a l y t i c a l c r i t e r i o n of s t a b i l i t y dependent on the d i f f e r e n t i a l equations of motions w i l l have to be used. Since i t i s p o s s i b l e t o produce s e v e r a l c r i t e r i a of s t a b i l i t y a n a l y t i c a l l y , another dilemma i s

encountered. I n an a n a l y s i s of t h i s t y p e , i t i s customary t o l i n e a r i z e the problem. The procedure i s to d i s p l a c e the body from e q u i l i b r i u m by a small amount and expand the d i f f e r ­ e n t i a l equations of motion i n t o a power s e r i e s . The v a r i a t i o n a l equations a r e then s o l v e d . This type of a n a l y s i s showed that the p a r t i c u l a r s o l u t i o n s of the problem of three b o d i e s a r e u n s t a b l e f o r the c o l i n e a r and s t a b l e f o r the e q u i l a t e r a l l i b r a t i o n p o i n t s . The e f f e c t of higher o r d e r terms, which has been n e g l e c t e d , may be of g r e a t importance. Hence approximate a n a l y s i s p r o v i d e s an u n s a t i s f a c t o r y answer t o the s t a b i l i t y q u e s t i o n . A more g e n e r a l c r i t e r i o n of the s t a b i l i t y of motion must be c o n s i d e r e d , i . e . , L y a p u n o v , Jacobi-Stephanov and

Zhukovskey.

Summarized in the preceding d i s c u s s i o n a r e the f i n d i n g of l i b r a t i o n r e g i o n s , w i t h the d e s i r e d p r o p e r t i e s , i n an

N-body problem, and the s t a b i l i t y of motion of a v e h i c l e w i t h i n these r e g i o n s .

D. N o n g r a v i t a t i o n a l E f f e c t s

The s t a b i l i t y of motion on the neighborhood of the l i b r a t i o n r e g i o n s w i l l be influenced by the prescence of non- g r a v i t a t i o n a l e f f e c t s . Dust and meteoroids a r e considered as a r e s i s t i n g media r e s u l t i n g i n e f f e c t i v e drag on the v e h i c l e . Hence the d i f f e r e n t i a l equations of motion must be augmented by an a p p r o p r i a t e term. S i n c e , then, the nonconservative nature of the a d d i t i o n a l f o r c e s prevents the e x i s t e n c e of c l o s e d i n t e r v a l s f o r q u a l i t a t i v e r e s u l t s .

The e f f e c t of r a d i a t i o n p r e s s u r e corresponds t o a r e p u l s i v e f o r c e i n the equations of motion. Attempts t o i n v e s t i g a t e

t h i s problem under a very r e s t r i c t e d set of conditions i n d i c a t e that there e x i s t seven l i b r a t i o n p o i n t s . The two a d d i t i o n a l p o i n t s occur outside the plane of motion of the main masses.

E. E f f e c t of the Mass of the V e h i c l e

An e s s e n t i a l assumption of the r e s t r i c t e d three-body problem i s that the t h i r d body i s i n f i n i t e s i m a l . When t h i s r e s t r i c t i o n i s r e l a x e d , the problem w i l l become even more

" r e s t r i c t e d . " The only known s o l u t i o n s a r e embraced i n the theorem of Lagrange which s t a t e s that i t i s p o s s i b l e to s t a r t three f i n i t e b o d i e s i n such a manner that the o r b i t s w i l l be s i m i l a r e l l i p s e s . Hence, the r a t i o s of the mutual d i s t a n c e s of the b o d i e s a r e constant.

441

l i b r a t i o n r e g i o n ( s ) i s dependent on the c h a r a c t e r i s t i c of the powered t r a j e c t o r y of the a v a i l a b l e v e h i c l e . Despite the lack of information a t the present time, the g e n e r a l methods

presented a r e a p p l i c a b l e i n t h i s study.

1. T r a n s f e r t r a j e c t o r y to the L i b r a t i o n Region

Since the conditions r e q u i r e d to s p e c i f y the mission (launch l o c a t i o n , launch time, i n j e c t i o n p o i n t ) a r e needed to d e f i n e the launch zone (mission time, a r r i v a l p o i n t near the l i b r a t i o n r e g i o n ) , an optimum t r a j e c t o r y can be e s t a b l i s h e d when these parameters a r e s e l e c t e d . To s a t i s f y s p e c i f i c boundary conditions a t the l i b r a t i o n r e g i o n ( s ) , the i n i t i a l conditions r e q u i r e d w i t h i n the i n j e c t i o n zone are subjected t o p e r m i s s i b l e e r r o r s . Hence the accuracy of the i n j e c t i o n conditions i s determined by an e r r o r d i s t r i b u t i o n l a w , and t h e i r e f f e c t s on the d e s i g n t r a j e c t o r y a r e estimated by a maximum likehood method o r one of i t s m o d i f i c a t i o n s . A p e r m i s s i b l e e r r o r tube w i l l be g e n e r a t e d , and enroute guidance w i l l be i n d i c a t e d i f the probable e r r o r s i n p o s i t i o n and v e l o c i t y of the v e h i c l e exceed those q u a n t i t i e s defined by the p e r m i s s i b l e e r r o r t u b e . This s i t u a t i o n may occur i f the r e q u i r e d boundary conditions a t the l i b r a t i o n r e g i o n ( s ) impose severe t o l e r a n c e s on the i n j e c t i o n c o n d i t i o n s , and the l a c k of knowledge of p h y s i c a l constants e n t e r i n g i n t o the problem may introduce unavoidable e r r o r s .

2. T r a n s f e r i n t o an O r b i t w i t h i n a L i b r a t i o n Region Having f o l l o w e d an optimum d e s i g n t r a j e c t o r y , the v e h i c l e a r r i v e s a t the proper point and w i t h the proper v e l o c i t y near the l i b r a t i o n r e g i o n . Because of input e r r o r s t o the t r a n s f e r t r a j e c t o r y , a t the time of the t r a n s f e r i n t o a l i b r a t i o n o r b i t , the p o s i t i o n and v e l o c i t y w i l l be d e f i n e d w i t h i n a c e r t a i n p r o b a b l e e r r o r . Since t h i s operation p l a c e s the v e h i c l e w i t h conditions which d e v i a t e from the d e s i g n o r b i t , an " e r r o r " doughnut i s generated about the d e s i g n o r b i t . Whenever the e r r o r s exceed those s p e c i f i e d by the p e r m i s s i b l e e r r o r t u b e , subsequent guidance and c o r r e c t i v e maneuvers w i l l be r e q u i r e d . I f the motion i n the r e g i o n of i n t e r e s t i s n a t u r a l l y u n s t a b l e , the amount of energy, i n the form of t h r u s t , r e q u i r e d t o maintain the v e h i c l e i n t h i s r e g i o n w i l l be determined i n s p e c i f i c c a s e s .

G. Equations of Motion

An N-body t r a j e c t o r y program has been designed to

442

numerically i n t e g r a t e the d i f f e r e n t i a l equations d e s c r i b i n g the motion of a v e h i c l e i n space. Some of the g e n e r a l f e a t u r e s of the program a r e an enhemerides of the p l a n e t s and moon,

freedom i n the s e l e c t i o n of an i n t e g r a t i o n i n t e r v a l in the Runge- K u t t a - G i l l numerical i n t e g r a t i o n method, and the f l e x i b i l i t y i n the use of both Cowell and Encke schemes. The motion of the v e h i c l e of mass "m" r e f e r r e d to a coordinate system centered a t mass can be d e s c r i b e d by

+ I d Φ/ d xⁿ

i = 1 ⁿ

where R^mK # R{k fa^s Ί 2^{/ M},^;i V^lt^ k ) a r e the p o s i t i o n v e c t o r s of m and Mi with respect to Mk; φ i s the g r a v i t a t i o n a l p o t e n t i a l of the o b l a t e n e s s of the o b l a t e s p h e r o i d a l e a r t h of nonuniform d e n s i t y and X ⁿ, ^s a r e the coordinates of the r e f e r e n c e system.

Upon completion of a s u c c e s s f u l study, the information w i l l be supplemented with experimental data to provide a v a l i d and comprehensive a n a l y s i s .

Section I I

LIBRATION POINT SPACE PROBES AND SYSTEMS Anthony C. Diana

A . P o s s i b l e Missions and V e h i c l e s

A t h e o r e t i c a l i n v e s t i g a t i o n of the s t a b i l i t y of the l i b r a t i o n p o i n t s i n our Earth-Moon space cannot be accented as theonly source f o r v a l i d a t i o n of the theory. An experimental probe or probes must be placed i n the v i c i n i t y of a l i b r a t i o n point t o p r o v i d e a d d i t i o n a l proof f o r the acceptance of the theory. F i g u r e 1 shows the r e l a t i v e p o s i t i o n s of e a r t h , moon, and l i b r a t i o n P o i n t s .

1, A f i r s t space probe of t h i s type may have d i f f e r e n t missions. The f i r s t type of mission would be a combination of s t u d i e s , w i t h almost equal emphasis placed on environmental c h a r a c t e r i s t i c s and o r b i t a l measurements.

The environmental c h a r a c t e r i s t i c s measured would c o n s i s t p r i m a r i l y of: ( l ) r a d i a t i o n measurements to determine the r e l a t i v e abundance of the d i f f e r e n t s p e c i e s of charged p a r t i c l e s and to i n d i c a t e t h e i r energy d i s t r i b u t i o n , ( 2 )

magnetic f i e l d measurements t o determine magnitude and d i r e c t i o n of magnetic f i e l d s , and ( 3 ) microraeteorite measurements t o determine times and extent of impact of micrometeorites. A l l

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i n the payload w i l l permit two-way communication. The pay- load t r a n s m i t t e r s w i l l transmit telemetry information t o the e a r t h and a h i g h - s e n s i t i v i t y r e c e i v e r i n the payload w i l l permit the r e c e p t i o n of e a r t h - t r a n s m i t t e d commands. P o s s i b l e a d d i t i o n a l instrumentation may provide range r a t e information to h e l p determine the o r b i t a l mechanics of the v e h i c l e f o r t r a c k i n g . This g e n e r a l purpose payload w i l l provide information d i r e c t l y to some c e n t r a l data processing unit on both e n v i r o n ­ mental c h a r a c t e r i s t i c s and o r i i t a l mechanics.

Many v e h i c l e s can be designed to meet the requirements f o r the f i r s t mission. P o s s i b l y f o r economical r e a s o n s , a v e h i c l e which has been d e s i g n e d , b u i l t and launched should be chosen f o r t h i s m i s s i o n . Many v e h i c l e s can be considered i n t h i s c l a s s , but f o r the purpose of t h i s p a p e r , the Pioneer V payload w i l l be the only space v e h i c l e which w i l l be d i s c u s s e d , a l t h o u g h , other v e h i c l e s such as Pioneer IV and E x p l o r e r V I can, w i t h s l i g h t m o d i f i c a t i o n , meet the requirements of t h i s mission.

Although Pioneer Vfs mission was very much d i f f e r e n t than the proposed l i b r a t i o n p o i n t m i s s i o n , i t s payload can r e a d i l y be adopted to meet the requirements.

Pioneer V i s a 26 diameter sphere weighing 94.8 l b s . The instrumentation c o n s i s t s of sensing and measuring equipment f o r environmental experiments, the t e l e b i t u n i t , a doppler transponder c o n s i s t i n g of a command r e c e i v e r and t r a n s m i t t e r , a s o l a r c e l l power conversion system i n c l u d i n g s t o r a g e b a t t e r i e s and converter c i r c u i t r y , and a s s o c i a t e d l o g i c . The 150 watt t r a n s m i t t e r that e x i s t e d i n Pioneer V i s not needed i n a

" L i b r a t i o n Point Probe" because the d i s t a n c e r e q u i r e d to transmit w i l l not be as g r e a t the d i s t a n c e a t which Pioneer V had to t r a n s m i t . This space on the payload could accommodate a d d i t i o n a l instrumentation f o r environmental measurements, such as cosmic and s o l a r r a d i a t i o n . Primary measurements f o r Pioneer V were:

r a d i a t i o n , magnetic f i e l d s and micrometeorite d e n s i t y . One can r e a d i l y see how t h i s payload could f i t the mission r e q u i r e ­ ments f o r a L i b r a t i o n Point p a y l o a d . Pioneer V had transmitting and r e c e i v i n g equipment which conveyed telemetry information to the e a r t h and r e c e i v e d commands from the e a r t h to perform v a r i o u s f u n c t i o n s . When interconnected c o h e r e n t l y , the Pioneer V t r a n s m i t t e r and r e c e i v e d formed a transponder c a p a b l e of p r o v i d i n g range and range r a t e information f o r t r a c k i n g the p a y l o a d .

The b a s i c Pioneer V instrumentation seemed to meet the requirements of the f i r s t type of mission f o r a L i b r a t i o n Point

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probe, which was the acquiring of both orbital and environmental information. Modifications are necessary but should not

encompass as many d i f f i c u l t i e s as the designing, building and packaging of an entirely new payload.

2. A second type of mission would constitute placing main emphasis on orbital information alone. This type of space probe is entirely dependent upon the a v a i l a b i l i t y of ground tracking and observing stations. Also, any use of observations and optical equipment is directly dependent upon the size of the payload. The basic payload for this mission should be large enough for optical detection and should contain trans­

mitters which w i l l permit the radar ground tracking net to detect i t .

From this type of combined ground tracking net, orbital mechanics of a more refined nature might be obtained, but the consequences w i l l be the sacrificing of environmental character­

i s t i c s measurements and an additional increase in payload weight.

When selecting a vehicle to perform this type of mission, emphasis must be placed on either the size of the vehicle or some type of flashing beacon, in order to insure detection by observatories.

As soon as the trajectory and guidance requirements for the mission are known as accurately as possible, then a final analysis w i l l be made to determine what constitutes an adequate booster for a specific mission.

B. Applications of Libration Points Stations

I f stability of the libration points i s established through the theoretical investigations and experimental probes mentioned, then military applications of these points can be considered. The libration points could be used in some overall cislunar communications system. These communications stations could relay information from the far side of the moon to earth, from s a t e l l i t e to s a t e l l i t e and from s a t e l l i t e to earth, thus providing instantaneous communications links. Figure 1.

The establishment of an extremely long base line system to provide guidance for cislunar and translunar military vehicles could be considered. Strategic surveillance systems providing thorough coverage of t e r r e s t r i a l , lunar and cislunar space could be initiated, utilizing the libration points.

Although many applications of the libration points can be considered and in much greater d e t a i l , this brief points out only a few of their potentialities.

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