L U N A R MISSIONS: L A U N C H T O R E N D E Z V O U S A . B . Mickelwait*
Space Technology L a b o r a t o r i e s , Inc. , Redondo Beach, Calif.
A B S T R A C T
This paper deals with the broad characteristics of manned lunar flight between launch and rendezvous. Some of the p r o b l e m s and characteristics of the p o s s i b l e flight modes that can be treated without a detailed systems design a r e discussed. The m a t e r i a l presented is intended to provide a general background for the nonspecialist b e f o r e detailed analysis of specific a r e a s is undertaken.
I N T R O D U C T I O N
The purpose of this paper is to s u m m a r i z e generally for the nonspecialist those characteristics of manned lunar flight in 1965 to 1970 which can be usefully discussed today.
Since the b r o a d operational region of the lunar mission f r o m launch to rendezvous is under consideration h e r e , only a relatively few p r o b l e m a r e a s can be treated in detail. It is hoped, nevertheless, that the r e a d e r w i l l gain an a p p r e c i a - tion for the magnitude of effort r e q u i r e d to succeed in the mission of manned lunar landing and at the s a m e time some insight into the a l r e a d y partially understood p r o b l e m a r e a s .
Because of the breadth of the p r o b l e m to be treated and the space limitations, a subjective bias has crept into the sampling of m a t e r i a l to be presented. This bias naturally emphasizes those p r o b l e m s most f a m i l i a r to the author, but it should not lead the r e a d e r to believe that these a r e either a complete list, an accurate evaluation, or even the most potentially troublesome. M o r e o v e r , to limit the m a t e r i a l further, the discussion has been artificially limited to mission p r o b l e m s between launch and rendezvous. The
P r e s e n t e d at the A R S Lunar Missions Meeting, Cleveland, Ohio, July 17-19, 1962.
A s s o c i a t e D i r e c t o r , Systems R e s e a r c h L a b o r a t o r y .
Α . Β. MICKELWAIT
Teader understands, of c o u r s e , that u l t i m a t e r e s o l u t i o n of these p r o b l e m s r e q u i r e s an a n a l y s i s of the m i s s i o n as a w h o l e .
G E N E R A L MISSION C H A R A C T E R I S T I C S
T o set the s t a g e for i n d i v i d u a l p r o b l e m s and m o r e s p e c i a l i z e d t r e a t m e n t s a p p e a r i n g in other p a p e r s , it is a p p r o p r i a t e to outline f i r s t the g e n e r a l flight plan f o r s o m e of the p o s s i b l e lunar flight m o d e s . A l t h o u g h N A S A has r e c e n t l y announced a d e c i s i o n in f a v o r of the lunar o r b i t r e n d e z v o u s m o d e , i t is n e v e r t h e l e s s t r u e that each of the lunar flight m o d e s has f e a t u r e s that w i l l m a k e it useful in manned or unmanned l o g i s t i c support r o l e s , lunar b a s e e s t a b l i s h m e n t , i n t e r p l a n e t a r y flight, e t c . It i s not w a s t e d e f f o r t , then, to understand the u n d e r l y i n g p r o b l e m s of each.
T h e flight m o d e s can b e d i v i d e d into D i r e c t F l i g h t ( D F ) , E a r t h O r b i t a l R e n d e z v o u s ( E O R ) , Lunar O r b i t R e n d e z v o u s ( L O R ) , and L u n a r S u r f a c e R e n d e z v o u s ( L S R ) ; a l s o , s o m e advantageous f e a t u r e s of each can be gained by h y b r i d c o m b i n a t i o n s of these m o d e s , such as E O R c o m b i n e d with L O R .
T h e d i r e c t flight m o d e , as the n a m e s u g g e s t s , launches the c o m p l e t e c o m m a n d m o d u l e , m a i n deboost, and r e t u r n p r o p e l l a n t into a coasting o r b i t , s a y 100 naut. m i l e s , c i r c u l a r f o r c o n v e n i e n c e , i n j e c t s the lunar v e h i c l e at the a p p r o p r i a t e point in the c o a s t i n g a r c , and m a k e s suitable m i d c o u r s e m a n e u v e r s to i n s u r e a r r i v a l at the m o o n w i t h a p p r o p r i a t e a c c u r a c y . In o r d e r to e a s e the demands on b o o s t e r s i z e i m p o s e d by the d i r e c t flight m o d e , t h r e e v a r i a t i o n s f r o m the d i r e c t flight using s m a l l e r launch v e h i c l e s have been p r o p o s e d . T h e lunar o r b i t r e n d e z v o u s m o d e is i d e n t i c a l to the d i r e c t flight m o d e until i n j e c t i o n into a lunar s a t e l l i t e o r b i t , when a l i g h t w e i g h t lunar
e x c u r s i o n m o d u l e is e j e c t e d , d e b o o s t e d to the lunar s u r f a c e , launched, and r e j o i n e d w i t h the p a r e n t c o m m a n d m o d u l e f o r
r e t u r n to E a r t h . T h u s , much of the equipment n e e d e d for E a r t h r e - e n t r y i s not b o o s t e d in and out of a l l the lunar potential w e l l . T h e E a r t h o r b i t r e n d e z v o u s m o d e launches two v e h i c l e s into near E a r t h o r b i t s , r e f u e l s the manned v e h i c l e , and p r o c e e d s as the d i r e c t flight m o d e . T h e lunar
s u r f a c e r e n d e z v o u s m o d e lands on the lunar s u r f a c e through a d i r e c t flight m o d e using unmanned v e h i c l e s i n i t i a l l y ,
r e f u e l s an unmanned r e t u r n v e h i c l e , lands a manned c o m m a n d m o d u l e near the r e f u e l e d and c h e c k e d - o u t r e t u r n craft, and f i n a l l y r e t u r n s the c r e w to E a r t h .
T R A J E C T O R Y C O N S I D E R A T I O N S
B e f o r e passing directly to the details of the different lunar modes, there a r e a number of systems considerations that can be approached within the f r a m e w o r k of trajectory selection. In general, there a r e two physical constraints on the choice of trajectory. The f i r s t relates to the geometrical properties and the second to the relative phasing of the moon and the vehicle, A lunar trajectory can be r e g a r d e d as a special case of direct rendezvous with a satellite in orbit.
But, since the lunar orbit plane does not pass through the launch site (i. e. , Cape C a n a v e r a l ) , it is i m p o s s i b l e to fly directly into a lunar transit trajectory that is coplanar with the lunar orbit without a relatively expensive dogleg maneuver.
The time of launch and launch azimuth therefore determine the phase angle in the orbit plane between launch site and lunar orbit. In addition, the phase angle and launch time must be selected such that the vehicle c r o s s e s the line of nodes of the vehicle plane and the lunar orbit plane at the same time the moon does. These conditions can generally be met, at least for a few days each month, by varying the launch azimuth. However, the allowable inclinations, or launch azimuths, a r e strongly limited to a rather n a r r o w band by range safety considerations, visibility f r o m telemetry and tracking sites, and the allowable dispersion of r e c o v e r y f o r c e s . If the total p o w e r e d a r c and the total coasting a r c after injection a r e fixed, then the a v a i l a b l e opportunities a r e limited to s e v e r a l days each month.
To i n c r e a s e the launch time on a given day and to i n c r e a s e the number of days in general for feasible lunar flights, a flexible coast a r c , or segment of satellite trajectory, is introduced into the p o w e r e d a r c . Then, by small variations in launch azimuth and rather l a r g e variations in the total coast angle, launch opportunities a r e available twice a day and, in general, on any day of the month. F i g . 1 shows the various central angles and associated great c i r c l e s projected on a M e r c a t o r projection, which shows the powered a r c and the flexible coasting a r c . The aximuths shown represent the usual limitations on a l l o w a b l e azimuths. Since Earth rotates underneath this pattern at a rate of 1/4 d e g / m i n , the launch opportunities with the l a r g e s t launch windows a r e obtained when lunar declination at encounter falls in the widest portion of the band illustrated. F o r example, for a positive lunar declination, injection should occur on the north to sourth leg of the coasting a r c and for a negative lunar declination injection should occur on a south to north leg.
Α . Β. M I C K E L W A I T
Since the band of launch azimuths i s n a r r o w and f i x e d , and s i n c e i n j e c t i o n takes p l a c e f r o m a c i r c u l a r c o a s t o r b i t , the only convenient r e m a i n i n g v a r i a b l e is the i n j e c t i o n e n e r g y o r , e q u i v a l e n t l y , the total t i m e of flight. A number of f a c t o r s i n f l u e n c e the c h o i c e of t i m e of flight, s o m e of w h i c h a r e the r e q u i r e m e n t f o r v i s i b i l i t y of k e y events f r o m c e r t a i n ground stations, the d e s i r e to m i n i m i z e the b o o s t e n e r g y e x p e n d i t u r e , and the d e s i r e to m i n i m i z e the deboost e n e r g y expenditure near the m o o n . T h e l a t e r two c o n s i d e r a t i o n s a l o n e would suggest the 9 0 - h r flight t i m e that is c l o s e to the m i n i m u m e n e r g y t r a n s i t t r a j e c t o r y . H o w e v e r , a c c u r a c y c o n s i d e r a t i o n s s u g g e s t f a s t e r t r a n s i t t i m e s , s i n c e , f o r m o s t guidance
s y s t e m s , the f a s t e r the t r a n s i t t r a j e c t o r y , the s m a l l e r the r e s u l t i n g d i s p e r s i o n s n e a r the m o o n f o r a g i v e n set of e r r o r s at i n j e c t i o n . F u r t h e r m o r e , the f a s t e r the t r a n s i t t r a j e c t o r y , the s m a l l e r the d i s p e r s i o n s after the l a s t m i d c o u r s e
c o r r e c t i o n . In addition, r e l i a b i l i t y and the w e i g h t of n e c e s s a r y l i f e support a r e i n c r e a s e d , and attitude c o n t r o l gas i s m i n i m i z e d on the f a s t e r t r a n s i t t r a j e c t o r y . T h e usually a c c e p t e d c o m p r o m i s e to t h e s e v a r i o u s f a c t o r s i s a t r a n s i t t r a j e c t o r y in the n e i g h b o r h o o d of 72 hr, w h i c h i s only about 100 fps a b o v e m i n i m u m e n e r g y .
When the r e q u i r e m e n t s in the v i c i n i t y of the m o o n a r e taken into account, t h e r e a r e further c o n s t r a i n t s on the t r a j e c t o r y . F o r e x a m p l e , i t m a y be d e s i r a b l e to have the m i s s i o n occur during c e r t a i n l i g h t i n g c o n d i t i o n s , s a y the beginning of a lunar day. A l s o , d i f f e r e n t landing s i t e
l o c a t i o n s w i l l r e q u i r e d i f f e r e n t a n g l e s b e t w e e n the a p p r o a c h h y p e r b o l a and the m o o n ' s o r b i t plane i f v e h i c l e plane
changes near the m o o n a r e to be m i n i m i z e d . Since p r o g r a m r e q u i r e m e n t s m a y m a k e i t d e s i r a b l e to i n i t i a t e the m i s s i o n during a p a r t i c u l a r band of m o n t h s , and at the s a m e t i m e to have a p a r t i c u l a r l i g h t i n g condition, s p e c i f i c t a i l o r i n g f o r a p a r t i c u l a r m i s s i o n p e r i o d during a g i v e n y e a r w i l l be r e q u i r e d . Without these p r o g r a m d e t a i l s , it i s not p o s s i b l e to m a k e g e n e r a l s t a t e m e n t s about e i t h e r the o p t i m u m r e l a t i v e p o s i t i o n of launch point and m o o n o r the p o s i t i o n of the m o o n in its o r b i t r e l a t i v e to its l i n e of n o d e s .
A s m e n t i o n e d e a r l i e r , an i m p o r t a n t shaping c o n s t r a i n t on the t r a j e c t o r y for manned flight is the d e s i r e f o r s u c c e s s - ful a b o r t and r e c o v e r y f r o m any s t a g e of the t r a j e c t o r y . It is d e s i r a b l e to have a b o r t c a p a b i l i t i e s at each phase in the t r a j e c t o r y with as l i t t l e p r o p u l s i v e r e q u i r e m e n t as p o s s i b l e and at the s a m e t i m e to hold the r e c o v e r y f o r c e to a m i n i m u m . E v e n f o r the c o a s t i n g t r a j e c t o r y b e f o r e i n s e r t i o n into the t r a n s i t t r a j e c t o r y to the m o o n , this dictates as n a r r o w a
band of azimuths as p o s s i b l e o r , conversely, as short a launch window as p o s s i b l e . M o r e o v e r , after insertion into the lunar transit trajectory, it is d e s i r a b l e to minimize the need for propulsion so that the trajectory is a ballistic c i r c u m - lunar trajectory that can return to some predictable r e c o v e r y site. Such a circumlunar trajectory implies that if no deboost is initiated near the moon the vehicle w i l l pass the moon and eventually return and r e - e n t e r at a d e s i r e d r e - e n t r y angle, velocity, and location. Such trajectories can be found which are consistent with the other constraints mentioned e a r l i e r , except for lunar landing site location. The f r e e return circumlunar trajectories have approach hyperbolas relative to the moon which a r e always within 10 inclination relative to the lunar equator. In this case, l a r g e plane changes a r e r e q u i r e d to land f r o m satellite orbits at northerly lunar latitudes. On the other hand, the noncircumlunar trajectory that returns with propulsion can be selected to have any inclination. Another class of abort trajectories that can be used with propulsion is obtained at any point along the lunar transit trajectory by firing towards Earth, along a r a d i a l direction, sufficient magnitude to obtain a m i r r o r image of the coasting trajectory. H o w e v e r , any discussion of abort capabilities is inadequate until a complete subsystems study is a v a i l a b l e which shows the likely characteristics of malfunctions that produce abort situations.
Another m a j o r system consideration intimately connected with trajectories is the launch window. This p r o b l e m is magnified for manned lunar flight, which, in g e n e r a l ,
r e q u i r e s l a r g e r launch windows than unmanned flights. It is generally felt that a launch window of at least 30 min. is required, and between 1 and 2 hr is d e s i r a b l e . A s has a l r e a d y been seen, this demands a v a r i a b l e launch azimuth and, to keep the launch azimuth variations as s m a l l as
p o s s i b l e , dictates the position of injection latitudes d e s c r i b e d e a r l i e r . F o r the m i s s i o n modes of lunar surface rendezvous, lunar orbit rendezvous, and direct flight, it is easy to obtain between 1 and 2 hr of launch window for a velocity penalty of 200 fps and an azimuth variation within r e a s o n a b l e limits, so that the p r o b l e m does not appear to be a s e v e r e one.
The E a r t h orbit rendezvous m i s s i o n is in a different category, however. H e r e two windows must be considered:
first, the window a v a i l a b l e for successful rendezvous in Earth orbit; and second, the window a v a i l a b l e for transit to the moon after rendezvous has been accomplished. A g a i n the condition for successful lunar flight is that the moon w i l l be passing through the line of nodes of the transit trajectory
Α . Β. MICKELWAIT
at the t i m e of lunar p a s s a g e . N o w , h o w e v e r , the plane of the c o a s t i n g t r a j e c t o r y has been p r e d e t e r m i n e d b y the i n i t i a l v e h i c l e launched unless plane changes a r e m a d e subsequent to this. T h e c o m b i n a t i o n of p r e c e s s i o n of the s a t e l l i t e o r b i t due to E a r t h o b l a t e n e s s of about 6. 6 d e g / d a y in a r e t r o g r a d e d i r e c t i o n and the o r b i t a l r a t e of the m o o n in its o r b i t of
1 3 - 1 / 2 d e g / d a y l e a d s to launch w i n d o w s a p p r o x i m a t e l y once e v e r y nine days ( 1 ) . T h e width of the w i n d o w at each opportunity depends on the a n g l e b e t w e e n the lunar o r b i t plane and the r e n d e z v o u s o r b i t plane at that p a r t i c u l a r t i m e . B y assuming that the n o m i n a l i n j e c t i o n opportunity o c c u r s when this a n g l e i s the s m a l l e s t , then f o r about 500-fps v e l o c i t y penalty f o r adjustments in the e s c a p e e n e r g y and s m a l l plane c h a n g e s , the launch window w i l l b e as much as 40 hr. T h e 4 0 - h r launch w i n d o w , of c o u r s e , a c t u a l l y c o n s i s t s of s m a l l e r i n t e r v a l s o c c u r r i n g o n c e each 9 0 - m i n . r e v o l u t i o n w i t h a duration of 2 to 3 m i n . each. T h u s , b e c a u s e of the p r o b l e m s of the r e n d e z v o u s m a n e u v e r , this w i d e
launch window a p p e a r s d e s i r a b l e . T h e l o n g t i m e b e t w e e n s u c c e s s i v e launch o p p o r t u n i t i e s , nine d a y s , i m p o s e s s o m e demands on the d e s i r a b l e launch r a t e and number of v e h i c l e s r e a d y f o r a g i v e n m i s s i o n . T o a v o i d the n i n e - d a y d e l a y w i t h the consequent p r o p e l l a n t s t o r a g e p r o b l e m s in o r b i t and p o s s i b l e need for c r e w r e t u r n to E a r t h , sufficient t i m e must be a l l o w e d so that s u c c e s s f u l r e n d e z v o u s has b e e n c o m p l e t e d w e l l b e f o r e the launch window opens. A d e s i r e to i n s u r e a successful c o m p l e t i o n of a m i s s i o n c y c l e f o r the n i n e - d a y w a i t m a y a l s o r e q u i r e that m o r e than one launch v e h i c l e b e r e a d y on the launch pad, both manned and unmanned.
T h e launch w i n d o w f o r r e n d e z v o u s in E a r t h o r b i t is m o r e c o m p l e x than that f o r e s c a p e f r o m E a r t h o r b i t to the m o o n , w h i c h has a l r e a d y been d i s c u s s e d . Fundamental g e o m e t r i c a l and d y n a m i c p r o b l e m s , as w e l l as o p e r a t i o n a l q u e s t i o n s , must be d e c i d e d s i m u l t a n e o u s l y . Since this m o d e has p r o b a b l y r e c e i v e d as much attention o r m o r e than the other m o d e s ( 1 , 2 ) , a l a r g e number of p o s s i b l e a p p r o a c h e s h a v e b e e n u n c o v e r e d w h i c h a r e difficult to c o v e r b r i e f l y . T h e t w o m o s t s u i t a b l e flight m o d e s a p p e a r to bQ f i r s t , a d i r e c t a p p r o a c h by the chasing v e h i c l e that i s launched on o r n e a r a Hohmann t r a n s f e r e l l i p s e at the p r o p e r t i m e to i n t e r c e p t the t a r g e t at the t a r g e t ' s o r b i t . T h e other m o d e of o p e r a t i o n i n v o l v e s a parking o r d r i f t o r b i t , in w h i c h the c h a s e r has f i r s t been put into a c o p l a n a r o r b i t not at the s a m e altitude as the t a r g e t and then w a i t s until the d i f f e r e n t i a l angular r a t e puts the
N u m b e r s in p a r e n t h e s e s i n d i c a t e R e f e r e n c e s at end of paper,
chasing vehicle into the p r o p e r position. Then the chase vehicle receives a second impulse that follows a near Hohmann transfer to the generally higher altitude orbit of the target w h e r e c i r c u l a r i t y is achieved and the rendezvous completed. The direct launch approach to E O R has been generally ruled out for manned flights, since it places m o r e stringent restrictions on available launch window. F o r example, 1 min of launch delay can r e q u i r e 250 fps additional velocity in order to meet a target in a 300-mile orbit. The drift target mode shown in F i g . 2 can be s u m m a r i z e d as follows: the target vehicle is first launched into a 300-naut- mile orbit; its ephemeris is determined accurately and supplied to a chase vehicle. The 300-naut-mile altitude is a c o m p r o m i s e between a d e s i r e for higher altitude for m o r e accurate ephemeris determination and a minimization of the drag fluctuation effects and the d e s i r e for l o w e r altitudes to avoid radiation damage. The chase vehicle is then launched into a l o w e r orbit, say 100 naut m i l e s , that is oriented with a time varying azimuth so that the chaser coast a r c in the
100 naut m i l e orbit is always 90 f r o m the launch site to the line of intersection of target and chaser planes (line of nodes).
The chaser orbit plane orientation which puts the launch position 90° back f r o m the line of notes is chosen to yield the minimum angle inclination between the chaser plane and the target for any launch delay. The chase vehicle after injection drifts until it reaches the line of nodes, when a correcting impulse produces coplanarity with the target orbit plane. The chaser then remains in the l o w e r orbit, say 100 naut m i l e s , until the relative phasing of the chaser and the target a r e appropriate. A t this time, the chase vehicle receives a second impulse to travel higher and coast on a near Hohman transfer a r c to the higher altitude orbit, w h e r e a rendezvous maneuver essentially c i r c u l a r i z e s the chaser orbit and brings the two vehicles together. If the target has been launched into a nearly due east trajectory and the chaser vehicle launched when the launch site is closest to the target plane, relatively s m a l l azimuth changes a r e r e q u i r e d to minimize inclination between the two planes.
For example, to make the two orbits coplanar, only about 190 fps is r e q u i r e d for a 2-hr launch window, and by this time the launch azimuth has been changed by about 16°.
If the chaser vehicle has been launched without consideration of the target angular position in its orbit, then the chaser may have to wait in its 100-mile c i r c u l a r orbit until it has gained one complete revolution, which, for the example here, is equivalent to 12 target revolutions or about 19 hr. If, on the other hand, r a n g e safety or r e s c u e considerations r e q u i r e that launch azimuths be fixed, a velocity penalty in excess of
Α . Β. M I C K E L W A I T
8000 fps f o r the s a m e t w o launch w i n d o w s w o u l d b e r e q u i r e d . C l e a r l y , then, t h e r e w i l l be a c o m p r o m i s e b e t w e e n s i z e of r e s c u e o p e r a t i o n and a l l o w a b l e p a y l o a d . A p o s s i b l e
a l t e r n a t i v e of o r b i t m o d e has the c h a s e r i n s e r t e d f i r s t into an e l l i p t i c a l o r b i t w i t h a p o g e e at the t a r g e t altitude. T h e plane change i s m a d e at a p o g e e of the parking o r b i t w h e r e r e l a t i v e l y s m a l l v e l o c i t y i n c r e m e n t s a r e r e q u i r e d . T h e c h a s e r drifts in this e l l i p t i c a l o r b i t , w h o s e a p o g e e i s c o i n c i d e n t w i t h the t a r g e t c i r c u l a r o r b i t . S i n c e i t has a d i f f e r e n t s e m i m a j o r a x i s and thus a d i f f e r e n t p e r i o d , the c h a s e r w i l l g r a d u a l l y c o m e into phase w i t h the t a r g e t . When the t a r g e t is n e a r i n g the p r o p e r phase w i t h the c h a s e v e h i c l e , a s e c o n d c o r r e c t i o n is m a d e at a p o g e e b y the
c h a s e r to change the s e m i m a j o r a x i s of the e l l i p t i c a l parking o r b i t so that on the next r e v o l u t i o n the t w o v e h i c l e s a r e w i t h i n r e n d e z v o u s d i s t a n c e . A t this t i m e , the r e n d e z v o u s m a n e u v e r i s c o m p l e t e d .
In addition to t r a j e c t o r y a l t e r n a t i v e s , t h e r e a r e a number of p o s s i b l e o p e r a t i o n a l v a r i a t i o n s . E i t h e r the manned v e h i c l e or the r e f u e l i n g v e h i c l e can b e launched f i r s t into
e i t h e r the high o r l o w o r b i t . Since it a p p e a r s d e s i r a b l e f o r the c r e w to spend the l e a s t p o s s i b l e t i m e in o r b i t , the manned v e h i c l e w i l l p r o b a b l y b e launched l a s t . F u r t h e r m o r e , it m a y be d e s i r a b l e f o r the higher o r b i t to be launched f i r s t , ânce its orbit w i l l be m o r e stable. I f the tanker is in the higher orbit and launched f i r s t and the chasing maneuver done with the manned v e h i c l e launched second at a l o w e r altitude, then the ephemer is determination of the tanker p r o v i d e s the n e c e s s a r y data for computing the t r a j e c t o r y to the m o o n on the ground. The data can then be stored in the chase v e h i c l e b e f o r e launch, thus easing the onboard computational p r o b l e m s that would o t h e r w i s e a r i s e .
G U I D A N C E C O N S I D E R A T I O N S Launch Guidance
_ _ _ _ _ _ _ \
So far in this discussion of t r a j e c t o r y considerations near Earth, a c c u r a c y r e q u i r e m e n t s at injection and the i m p l e m e n - tation n e c e s s a r y to a c h i e v e the r e q u i r e d a c c u r a c y have not been considered. F r o m a b r i e f look at t r a j e c t o r y c o n s i d e r a - tions, a w o r d can be said i m m e d i a t e l y about the type of launch guidance which w i l l probably be used f o r the lunar m i s s i o n (3). Since the injection point for a lunar m i s s i o n m o v e s quite w i d e l y o v e r E a r t h ' s surface, depending on the particular launch constraints, it would be highly d e s i r a b l e to have an i n e r t i a l guidance s y s t e m instead of a r a d i o , ground
b a s e d guidance system that would r e q u i r e a mobile shipboard guidance site to match the v a r i a b l e injection location.
Although a radio guidance system can, in principle, deliver higher a c c u r a c y at burnout than present state of the art a l l - i n e r t i a l s y s t e m s , inertial guidance systems within the state of the a r t a r e quite adequate for most mission
requirements ( 4 ) . Shown in F i g . 3 is the guidance dispersion that might be expected at the end of injection using an inertial guidance system of present day accuracy. A l s o shown in Fig. 3 a r e the effects of these dispersions near the moon.
The usual quantity used to m e a s u r e dispersion near the moon is the e r r o r in impact p a r a m e t e r , that i s , the e r r o r in the perpendicular distance f r o m the center of the moon to the asymptote of the approach hyperbola. The e r r o r s shown in F i g . 3 a r e obviously too l a r g e to meet system requirements and r e q u i r e subsequent correction at l a t e r points along the orbit. The final a c c u r a c y near the moon is therefore p r i m a r i l y a function of the accuracy with which these m i d c o u r s e corrections have been executed and, while the injection e r r o r s have no great effect on final accuracy, the m i d c o u r s e fuel requirements do depend upon the
magnitude of injection e r r o r .
Onboard computational p r o b l e m s for efficient launch guidance must be considered carefully in o r d e r to avoid excessively l a r g e computers in the vehicle. Since exact knowledge of a lunar trajectory r e q u i r e s solution of the complete three-body p r o b l e m , a p r e c i s e solution demands a computer far too l a r g e to be c a r r i e d on b o a r d a vehicle.
On the other hand, during the boost burning phase some solution must be obtained in r e a l time to guide the vehicle, and some approximation must be made to implement the guidance equations on board. T h e r e a r e two g e n e r a l approaches to guidance equation implementation (3, 5):
first, a l i n e a r expansion about some nominal t r a j e c t o r y with constants stored in the onboard computer; and second, an approach that simplifies the physical p r o b l e m in such a way that approximate solutions can be solved exactly in an onboard computer with results that match the m o r e complex r e a l w o r l d with sufficient precision. Both of the methods have been studied extensively and used on unmanned flights already. They appear to pose no peculiar implementation p r o b l e m s for future manned flights. Both of these
approaches allow the vehicles to move away f r o m a nominal trajectory as a result of dispersions and do not attempt to return the vehicle to the nominal path but essentially derive an alternate trajectory that is equally suitable for each instant along the flight path.
Α . Β. MICKELWAIT
T h e r e a r e other requirements on this guidance system which w i l l impose additional complexities. F i r s t , it should be capable of accepting additional intelligence after injection, such as ground-based tracking results f r o m doppler sites or interferometers; second, the system should be applicable to a multiplicity of missions and therefore must be inherently flexible; third, it may be d e s i r a b l e to c a r r y on additional p a r a m e t e r optimization rather than that d e s c r i b e d previously (for instance, the total propellant usage could be minimized);
and fourth, it might be d e s i r a b l e to have another inertial guidance system in the command module with identical inputs so that man may a s s i s t in the guidance of the final stage. This inertial guidance platform in the command module w i l l a l s o operate open loop during the ascent and after injection be operated as the p r i m a r y inertial guidance and attitude reference. If the two inertial guidance systems a r e to be s i m i l a r , there is c l e a r l y a much wider range of requirements imposed on this guidance system than is n o r m a l l y the case.
The Earth orbit rendezvous guidance r e q u i r e s some additional discussion. Subsequent to injection, which may be achieved with an inertial guidance system of the sort a l r e a d y described, it w i l l be n e c e s s a r y to have a m i d c o u r s e guidance during the drift phase and during the e a r l y portion of the acquisition phase when the chaser is transferring to the target orbit along the Hohmann transfer ellipse. T h e r e f o r e , it w i l l be n e c e s s a r y first to establish the ephemeris of the target by ground based tracking. This information should be stored in the chasing vehicle. Next, it w i l l probably be d e s i r a b l e to determine the ephemeris of the chasing vehicle f r o m ground b a s e d tracking for back-up purposes, at least, while the chasing vehicle is in the drift o r b i t . The results of this tracking should also be transmitted to the chasing
vehicle. It should be mentioned here that, if the orbit in question is low enough, drag fluctuations w i l l play an important r o l e in perturbing the trajectory after its ephemeris has been determined. F o r example, at
100 naut m i l e s , if the weight to drag ratio is of the o r d e r of 50 psf, the tracking should be continued up until about one half of an orbit before the time when position and velocity a r e being estimated. A s an example of present day state of the art, a M e r c u r y - t y p e network, tracking a 100-mile c i r c u l a r orbit for s e v e r a l hours, can reduce the position uncertainty to l e s s than 500 ft and velocity uncertainty to l e s s than 1 fps, which is m o r e than adequate for the r e q u i r e - ments at hand.
D r a g fluctuation, however, can produce orbit perturbations o r d e r s of magnitude l a r g e r than this ephemeris uncertainty and a r e therefore the essential limit to ephemeris accuracy.
M o r e must be understood about solar phenemena and its interaction with Earth's atmosphere in o r d e r to predict and reduce this source of e r r o r . Once acquisition between chaser and target has been achieved and a determination has been made that the time is appropriate for the Hohmann transfer of the l o w e r orbital vehicles to the higher, the m i d c o u r s e rendezvous guidance phase begins. A t the beginning of this midcourse phase, it is reasonable to expect positional e r r o r s of s e v e r a l miles and velocity e r r o r s ranging f r o m 5 fps along the trajectory to 15 fps in the out-of-plane direction. These e r r o r s a r i s e f r o m e r r o r s in the initial injection, guidance, g r o u n d - b a s e d ephemeris e r r o r s , and drag fluctuations.
The guidance during the transfer ellipse depends intimately on the mode of implementation. H o w e v e r , a proportional navigation approach that holds the line-of-sight rate to z e r o , thus maintaining a collision course between the two vehicles, has usually been assumed. Another approach is the s o - c a l l e d celestial mechanics method, which solves a set of equations of motion which, when followed, w i l l ultimately lead the chasing vehicle to the target not n e c e s s a r i l y with z e r o l i n e - of-sight rate.
When the chaser vehicle is in the vicinity of the target, the braking phase begins which in essence is a phase in which the energy of the chasing vehicle is i n c r e a s e d at apogee to
match the c i r c u l a r orbit of the target vehicle. The relative velocity at the end of the braking phase may be z e r o or may have some minimum value, depending on the type of docking chosen. The hard docking maneuver, w h e r e the two vehicles a r e joined (probably along the longitudinal axis for efficient energy absorption), r e q u i r e s a minimum velocity of the order of 1 fps and a m a x i m u m velocity p r o b a b l y l e s s than 3 fps.
The details of the docking mechanisms depend on the type of docking scheme chosen, such as modular transfer of fuel, transfer of men only (which is appropriate in the lunar orbit rendezvous c a s e ) , or t r a n s f e r of liquid propellants (as may be appropriate for the n e a r - E a r t h rendezvous). Any method w i l l have its peculiar p r o b l e m s for implementation. In any event, a detailed discussion of the m i d c o u r s e and braking phase of the rendezvous maneuver appears e l s e w h e r e . The implementation, however, is not beyond the state of the a r t
Α . Β. M I C K E L W A I T
of the p r e s e n t l o w thrust p r o p u l s i o n s y s t e m s , long r a n g e r a d a r s y s t e m s , i n e r t i a l p l a t f o r m s , and m e c h a n i c a l docking, l a t c h i n g , and fuel t r a n s f e r m e c h a n i s m s . It a l s o should be noted that the final docking m a n e u v e r can b e a u t o m a t i c , w h i c h is p r o b a b l y as s i m p l e and r e l i a b l e as w i t h a man in the l o o p . H o w e v e r , a r e c e n t study has shown that, g i v e n e s s e n t i a l l y the s a m e i n f o r m a t i o n as the automatic s y s t e m in a suitable d i s p l a y , p i l o t s in an E a r t h - b a s e d e n v i r o n m e n t had no
difficulty i n a c h i e v i n g the n e c e s s a r y s m a l l angular r a t e s and slow l i n e a r v e l o c i t i e s for successful docking o p e r a t i o n s . It r e m a i n s , of c o u r s e , to be s e e n w h e t h e r these o p e r a t i o n s can be s u c c e s s f u l l y c a r r i e d out under s p a c e e n v i r o n m e n t a l
conditions r a t h e r than l a b o r a t o r y c o n d i t i o n s . M i d c o u r s e Guidance
Since the usual i n j e c t i o n guidance e r r o r s a r e far too l a r g e f o r the r e q u i r e m e n t s of a manned lunar m i s s i o n , additional m i d c o u r s e c o r r e c t i v e m a n e u v e r s w i l l be r e q u i r e d subsequent to i n j e c t i o n . T h e c o r r e c t i v e m a n e u v e r s and t h e i r effect near the m o o n can be d i s c u s s e d in t e r m s of a c h i e v i n g the
a p p r o p r i a t e i m p a c t p a r a m e t e r p r e v i o u s l y d e f i n e d . A l t h o u g h , in t h e o r y , a s i n g l e v e l o c i t y i m p u l s e i s sufficient to r e m o v e a l l t w o - d i m e n s i o n a l e r r o r in the i m p a c t p a r a m e t e r n e a r the m o o n , it is difficult to i m p l e m e n t w i t h sufficient a c c u r a c y . T h i s a c c u r a c y of m i d c o u r s e c o r r e c t i o n m a y be i m p r o v e d by w a i t i n g until l a t e r along the t r a j e c t o r y . H o w e v e r , the s e n s i t i v i t y of the t r a j e c t o r y c o n v e r s e l y d e c r e a s e s w i t h t i m e along the t r a j e c t o r y so that m o r e fuel is r e q u i r e d . In o r d e r to m i n i m i z e fuel r e q u i r e m e n t s and maintain high a c c u r a c y , a c o m p r o m i s e of m u l t i p l e c o r r e c t i o n s at d i f f e r e n t t i m e s is r e q u i r e d . M o r e o v e r , at any instant of t i m e , t h e r e is an o p t i m u m d i r e c t i o n f o r f i r i n g this c o r r e c t i o n . If f i r i n g s a r e m a d e along this d i r e c t i o n , then the fuel r e q u i r e m e n t is m i n i m i z e d . It can be concluded i m m e d i a t e l y that numerous r e o r i e n t a t i o n s w i l l be r e q u i r e d f o r the n e c e s s a r y c o r r e c t i v e f i r i n g s after i n j e c t i o n . It is undoubtedly t r u e that the
m i s s i o n w i l l r e q u i r e both an automatic or E a r t h - b a s e d c a p a b i l i t y and a w h o l l y s e l f - c o n t a i n e d c a p a b i l i t y within the c o m m a n d m o d u l e . T h e E a r t h - b a s e d c a p a b i l i t y can b e obtained f r o m a t r a c k i n g n e t w o r k such as the D e e p Space I n s t r u m e n t a t i o n F a c i l i t y , which is p r e s e n t l y c a p a b l e of d e t e r m i n i n g a lunar t r a j e c t o r y w i t h a c c u r a c y as a function of t i m e shown in F i g . 4, When the e p h e m e r i s d e t e r m i n a t i o n a c c u r a c y i s s m a l l c o m p a r e d to the effect of r e s i d u a l e r r o r near the m o o n , b a l a n c e d by the d e s i r e to m i n i m i z e the fuel due to the d e c r e a s i n g s e n s i t i v i t y , the f i r s t m i d c o u r s e c o r r e c t i o n w i l l b e f i r e d . R e s i d u a l e r r o r s in the e p h e m e r i s
d e t e r m i n a t i o n and attitude c o n t r o l e r r o r s , as w e l l as e r r o r s in total i m p u l s e during the c o r r e c t i v e f i r i n g , w i l l r e q u i r e a second, and p r o b a b l y a t h i r d , c o r r e c t i o n . F o r e x a m p l e , an automatic s y s t e m w i t h two m i d c o u r s e c o r r e c t i o n s l e a v e s a r e s i d u a l e r r o r (99 I ο p r o b a b i l i t y ) after the s e c o n d f i r i n g of 6 naut m i l e s in i m p a c t p a r a m e t e r near the s u r f a c e of the m o o n . M o s t of this r e s i d u a l e r r o r is the r e s u l t of p r e s e n t - day u n c e r t a i n t i e s in the m a s s of E a r t h and the p r e c i s e l o c a t i o n of the t r a c k i n g stations r e l a t i v e to the c e n t e r of m a s s of E a r t h , both of w h i c h y i e l d e r r o r s in e p h e m e r i s d e t e r m i n a t i o n . T h e total fuel r e q u i r e m e n t f o r the t w o
m i d c o u r s e c o r r e c t i o n m a n e u v e r d e s c r i b e d h e r e i s 120 fps ( 3 σ ) . The v a l u e s quoted a r e c o n s i s t e n t w i t h the i n j e c t i o n e r r o r s d e s c r i b e d e a r l i e r and r e p r e s e n t the p r e s e n t - d a y state of the a r t .
The e a r l y phases of the lunar s u r f a c e r e n d e z v o u s flight m o d e , f o r e x a m p l e , would r e l y e n t i r e l y upon the automatic m o d e of o p e r a t i o n f o r the i n i t i a l flight and w o u l d p r o b a b l y r e q u i r e a t e r m i n a l m a n e u v e r near the s u r f a c e of the m o o n to land the unmanned v e h i c l e p r e c i s e l y . If the p o s i t i o n e r r o r is l a r g e near the t e r m i n a l p h a s e of the landing m a n e u v e r , the fuel r e q u i r e m e n t f o r t e r m i n a l m a n e u v e r s is a l s o l a r g e . H o w e v e r , as the v e h i c l e a p p r o a c h e s the lunar g r a v i t a t i o n a l f i e l d , the e p h e m e r i s d e t e r m i n a t i o n c a p a b i l i t y of an E a r t h - b a s e d t r a c k i n g s y s t e m i n c r e a s e s d r a m a t i c a l l y , so that within a r e l a t i v e l y s h o r t s p a c e of t i m e the e r r o r s r e s u l t i n g f r o m E a r t h constants and station l o c a t i o n u n c e r t a i n t i e s can be r e m o v e d w i t h a r e s i d u a l e r r o r of p e r h a p s t w o to t h r e e m i l e s . T h e fuel r e q u i r e m e n t s for the t e r m i n a l m a n e u v e r to land at a p r e c i s e l o c a t i o n on the lunar s u r f a c e can then be held to r e a s o n a b l e v a l u e s . A s m e n t i o n e d e a r l i e r , it is a l s o d e s i r a b l e to p r o v i d e a c o m p l e t e l y s e l f - s u f f i c i e n t , onboard c a p a b i l i t y f o r a c h i e v i n g the m i d c o u r s e c o r r e c t i o n ( 6 ) . A n i n t e g r a l p a r t of this c a p a b i l i t y i s the i n e r t i a l guidance p l a t f o r m in the c o m m a n d m o d u l e . T h e guidance c o m p u t e r w i l l a l s o p e r f o r m c o m p u t a t i o n s , s e q u e n c e s , and data p r o c e s s i n g . T h i s c o m p u t e r w i l l a l s o compute a b o r t and
e m e r g e n c y r e t u r n guidance data, d i s p l a y s , and c o m m a n d s throughout the flight.
A s p a c e sextant w i l l b e p r o v i d e d so that a n g l e data f o r s i g h t i n g s b e t w e e n E a r t h and the s t a r s and the m o o n can be obtained both m a n u a l l y and a u t o m a t i c a l l y f o r n a v i g a t i o n a l f i x e s . T h e s e s t a r - s i g h t i n g s w i l l b e used throughout to update p l a t f o r m attitude r e f e r e n c e p e r i o d i c a l l y . Although t h r e e independent angular f i x e s at one instant of t i m e uniquely fix the v e h i c l e ' s t r a j e c t o r y , i m p l e m e n t a t i o n e r r o r s m a k e it
Α . Β. MICKELWAIT
d e s i r a b l e to take a continuing s e q u e n c e of o b s e r v a t i o n s and c o m b i n e t h e m a c c o r d i n g to s o m e s t a t i s t i c a l p r o c e d u r e w i t h due r e f e r e n c e to d y n a m i c a l l a w s of m o t i o n . T h e e s s e n t i a l p r o b l e m , of c o u r s e , is to k e e p the computations w i t h i n c a p a b i l i t i e s of onboard c o m p u t e r s . A t the s a m e t i m e , the a p p r o x i m a t i o n s and s e n s o r e r r o r s should not s i g n i f i c a n t l y d e g r a d e final a c c u r a c y , l o w e r r e l i a b i l i t y by e x c e s s i v e m a n e u v e r i n g , or demand e x c e s s i v e fuel e x p e n d i t u r e .
In T a b l e 1 a r e shown s o m e r e p r e s e n t a t i v e p e r f o r m a n c e f i g u r e s for such a s y s t e m . P r e c i s e p r e d i c t i o n of performance a w a i t s , of c o u r s e , m o r e d e t a i l e d k n o w l e d g e of the i m p l e m e n - tation and r e l a t i v e p o s i t i o n of c e l e s t i a l b o d i e s f o r r e a l i s t i c launch d a t e s . It should b e noted that the number of r e - o r i e n - tation m a n e u v e r s r e q u i r e d f o r the onboard n a v i g a t i o n w i l l e s t a b l i s h c o n t r o l gas r e q u i r e m e n t s o v e r and a b o v e those f o r usual i n e r t i a l guidance. In s u m m a r y , then, e i t h e r a p p r o a c h a p p e a r s to p r o v i d e a c c e p t a b l y s a f e , e f f i c i e n t , and a c c u r a t e m i d c o u r s e guidance, w h i c h w i l l p r o v i d e the n e c e s s a r y i n j e c t i o n a c c u r a c y n e a r the m o o n f o r the subsequent lunar o r b i t or d i r e c t d e s c e n t .
O P E R A T I O N A L M O D E S D i r e c t F l i g h t M o d e
T o b e g i n the d i s c u s s i o n of o p e r a t i o n a l m o d e s , l o o k at the c o n c e p t u a l l y s t r a i g h t f o r w a r d d i r e c t flight m o d e shown in F i g . 5. In T a b l e 2 is shown a s i m p l i f i e d s e q u e n c e of events for this m o d e of o p e r a t i o n . None of the t i m e s and v e l o c i t i e s a r e p r e c i s e , but they i n d i c a t e the o r d e r of magnitude of these quantities. F r o m the v e l o c i t i e s i n d i c a t e d , w h i c h include g r a v i t y l o s s e s , d r a g , etc. ( 7 ) , it is c l e a r that the r e p r e s e n t a t i v e total v e l o c i t y r e q u i r e m e n t s to land on the lunar s u r f a c e is about 50, 000 fps. If d i f f e r i n g guidance
r e q u i r e m e n t s a r e i g n o r e d , the s a m e c h a r a c t e r i s t i c v e l o c i t y a p p l i e s to a l l flight m o d e s . T h e d i f f e r i n g b o o s t e r r e q u i r e - m e n t s , which w i l l b e d i s c u s s e d l a t e r , a r e brought about by d i f f e r i n g r e q u i r e m e n t s f o r equipment and p r o p u l s i o n
j e t t i s o n i n g . I f it is a s s u m e d that a w e i g h t of about 10,0001b i s to be r e t u r n e d to E a r t h , then the total launch w e i g h t r e q u i r e d is about 7 χ 10° l b f o r a l l m o d e s e x c e p t L O R . T h i s launch w e i g h t m a y be d i v i d e d into s m a l l e r v e h i c l e s by the L O S and L S R techniques.
Since the d i r e c t flight manned m i s s i o n uses no r e n d e z v o u s technique, it has the l a r g e s t e n e r g y r e q u i r e m e n t s f o r a s i n g l e b o o s t e r . T h i s m i s s i o n r e q u i r e s , t h e r e f o r e , a v e r y l a r g e b o o s t e r such as a N o v a w i t h 150, 000-lb i n j e c t i o n c a p a b i l i t y o r , if a s m a l l e r b o o s t e r such as the C - 5 w i t h an
injection capability of about 85, 000 lb ( 8 ) is used, a r e l a t i v e l y s m a l l command module of the o r d e r of 9 to
10, 000 lb and a pump fed H 2 / O 2 main deboost stage. Such a s m a l l module s i z e i m p l i e s a 10-day or shorter m i s s i o n , a constraint upon redundancy and hence r e l i a b i l i t y , perhaps a t w o - m a n c r e w as w e l l as the development of a new H 2 / O 2 main deboost stage, and even an H 2 / O 2 lunar take-off stage.
In g e n e r a l , then, the p r i n c i p a l p r o b l e m s of the d i r e c t flight m i s s i o n a r e the development of v e r y l a r g e booster or new high p e r f o r m a n c e stages and a reduced s i z e command module.
Lunar Orbit R e n d e z v o u s
The L O R flight sequence p r o c e e d s in somewhat the s a m e manner as the d i r e c t flight as shown in F i g . 6, except that there m a y be a r e q u i r e m e n t to change the position m e c h a n i - cally of the excursion module ( L E M ) f r o m its aft stowed position during boost to a f o r w a r d position p r i o r to execution of the f i r s t m i d c o u r s e c o r r e c t i o n at 3 hr to save abort
r o c k e t w e i g h t . This opens up the propulsion unit in the s e r v i c e module. A f t e r establishment of the 100-naut m i l e s c i r c u l a r lunar orbit, the t w o - m a n L E M separates and p r o c e e d s throughout the sequence of events d e s c r i b e d in T a b l e 3. N o t i c e that the L O R m o d e does not deboost the equipment n e c e s s a r y for Earth r e - e n t r y and other equipment not needed on the lunar surface so that, although the same ultimate v e l o c i t y of about 50, 000 fps to land is r e q u i r e d , a p r o p u l s i v e weight saving is p o s s i b l e .
It should be noted h e r e that the establishment of an
accurate c i r c u l a r orbit around the moon is n e c e s s a r y for the L O R mode and p l a c e s , t h e r e f o r e , m o r e stringent r e q u i r e - ments on the m i d c o u r s e a c c u r a c y p r i o r to establishment of this orbit. N o t i c e that a rendezvous maneuver of the type discussed below is r e q u i r e d but under m o r e stringent conditions. Since it is c o s t l y to deboost l a r g e amounts of fuel to the lunar surface needed l a t e r for plane changes, c o r r e c t i v e m a n e u v e r s , t e r m i n a l docking, etc. , to s a v e e n e r g y and insure r e l i a b i l i t y , s o m e of this capability in the command module ( C M ) is left in orbit. This in turn demands knowledge in the L E M of the C M e p h e m e r i s , knowledge of L E M landing site and nominal rendezvous t r a j e c t o r y in the C M , and appropriate rendezvous and docking radar and optical d e v i c e s in both. T h e s e r e q u i r e m e n t s , in turn,
necessitate certain duplication of DSIF v o i c e , t e l e m e t r y , and T V links, L E M - C M v o i c e links, and guidance and naviga- tion subsystems.
Α . Β. MICKELWAIT
L u n a r Surface R e n d e z v o u s
T h e lunar s u r f a c e r e n d e z v o u s m o d e has a flight s e q u e n c e , t i m i n g , and v e l o c i t y r e q u i r e m e n t s s i m i l a r to the d i r e c t flight m o d e f r o m launch to v i c i n i t y of the m o o n . T h e r e is one fundamental d i f f e r e n c e in the m o d e , h o w e v e r , s i n c e at l e a s t one of the flights is unmanned and must be E a r t h
c o n t r o l l e d . T h e L S R m o d e lands on the lunar s u r f a c e either a manned o r an unmanned C M and d r y s e r v i c e m o d u l e and c l o s e by a tanker m o d u l e . N o m a t t e r what b o o s t e r c a p a b i l i t y m i g h t e v e n t u a l l y be chosen f o r this m o d e , a k e y e l e m e n t would b e the r e m o t e r e f u e l i n g and checkout of the r e t u r n v e h i c l e b e f o r e man is c o m m i t t e d to the s y s t e m . R e f u e l i n g is done by T V c o n t r o l f r o m E a r t h , and subsequently the unmanned, r e f u e l e d , r e t u r n v e h i c l e i s r e m o t e l y c h e c k e d out b e f o r e c o m m i t t i n g the t h i r d ( o r fourth) flight containing the c r e w and enough fuel to land but not r e t u r n .
It can b e i m m e d i a t e l y noted that an obvious p r o b l e m a r e a is the c o m m u n i c a t i o n and s e n s o r r e q u i r e m e n t for this r e m o t e checkout o p e r a t i o n . A n o t h e r p r o b l e m a r e a is the r e m o t e r e f u e l i n g and l o n g - t e r m s t o r a g e o p e r a t i o n , w h i c h is subject to the unknowns of lunar dust, m e t e o r i t e d a m a g e , g r o s s s u r f a c e i n h o m o g e n e i t i e s , long t e r m v a c u u m c o n d i t i o n s , and w i d e t e m p e r a t u r e e x t r e m e s . P e r h a p s one of the m o s t
c r i t i c a l t e c h n i c a l a r e a s is the d e t e c t i o n of d a m a g e in the r e t u r n p r o p u l s i o n s y s t e m which m i g h t be e i t h e r s o l i d o r s t o r a b l e s .
T h e unmanned landing would p r o b a b l y be d i r e c t d e s c e n t guided e i t h e r w i t h a b e a c o n at a p r e - a r r a n g e d s i t e o r through a T V r e m o t e c o n t r o l l e d m o d e . E i t h e r med e could b e
a c h i e v e d with state of the a r t h a r d w a r e to -30 ft a c c u r a c y . T h e s e landing m o d e s a r e , in turn, suitable for m a n - i n - t h e - l o o p o p e r a t i o n on the manned flight so that a c o m p l e t e s i m u - l a t i o n of the manned landing would be a c h i e v e d p r i o r to c o m m i t t i n g man to the s y s t e m . Landing a c c u r a c y is c r i t i c a l in this m o d e , s i n c e v a g a r i e s of the lunar s u r f a c e p r o b a b l y r e q u i r e a fuel t r a n s f e r by b o o m d e p l o y m e n t w h i c h is only f e a s i b l e o v e r distances of 20 to 60 f t . F u r t h e r m o r e , l o n g - t e r m r e l i a b i l i t y (up to a month) i s c l e a r l y dictated by the r e q u i r e m e n t to c o m p l e t e at l e a s t t w o successful landings b e f o r e a r e t u r n i s a t t e m p t e d .
E a r t h O r b i t R e n d e z v o u s
T h e e a r l y p o r t i o n of the E a r t h o r b i t r e n d e z v o u s m o d e up to r e n d e z v o u s d e s e r v e s s p e c i a l attention, s i n c e i t d i f f e r s
m a r k e d l y f r o m the other t h r e e , although once the near
E a r t h r e n d e z v o u s has b e e n c o m p l e t e d , the m i s s i o n s e q u e n c e of events i s i d e n t i c a l to the d i r e c t flight m o d e d e s c r i b e d p r e v i o u s l y . T h e o p e r a t i o n a l s e q u e n c e up to r e n d e z v o u s m a y p r o c e e d as d e s c r i b e d in T a b l e 4.
In the s e q u e n c e g i v e n f o r E O R (shown in F i g . 2 ) , the tanker i s p a s s i v e until docking has b e e n c o m p l e t e d . T h e tanker i s p l a c e d at 300 naut m i l e s to f a c i l i t a t e ground t r a c k i n g v i s i b i l i t y and d e c r e a s e d r a g fluctuations ( t r a c k i n g l o c a t i o n a c c u r a c y after 1 day +1 naut m i l e at 300 naut m i l e s ) . A f t e r i t s e p h e m e r i s i s a c c u r a t e l y d e t e r m i n e d , the c o m p u t a - tion of E a r t h to m o o n t r a j e c t o r y and r e l a t e d guidance constants can be c a r r i e d out on E a r t h and i n s e r t e d in the manned c h a s e r v e h i c l e . Since the tanker is undisturbed during the r e n d e z v o u s m a n e u v e r , the final i n j e c t i o n can be b a s e d p u r e l y on t i m e and is independent, w i t h i n l i m i t s , of c h a s e r launch t i m e and b o o s t e r p e r f o r m a n c e . F u r t h e r m o r e , an a c c u r a t e p i c t u r e of the tanker o r b i t is contained in the c h a s e r b e f o r e c h a s e r launch.
A n e x a m i n a t i o n of the r e n d e z v o u s s e q u e n c e shows that this m o d e of o p e r a t i o n w i l l r e q u i r e l o w thrust o r b i t c o r r e c - tion p r o p u l s i o n , long l e a d t i m e attitude c o n t r o l , d o c k i n g - latching and e n e r g y a b s o r p t i o n s t r u c t u r e s , and r e f u e l i n g s u b s y s t e m s . A n o t h e r p o s s i b l y c r i t i c a l p r o b l e m i s r e a d i l y a p p a r e n t s i n c e , a c c o r d i n g to the s c h e d u l e i n T a b l e 4, the tanker m u s t spend at l e a s t 1 to 2 days in o r b i t b e f o r e m o d u l e or fuel t r a n s f e r . S i n c e Hz/Oz p r o p e l l a n t is p r o b a b l y
r e q u i r e d to a c h i e v e the n e c e s s a r y E a r t h e s c a p e w e i g h t s , this m o d e of o p e r a t i o n m a y p r e s e n t a p r o b l e m in l o n g - t e r m s t o r a g e of c r y o g e n i c p r o p e l l a n t s in a s p a c e e n v i r o n m e n t . T h i s p r o b l e m can b e s o l v e d , but when b o o s t e r r e l i a b i l i t i e s a r e c o n s i d e r e d and a high d e g r e e of c o n f i d e n c e in m i s s i o n s u c c e s s is r e q u i r e d , the l o g i s t i c p r o b l e m s of E O R a r e s i g n i f i c a n t .
A C K N O W L E D G M E N T
The author e x p r e s s e s g r a t i t u d e to H. A . L a s s e n , R . A . P a r k , and H. S B r a h a m f o r i n f o r m a l c o m m u n i c a t i o n and d i s c u s s i o n in the p r e p a r a t i o n of this p a p e r .
R E F E R E N C E S
1 Houbolt, J. C , " P r o b l e m s and p o t e n t i a l i t i e s of s p a c e r e n d e z v o u s , 11 I n t e r n a t i o n a l A s t r o n a u t i c a l F e d e r a t i o n
(June 1961. )
Α . Β. M I C K E L W A I T
2 H e i l f r o n , J. and Kaufman, F . Η. , " R e n d e z v o u s and docking techniques, 11 A R S P r e p r i n t 2460-62 (July 1962).
3 G e i s s l e r , C. D . , and H a e u s s e r m a n n , W . , "Saturn guidance and c o n t r o l , " A s t r o n a u t i c s 7 , 44 ( F e b r u a r y 1962).
4 G o r d o n , H. J. , " A study of i n j e c t i o n guidance accuracy as a p p l i e d to lunar and i n t e r p l a n e t a r y m i s s i o n s , " A R S
P r e p r i n t 1960-61 ( A u g u s t 1961).
5 S c h r o e d e r , W . and P i t t m a n , C . W . , " A guidance technique f o r i n t e r p l a n e t a r y and lunar v e h i c l e s , " Space T e c h n o l o g y L a b s . ( A u g u s t 1959).
6 Battin, R Η . , " A s t a t i s t i c a l o p t i m i z i n g n a v i g a t i o n p r o c e d u r e for space flight, " I n s t r u m e n t a t i o n L a b . , M a s s . Inst. T e c h . ( S e p t e m b e r 1961); r e v i s e d M a y 1962.
7 A m s t e r , W Η. , " L a u n c h v e h i c l e p e r f o r m a n c e , "
A R S P r e p r i n t 2457-62 (July 1962).
8 V o n Braun, W . , "Saturn and the future, " A s t r o n a u t i c s 7_, 22 ( F e b r u a r y 1962).
T a b l e 1 S u m m a r y of m i d c o u r s e p e r f o r m a n c e onboard n a v i g a t i o n
N u m b e r of sightings
M i d c o u r s e Δ ν
N u m b e r of m i d - c o u r s e c o r r e c t i o n s
F i n a l p o s i t i o n e r r o r , 9 9 ° / o
60 100 fps 5 10 naut m i l e s
T a b l e 2 D i r e c t launch m o d e
P h a s e Δ ν fps T i m e E v e n t
B o o s t to o r b i t 30, 000 0 to 12 m i n
E a r t h parking or oit
B o o s t to lunar 10, 600 i n j e c t i o n
C o a s t
T r a n s f e r c o m - munications to D S I F
C o a s t
M i d c o u r s e 250
0. 2 to 1. 9 hr
2 hr + 5 m i n
2. 0 to 2. 4 hr
2. 4 hr
Launch v e h i c l e liftoff at T=0, third s t a g e S - I V B shutdown at T = 1 2 m i n C o a s t to lunar i n j e c t i o n point in 100-naut m i l e c i r c u l a r o r b i t - - c o n d u c t onboard checkout
T h i r d s t a g e r e s t a r t and burnout injection 90, 00C lb to 150, 000 l b to m o o n on 72-hr t r a j e c t o r y C i s l u n a r coast; s p a c e - craft is a l i g n e d t o w a r d s the sun except f o r n a v i - gation sightings
When s p a c e c r a f t g e t s about 8000 naut m i l e s away f r o m E a r t h , c o m - munication link is D S I F 2. 4 to 3 hr C i s l u n a r c o a s t
3 hr 8 hr 23 hr 55 hr 65 hr
F i v e m i d c o u r s e c o r r e c t i o n s a r e m a d e - - t y p i c a l of M I T s y s t e m - - t i m e s a r e t y p i c a l e x a m p l e s
Coast 4 to 74 hr In b e t w e e n m i d c o u r s e c o r -
r e c t i o n s , cislunar coast
Α . Β. M I C K E L W A I T
T a b l e 2 D i r e c t launch m o d e (Cont'd)
P h a s e Δ ν fps T i m e E v e n t
A r r i v e lunar v i c i n i t y
74 hr A l l n a v i g a t i o n and
d i s p l a y s u b s y s t e m e q u i p - ment turned on and c h e c k - ed out
P e r i c y n t h i a n r e t r o
3200 75 hr +
170 sec
M a i n r e t r o f i r e s at h y p e r - b o l i c p e r i c y n t h i a n to inject s p a c e c r a f t into
100 naut m i l e c i r c u l a r lunar o r b i t
Lunar parking orbit and plane change
0 to 206
75. 1 to 78 hr
S p a c e c r a f t c o a s t s in o r b i t , adjusts o r b i t i n c l i n a t i o n to s e l e c t the landing s i t e
Hohmann deboost
450 78 hr +
18 sec
R e t r o into Hohmann e l l i p s e w i t h 50, 000-ft p e r i c y n t h i a n altitude. In v i c i n i t y of the landing s i t e , turn on landing r a d a r s C o a s t e l l i p s e 78 to 79 hr M o n i t o r a l t i m e t e r
Main r e t r o 6000 79 hr +
224 s e c
T u r n on landing T V ; f i r e m a i n r e t r o until s p a c e c r a f t d e s c e n d s to an altitude of
1000 ft, then j e t t i s o n the r e t r o
V e r n i e r 1500 79 hr +
224 to 342 sec
S e l e c t landing s i t e ,
t r a n s l a t e h o v e r , and land
T a b l e 3 Lunar o r b i t r e n d e z v o u s
P h a s e Δ ν fps T i m e E v e n t
( F o r t i m e <78 hr + 18 s e c , s e e T a b l e 2) L E M deboost 475
C o a s t e l l i p s e M a i n r e t r o
R e n d e z v o u s
6000
Lunar a s c e n t 6745
700
78 hr + 18 s e c . R e t r o into equal p e r i o d e l l i p s e w i t h 50, 000 ft p e r i c y n t h i o n altitude in v i c i n i t y of landing s i t e 78 to 78. 5 hr M o n i t o r a l t i m e t e r 78. 5 + 400 sec M a i n r e t r o at 50, 000 ft
102. 5 hr to 102. 6
104. 7 hr
M a i n r e t r o ( s a m e as d i r e c t flight m o d e ) L E M p o w e r e d a s c e n t to 50, 000 ft, Hohmann t r a n s f e r to 100-naut m i l e parking o r b i t
R e n d e z v o u s , and docking in 100-naut m i l e lunar parking o r b i t ; both L E M and c o m m a n d m o d u l e r e q u i r e d to have r e n d e z - vous and docking
c a p a b i l i t y .
Α . Β. MICKELWAIT
T a b l e 4 E a r t h o r b i t r e n d e z v o u s
P h a s e Δ ν fps T i m e Ev ent
T a n k e r launch 30, 000 Τ = 0
T a n k e r e p h e m e r i s determination
0 to 1 day
Launch of tanker in 300 naut m i l e c i r c u l a r o r b i t
E a r t h based e p h e m e r i s d e t e r m i n a t i o n and g u i d - ance constant i n s e r t i o n in manned c h a s e r v e h i c l e C h a s e r launch 30, 000 1 day
P l a n e change
Drift phase
180
C h a s e r launched into 100-naut m i l e o r b i t when launch point near tanker o r b i t plane
1 day + Ζ2 m i n P l a n e change by c h a s e r to a c h i e v e c o p l a n a r i t y at l i n e of nodes of tanker and chaser o r b i t
24 to 36 hr
B o o s t to tanker 200 24 hr o r b i t
T e r m i n a l r e n d e z - 24 hr + 40 vous 180 to to 50 m i n
300
Docking and fuel t r a n s f e r
C h a s e r d r i f t s until d i f f e r - ential drift r a t e a l l o w s c h a s e r to m a k e long r a n g e a c q u i s i t i o n of tanker
C h a s e r r e - i g n i t e s l a s t s t a g e and executes Hohmann t r a n s f e r to v i c i n i t y of tanker in
300-naut m i l e o r b i t
C h a s e r t e r m i n a l r a d a r and o p t i c a l s y s t e m s adjust to final c l o s i n g r a t e of 1 fps and p o s i t i o n e r r o r of 1 to
5 ft
S p a c e c r a f t a r e docked and l a t c h e d , e l e c t r i c a l and fueling connections m a d e , and p r o p e l l a n t t r a n s f e r r e d
Fig. 1 Injection conditions for Earth-moon transit trajectory
T A R G E T A T
C H A S E R D O C K I N G
ACQUISITION
F i g . 2 E a r t h o r b i t r e n d e z v o u s
γ
F i g . 3 99 U/ o e r r o r e l l i p s e s at the m o o n f r o m u n c o r r e c t e d launch guidance d i s p e r s i o n s ( m i l l i o n s of f e e t ) .
T y p i c a l i n j e c t i o n e r r o r s f o r p r e s e n t day i n e r t i a l guidance s y s t e m (72 hr E a r t h - m o o n t r a j e c t o r y ) a r e : v e l o c i t y magnitude, + 50 fps; v e l o c i t y e l e v a t i o n , + 0. 1 ° ; altitude, + 6 naut m i l e s ; and i n j e c t i o n l o c a t i o n , + 6 to 10 naut m i l e s
S I Z E O F DISPERSIONS DUE T O T R A C K I N G I F R O M I N J E C T I O N
I E L L I P S E A T M O O N ZRRORS VS T I M E
ASSI
\ S T /
\ A C C U R
J M E D Γ A N G U L A R A
? ° 3P F P^ SREC
C C U R A C Y - 0. 3 D E G C C U R A C Y ^
1.0
0.1
0.01
0. 00 20 40 T I M E F R O M I N J E C T I O N (HOURS)
60
F i g . 4 D i s p e r s i o n e l l i p s e at the m o o n as a function of t r a c k i n g t i m e
Fig. 5 Direct flight mission profile A. B. MICKELWAIT
Fig. 6 Lunar orbit rendezvous mission profile
