n.:.:.:.:.:.:.:.:.:.:. ;;;e- - ibibliothe lm ascent and rendezvous profiles are being continually...

. . . . . . . ........... ............ ........... ............ .......... ............ ....... , ... N.:.:.:.:.:.:.:.:.:.:. ............ ........... .......... ............ ........... ............ ........... ;;;e- ...........

- 1 &4 a - c

al

b

.. N A T I O N A L AERONAUTICS A N D SPACE A D M I N I S T R A T I O N .. ..... ............ ........... p ....................... ............ ........... ............ ........... MSC INTERNAL NOTE NO. 69-FM-39 -+ ....................... ............ ........... ............ ........... ............ ........... ............ ........... ............ .......................

........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... February 19, 1969 ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ Y .:.:.:.:.:.:.:.:.:.:.:. w - J 'c

9

............ ........... ....................... y ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ............ ........... ........... PRELIMINARY AND CSM ............ a ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............

RESCUE PLAN FOR APOLLO MISSION G

VOLUME II a ........... ............ ........... ............ ........... ............ ........... ............ . . . . . . . . . . . ............ . . . . . . . . . . . ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ...........

- RENDEZVOUS F

............ ........... ANYTIME LM ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... . . . . . . . . . . . ............ ........... ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... ............ ........... . . . . . . . . . . . . ........... ............ ........... ............

4 ............ + ............

- 20324

........... . . . . . . . . . . . . . . . . . . . . . . . ............ ........... ............ ............ ........... 955 L l ~ n f ~ ; ~ - ; yLa:,.A L

........... .... .... Washington, D. c .

A MISSION PLANNING AND ANALYSIS DIVISION U MANNED SPACECRAFT CENTER

Y l c 'qr H 0 U STON , T E X A S b :!. . .4

[&* :::::I::::: ...... ...... ..... (liASA-Tli-X-69811) PRELIMINABY LM AEORT N74-70724 1

: :::: A N C CSM RESCUE PLAN FOB APOLLG MISSXON

.w.

...... ..... ..... :::::: . . . . . G - VOLUME 2: RENDEZVOUS F O L L O W I N G ...... ..... ...... Unclas ...... . . . . . A N Y T I f l E L H LIFE-CFF ( N A S A ) 87 p I . . . . . 00/99 1 6 4 3 5

MSC INTERNAL NOTE NO. 69-FM-39

c

Y

P R O J E C T A P O L L O

P R E L I M I N A R Y L M ABORT A N D C S M RESCUE P L A N FOR A P O L L O MISSION G

V O L U M E II R E N D E Z V O U S F O L L O W I N G A N Y T I M E L M L I F T - O F F

By E. Lloyd J . H. Mashburn

Orbital Analysis Section TRW Systems Group

February 19, 1969

MISSION PLANNING AND ANALYSIS DIVISION NATIONAL AERONAUT IC S A N D SPACE ADM I N ISTRAT IO N

MANNED SPACECRAFT CENTER HOUSTON , TEXAS

MSC Task Monitor J. A. Bell

Orbital M i s s i o i Analysis Branch

/

CONTENTS

Section Page

.

c

I -'

1. SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3. ABBREVIATIONS AND SYMBOLS . . . . . . . . . . . . . . . . . . . 5

7 4. CONSTRAINTSy GROUNDRULES, AND ASSUMPTIONS. . . . . 5. RENDEZVOUS ABORT AND RESCUE PLAN AND

DECISION FLOW LOGIC ....................... 9

5.1 Rendezvous Abort and Rescue P lan . . . . . . . . . . . . . . 9

5.2 Decision Flow Logic ........................ 10

6. DETAILED RENDEZVOUS ABORT AND RESCUE SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6.1 Nominal Phase Angle Region . . . . . . . . . . . . . . . . . . 13

6.1. 1 LM-Active rendezvous . . . . . . . . . . . . . . . . . 13 6.1.2 CSM-Active rendezvous . . . . . . . . . . . . . . . . . 15 6. 1. 3 LM-Active CSI, CSM-Active CDH . . . . . . . . . . 15

6 .2 Post-Nominal Phase Angle Region. . . . . . . . . . . . . . . 15

6.3 Pre-Nominal Phase Angle Region . . . . . . . . . . . . . . . 17

6. 3. 1

6.3.2

6.3.3

CSM-Active rendezvous following LM thrust

CSM rescue using the five impulse extended

CSM rescue using the six impulse extended

....................... 17 at insertion

coelliptic sequence . . . . . . . . . . . . . . . . . . 17

coelliptic sequence . . . . . . . . . . . . . . . . . . 18

7. EXAMPLES O F RENDEZVOUS FOLLOWING ANYTJME L I F T - O F F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7 . 1 Lift-off at Touchdown . . . . . . . . . . . . . . . . . . . . . . . 19

7. 2 Lift-off 17 Minutes after Touchdown . . . . . . . . . . . . . 20

7. 3 Lift-off 60 Minutes after Touchdown . . . . . . . . . . . . . 21

7 .4 Lift-off 100 Minutes after Touchdown . . . . . . . . . . . . 2 1

7. 5 Lift-off 116 Minutes after Touchdown . . . . . . . . . . . . 22

ii i

Section Page

8. C O N C L U S I O N S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 9

iv

a

Y

-

TABLES

~ Table

I

I1

I

111

V

IV

V

VI

VI1

v I11

IX

X

XI

Page

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off a t LM Touchdown - LM- Active Coelliptic Sequence . . . . . . . . . . . . . . . . . 27

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off at LM Touchdown - CSM- Active Coelliptic Sequence . . . . . . . . . . . . . . . . 28

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off at LM Touchdown - LM-Active CSI, CSM Rescue . . . . . . . . . . . . .

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 17 Minutes After Touchdown . LM-Active Coelliptic Sequence. . .

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 17 Minutes After Touchdown - CSM-Active Coelliptic Sequence . .

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 17 Minutes After Touchdown . LM-Active CSI, CSM Rescue . . . .

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 60 Minutes After Touchdown . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . 29

. . . . . 30

. . . . . 31

. . . . . 32

. . . . . 33

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 100 Minutes After Touchdown 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Maneuvers and State Vectors After Each Maneuver During CSM Rescue fo r Lift-off 100 Minutes After Touchdown 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Maneuvers and State Vectors After Each Maneuver During Rendezvous for Lift-off 116 Minutes After Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Maneuvers and State Vectors After Each Maneuver During CSM Rescue for Lift-off 116 Minutes After Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

V

FIGURES

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Regions of Applicability of Rendezvous and Rescue Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Selection of Rendezvous Techniques Following Anytime LM Lift-off. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Geometric Illustrations of Rendezvous Techniques. . . . . . Decision Flow Logic for Rendezvous Following

Anytime LM Lift-off. . . . . . . . . . . . . . . . . . . . . . . . Input P a r a m e t e r s and Resultant Coelliptic Differential

Altitude for the LM- Active Four Impulse Coelliptic Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Performance and Time Requirements fo r the LM- Active Four Impulse Coelliptic Sequence . . . . . . . . . .

Input P a r a m e t e r s and Resultant Coelliptic Differential Altitude for the CSM-Active Four Impulse Coelliptic Sequence . . . . . . . . . . . . . . . . . . . . . . . .

Performance and Time Requirements for the CSM- Active Four Impulse Coelliptic Sequence . . . . . . . . . .

Performance, Time, and Coelliptic Differential Altitude for LM-Active CSI, CSM Rescue . . . . . . . . . .

Input P a r a m e t e r s f o r the CSM High Apocynthion Dwell Followed by LM-Active Coelliptic Sequence . . . . . . . .

Performance and Time Requirements f o r the CSM High Apocynthion Dwell Followed by LM- Active Coelliptic Sequence . . . . . . . . . . . . . . . . . . . . . . . .

Input P a r a m e t e r s and Performance Requirements for CSM- Active Rendezvous Following a Planned LM Thrust at Inser t ion. . . . . . . . . . . . . . . . . . . . . . . . .

Input P a r a m e t e r s and Performance Requirements for the CSM- Active Five Impulse Extended Coelliptic Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Input P a r a m e t e r s and Per formance Requirements for the CSM- Active Six Impulse Extended Coelliptic Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page

38

39

40

42

44

45

46

47

48

49

50

5 1

52

53

vi i

Figure

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

Insertion Phase Angle as a Function of Lift-off Time . . . .

Timeline for Rendezvous Following Lift-off at LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Relative Motion (Curvi l inear , CSM- Centered) During Rendezvous Following Lift-off at LM Touchdown . . . . .

Range and Range Rate During Rendezvous Following Lift-off at LM Touchdown . . . . . . . . . . . . . . . . . . . .

Timeline f o r Rendezvous Following Lift- off 17 Minutes after LM Touchdown. . . . . . . . . . . . . . . . . . . . . . . .

Relative Motion (Curvi l inear , CSM- Centered) During Rendezvous Following Lift- off 17 Minutes after LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . .

Range and Range Rate During Rendezvous Following Life-off 17 Minutes after LM Touchdown . . . . . . . . . .

Timeline for Rendezvous Following Lift- off 60 Minutes after LM Touchdown. . . . . . . . . . . . . . . . . . . . . . . .

Relative Motion (Curvilinear, CSM- Centered) During Rendezvous Following Lift- off 60 Minutes after LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . .

Range and Range Rate During Rendezvous Following Lift-off 60 Minutes a f te r LM Touchdown

Timeline fo r Rendezvous Following Lift-off

. . . . . . . . . .

100 Minutes after LM Touchdown . . . . . . . . . . . . . . .

Relative Motion (Curvilinear, LM- Centered) During Rendezvous Following Lift-off 100 Minutes a f te r LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . .

Range and Range Rate During Rendezvous Following Lift-off 100 Minutes a f te r LM Touchdown. . . . . . . . . .

Timeline fo r CSM Rescue Following Lift-off 100 Minutes af ter LM Touchdown . . . . . . . . . . . . . . .

Relative Motion (Curvi l inear , LM- Centered) During CSM Rescue Following Lift-off 100 Minutes a f te r LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

viii

Figure Page

30 Range and Range Rate During CSM Rescue Following Lift-off 100 Minutes af ter LM Touchdown. . . . . . . . . . 6 9

3 I Timeline for Rendezvous Following Lift-off 116 Minutes af ter LM Touchdown 70 . . . . . . . . . . . . . . .

32 Relative Motion (Curvilinear, LM- Centered) During Rendezvous Following Lift-off I 1 6 Minutes a f te r LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

33 Range and Range Rate During Rendezvous Following 72 Lift-off 116 Minutes after LM Touchdown . . . . . . . . .

34 Timeline fo r CSM Rescue Following Lift-off 116 Minutes af ter LM Touchdown 7 3 . . . . . . . . . . . . . . .

35 Relative Motion (Curvilinear, LM- Centered) During CSM Rescue Following Lift-off 116 Minutes a f te r LM Touchdown . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

36 Range and Range Rate During CSM Rescue Following Lift-off 116 Minutes after LM Touchdown. 75 . . . . . . . . .

37 Per formance and Time Requirements f o r Rendezvous 76 Following Anytime LM Lift- off . . . . . . . . . . . . . . . . .

38 Performance and Time Requirements fo r CSM Rescue 77 Following Anytime LM Lift - off . . . . . . . . . . . . . . . . .

ix

PRELIMINARY LM ABORT AND CSM RESCUE PLAN

.II

'.'

FOR APOLLO MISSION G

VOLUME I1

RENDEZVOUS FOLLOWING ANYTIME LM LIFT-OFF

By: E. Lloyd J. H. Mashburn

Orbital Analysis Section

TRW Systems Group

I. SUMMARY

The prel iminary mission G rendezvous abort and rescue plan f o r LM anytime lift off is presented in this document. LM lift-off will occur a t one discrete time during each CSM revolution. However, if required, rendezvous following anytime l i f t -off can be accomplished within the systems constraints by using the techniques presented in this repor t . using existing programs. No new systems, o r modification of existing systems, a r e required, and no problem a r e a s have been identified. Since the cu r ren t policy is to consider only d iscre te launch t imes (because no fai lure which would require anytime lift-off has been identified), the study of anytime lift-off will be concluded upon publication of this document.

As current ly planned,

These rendezvous and rescue techniques can be computed

0 A paramet r ic analysis of several candidate rendezvous techniques

The results of this analysis a r e documented in Because of constraints on performance and time, none of

determined the range of insertion phase angles over which each technique could be used. Reference 1. the techniques could be used over the full 360-degree range of possible inser t ion phase angles. This range has been divided into the following three regions:

0 Nominal ( 1 7 . 5 to 78. 5 degrees)

0

0

Post-Nominal (78. 5 to 325 degrees)

Pre-Nominal ( - 3 5 to 17. 5 degrees)

In the nominal region, the four impulse coelliptic sequence is performed by the LM. impulse coelliptic sequence by either the CSM alone o r with a LM-CSM combination. In the post-nominal region, the four impulse coelliptic sequence is again used; however, it is preceded by a two impulse, high apocynthion dwell maneuver by the CSM.

Rescues in this region a r e accomplished using the four 0 Rescues in the post-nominal

1

region a r e accomplished using the CSM high apocynthion dwell maneuver followed by the four impulse coelliptic sequence executed by either the CSM alone o r the LM-CSM combination. In the pre-nominal region, the LM performs a maneuver to r a i se a.pocynthion immediately following insertion. The CSM then t ransfers to a 20-nautical mile c i rcu lar orbit . Rendezvous is then completed by the CSM using the four impulse coelliptic sequence. In the pre-nominal region, rescues a r e performed using the five o r six impulse extended coelliptic sequences. niques for each phase angle region is i l lustrated in Figure 1.

The choice of tech-

As a verification of this plan, detailed rendezvous simulations were generated for five specific LM lift-off t imes. These lift-off t imes were chosen s o that each of the rendezvous techniques could be i l lustrated. data presented for each technique include relative motion, range, range rate , state vectors af ter each maneuver, and timelines showing sunlight/ shadow and communications blackout regions for each profile.

The

2

2 . INTRODUCTION

The prel iminary miss ion G rendezvous, abort , and rescue plan fo r This report is the LM anytime lift-off is presented in this document.

second of four volumes covering LM abort and CSM rescue for the lunar landing mission. Volume I contains recommendations for LM abort , CSM rescue, and CSM assist during descent and ascent. Volume 111 will cover t ime-cr i t ical rendezvous, and Volume IV will cover procedures for aborts during powered de scent. Publication of this repor t , Volume 11, concluded the activity related to anytime lift-off, since cur ren t policy specifies L M l i f t -of f a t one d iscre te time each CSM revolution. anytime lift-off can be performed within existing system constraints by using the plan presented i n this report.

Rendezvous following

,.

The LM ascent and rendezvous prof i les a r e being continually updated, and the basic prof i les used in this document (described in Reference 2 ) have been updated during publication of this report . changes between the basic profiles and the la tes t profiles is minor and does not invalidate the analysis of this plan. document should be used as a guide to methodology of rendezvous ra ther than fo r precis ion targeting values, Specific cases a r e presented in the document to ver i fy the techniques which comprise this plan.

I.’

The effect of the

It should be e.mphasized that this

3

a Vehicle Systems

3 . SYMBOLS

LM lunar module

CSM command service module

MSFN Manned Space Flight Network

RTCC Real- Time Computer Center

ARRS Apollo Real- Time Rendezvous Support P r o g r a m

Maneuver Designations

CSI coelliptic sequence initiation

CDH coelliptic differential height

SPS service propulsion s ys t em

RCS reaction control system

IMU iner t ia l measurement unit

LUMINARY lunar module computer program

COLOSSUS command module compater program

PGNCS p r imary guidance and navigation control subsystem

AGS abort guidance subsystem

Ground Svstems

TPI terminal phase initiation a.

T P F terminal phase finalization

CPM coelliptic phasing maneuver

P a r a m e t e r s

4 phase angle between CSM and LM radius vectors (positive for CSM ahead of LM)

Ah coelliptic differential altitude (positive for CSM above LM)

AV character is t ic velocity increment

5

0

D’

a

4. CONSTRAINTS, GROUNDRULES, AND ASSUMPTIONS

The following constraints, ground rules and assumptions were used in developing the decision flow logic and generating the pararrietric data presented in Section 6. data of Section 7. vous studies, while others a r e related to abort and CSM rescue. The validity of the assumptions should be determined, and any additional con- s t ra in ts o r ground rules should be identified.

They also can be applied to the detailed t ra jec tory Some of the ground rules a r e used i n a l l Apollo rendez-

1. All burns a r e simulated impulsively.

2. Dispersions, e r r o r s , underburns, and overburns a r e not c o ns ide red .

3. If a l l systems per form as specified, mos t maneuvers a r e computed onboard the L M o r the CSM.

4. Additional c rew training is minimized.

5. Out-of-plane situations a r e not considered.

6 . The LM will be tracked f o r 10 minutes by MSFN following ins e r tion.

7 . The LM will check IMU alignment and realign if necessary, beginning at 5 minutes af ter insertion. s ta te vector update.

This will take precedence over

8. sequences a re :

The maximum impulsive AV budgets for in-plane rendezvous

CSM SPS - 790 fps CSM RCS - 125 fps

LM RCS - 131 fps

9. The maximum ranges for tracking a re :

Rendezvous radar - 400 n mi Sextant - 400 n mi VHF - 200 n mi

I O . The maximum ranges for communication a re :

Voice - 550 n m i Telemetry - 320 n mi

11. The CSM-active CSI and CDH maneuvers a r e computed onboard In addition these maneuvers can be computed in the RTCC o r the CSM.

onboard the LM and transmitted to the CSM

7

12. Maneuver computation in the RTCC requires 7 minutes Maneuver t ransmission to, and verification by, the CSM requi res 2 minutes.

13. 10 minutes.

Preparat ion for a maneuver by either vehicle requires

14. No maneuver will be performed which inser t s e i ther vehicle into an orbit with pericynthion altitude less than 60, 000 feet.

15. F o r any maneuver in a LM-active rendezvous sequence, there must be a provision for CSM rescue in case the LM is unable to per form a s required. CSM failures a r e not considered.

16. The LM onboard s ta te vector must be updated 2 5 minutes before the CSI maneuver. sequence which provides for a second (corrected) CSI maneuver af ter rendezvous radar tracking is initiated.

This constraint may be relaxed for a rendezvous

17. The LM and the CSM must be in communication a t CSI.

18. Coelliptic differential altitudes should be within the range of 10 t o 20 nautical mi les . coelliptic orbit .

The LM will always be below the CSM in its

19. The LM will be the active vehicle during terminal phase, whenever possible. per form the terminal phase.

The CSM will be used a s a backup in case the LM cannot

2 0 . It is desirable, but not absolutely necessary, for the target vehicle to be in attitude hold during terminal phase.

21. TPI occurs when the passive vehicle is approximately at the midpoint of darkness. F o r LM lift-off during the f i r s t CSM revolution following touchdown, TPI occurs 90 degrees west of the insertion point.

22. The target vehicle t ravels 130 degrees during te rmina l phase.

23. Rendezvous, docking, and crew t r ans fe r a r e completed approximately 90 minutes af ter TPI.

24. Rendezvous, docking, and crew t r ans fe r must be completed within 11. 5 hours af ter LM insertion.

L 8

5. RENDEZVOUS ABORT AND RESCUE PLAN AND DECISION FLOW LOGIC

The rendezvous abort and rescue plan and the decision flow logic for this plan a r e presented in this section. t r a t e s the implementation of each of the rendezvous techniques in the plan. The resu l t s of the pa rame t r i c analysis of each of these techniques a r e presented in Section 6.

The decision flow logic i l lus-

5. 1 Rendezvous Abort and Rescue Plan

Rendezvous following anytime LM lift-off requi res rendezvous capability over the ent i re 360-degree range of possible insertion phase angles. In the pa rame t r i c study recently completed (Reference 1), no single technique was found which covered the en t i re range while staying within the constraints on AV and LM ascent stage l ifetime. used in this study is to divide the phase angle range into th ree regions: nominal, post-nominal, and pre-nominal. The choice of techniques fo r each of the regions i s i l lustrated i n the flow d iagram of F igure 2 and is discussed briefly below. detai l in another section of this report .

The approach

The individual techniques a r e covered in more

In the nominal region (17 . 5 degrees to 78. 5 degrees) rendezvous is accomplished using the standard four impulse coelliptic sequence. The sequence can be performed by the LM alone, the CSM alone, o r a combination of maneuvers by both vehicles ( F i g u r e s 3a through 3c). ca ses the LM will approach the CSM f r o m below during te rmina l phase.

In all

In the post-nominal region (78. 5 degrees to 325 degrees) the CSM pe r fo rms a two impulse, high apocynthion dwell sequence. This sequence inc reases the differential angular rate between the two vehicles so that when the CSM re turns to the 60-nautical mi le c i rcu lar parking orbi t it will be about 20 degrees ahead of the LM. with the four impulse coelliptic sequence used in the nominal region. This sequence can be performed by ei ther vehicle alone o r by combined maneuver with both vehicles.

Rendezvous is then completed

The techniques used in the pre-nominal region ( - 3 5 degrees to i-17. 5 degrees) are m o r e complex. f o r m s a 100-foot p e r second horizontal maneuver which r a i se s the apocynthion altitude to about 100 nautical mi les . CSM init iates a preplanned Hohmann t r ans fe r down to a 20-nautical mile c i r cu la r orbi t . F r o m this orbit the CSM completes the rendezvous using the four impulse coelliptic sequence a s shown in F igure 3d. If the LM is unable to th rus t following insertion, CSM rescue is accomplished using the five o r s ix impulse extended coelliptic sequences shown in F igures 3e and 3f. The f ive impulse sequence is used for negative insertion phase angles and the six impulse sequence for positive phase angles. c a s e s the LM i s below the CSM during te rmina l phase.

Immediately after insertion the LM pe r -

Ten minutes la te r the

In al l

9

5. 2 Decision Flow Logic

The decision flow logic f o r rendezvous abor t and rescue following anytime LM lift-off is shown in F igure 4. received by MSFN during ascent to the 30-nautical mile by 60,000-foot s tandard insertion orbi t , and an est imated inser t ion phase angle i s determined. (17 . 5 degrees to 325 degrees) MSFN will begin 10-minute postinsertion t racking and LM orbi t determination. it will be instructed to power up at f i r s t contact with MSFN. (Since any- t ime LM lift-off is considered only during the f i r s t CSM revolution following LM landing, it is unlikely that the CSM will be powered down.)

Te lemet ry f r o m the LM is

If the phase angle i s in the nominal o r post-nominal regions

If the CSM has been powered down,

If the insertion phase angle i s in the nominal region, the LM will check IMU alignment immediately af ter inser t ion and realign if necessary . After IMU realignment is verified, the LM and CSM begin t racking each o ther as soon a s contact is established in o r d e r to update the LM state vector. The input pa rame te r s for the LM-active and CSM-active four impulse coelliptic sequences a r e determined on the ground and t r ans - mitted to the two vehicles. onboard the LM and in the RTCC. The equivalent operations a r e a lso being performed fo r the computation of the CSM- active coelliptic sequence to be initiated 1 minute a f te r the t ime fo r initiation of the LM-active sequence. pre- thrus t ing programs f o r CSI and CDH (COLOSSUS P-32 and P-33) a r e in the CSM computer. If they a r e not, a s i s present ly the case , then the CSM-active sequence can be computed by the CSI and CDH pre- thrust ing p rograms on board the LM (LUMINARY P- 72 and P- 73) o r in the RTCC and t ransmit ted to the CSM.

The LM-active coelliptic sequence i s computed

This i s based on the assumption that the coelliptic sequence

The LM wil l pe r fo rm the coelliptic sequence initiation (CSI) maneu- v e r a t the appropriate t ime. coelliptic differential height (CDH) maneuver will be computed on board the LM. At the same t ime, the CSM wi l l be computing a backup CDH maneuver . As before, if the CSM does not have this capability (COLOSSUS P-33) then the backup CDH will be computed onboard the LM (LUMINARY P-73) o r i n the RTCC and t ransmit ted to the CSM. The LM will then per form CDH. the LM and the CSM will each compute the i r own te rmina l phase initiation (TPI) maneuvers. will be performed by the CSM. maneuvers will be computed and performed in the s a m e way.

If CSI i s performed satisfactorily, an updated

When the two vehicles a r e in coelliptic orbi ts ,

The LM will pe r fo rm TPI if possible: if not, the T P I The midcourse cor rec t ion and braking

If the LM was unable to pe r fo rm CSI then the CSM would pe r fo rm the CSI maneuvers which it computed. updated CDH maneuver and pe r fo rm it at the proper t ime. If the LM per formed CSI but was unable to pe r fo rm CDH, then the CSM would pe r - f o r m i t s precomputed CDH maneuver. In e i ther case , all te rmina l phase maneuvers a r e computed on board both vehicles and a r e per formed by the LM if possible.

The CSM will then compute an

10

When the insertion phase angle is in the post-nominal region, the CSM will pe r fo rm the high apocynthion dwell sequence before the coelliptic sequence is performed. o r th ree revolutions depending upon the insertion phase angle. When the phase angle is l e s s than 135 degrees, the CSM will s tay one revolution; l e s s than 230 degrees , two revolutions; and l e s s than 325 degrees , three revolutions. If the CSM is to stay two o r t h ree revolutions, then the LM will be powered down. The first dwell maneuver i s conz-pted in the RTCC and t ransmit ted to the CSM. LM postinsertion tracking, maneuver computation and t ransmission, and maneuver preparat ion require a total of 29 minutes. This is equivalent to about 87 degrees of t rave l angle in the CSM 60-nautical mile c i rcu lar parking orbit . Therefore, if the inser t ion phase angle is l e s s than 273 degrees, the f i r s t dwell maneuver will be performed over LM pericynthion, and if it is g rea te r than 273 degrees , the dwell maneuver will be performed 29 minutes after LM insertion.

The CSM will remain in the dwell orbi t one, two, a

0

I/

The CSM will be tracked after the first dwell maneuver, and the dwell orbit will be determined. the two- and three-revolution cases, it will be computed in the RTCC and t ransmit ted to the CSM. pericynthion pas sage. computed in the RTCC and transmitted to the CSM. tion, the CSM orbi t is determined by MSFN and t ransmit ted to the LM. Rendezvous is then completed using the coelliptic sequence described above.

If a correct ion maneuver is necessary for

The correction will be performed at the next The second dwell maneuver ( recircularization) is

After recircular iza-

If, during ascent f r o m the surface, the predicted phase angle is in

The LM is powered down af te r pe r - the pre-nominal range then the L M will p repare fo r a 100-foot pe r second th rus t immediately after insertion. forming the maneuver and i s tracked for 10 minutes by MSFN. L€ the 100-foot pe r second maneuver was performed satisfactorily, the CSM will initiate a preplanned Hohmann t ransfer to a 20-nautical mile c i rcu lar orbi t 10 minutes a f te r insertion. sequence a r e selected by MSFN and t ransmit ted to the CSM. computes a coelliptic sequence with CSI occurr ing a t the second passage over the LM pericynthion and CDH occurring one revolution la ter . This fixes the coelliptic differential altitude (Ah) a t about 10 nautical miles. After performing CSI, the CSM computes a n updated CDH maneuver and per forms it at the proper time. The decision flow logic fo r computation and performance of terminal phase maneuvers is the same as for the coelliptic sequence in the nominal phase angle region.

The input pa rame te r s fo r the coelliptic The CSM

If the LM does not per form the maneuver a t insertion, then one of F o r the extended coelliptic sequences w i l l be used for CSM rescue.

negative phase angles (-35 degrees to 0 degree) the five impulse sequence is used. and t ransmit ted to the CSM. passage over LM apocynthion and inser ts the CSM into a high dwell orbit . The CSM remains in this orbit three revolutions. The CSI maneuver i s computed on board the CSM and is performed over LM apocynthion. The CSM then computes a CDH maneuver to occur one half revolution la te r

The coelliptic phasing maneuver ( C P M ) is computed in the RTCC This maneuver is performed on the first a

over LM pericynthion. is completed using the standard LM-active terminal phase.

The LM is powered up, if possible, and rendezvous

11

F o r positive phase angles ( 0 degree to 17. 5 degrees) the six impulse sequence is used. f o r m s a preplanned Hohmann maneuver which inser t s it into a 60-nautical mile by 10-nautical mile elliptical orbit. and t ransmit ted to the CSM one- half revolution a f te r the Hohmann maneuver. lower than the LM orbit (but not l e s s than 10 nautical miles c i rcular) so that the CSM can gain on the LM. three and one-half revolutions. CSI is performed over LM apocynthion, and the remainder of the sequence is the same a s the five impulse extended coellipt ic sequence .

At first passage over LM apocynthion the CSM per -

CPM is computed in the RTCC CPM is performed over LM pericynthion

This orbi t is generally

The CSM remains in this orbi t for

>

12

6. DETAILED RENDEZVOUS ABORT AND RESCUE SEQUENCES

The resu l t s of the paramet r ic analysis of the rendezvous techniques a r e presented in this section. ments and the total rendezvous time a r e shown for each rendezvous .and rescue technique. decision flow logic of Section 5. 2 a re presented. The methods for computing these input pa rame te r s a r e defined so that they can be recalculated in the event of minor changes in the rendezvous profiles.

The CSM and LM performance require-

In addition, the input pa rame te r s called fo r in the

a 6. 1 Nominal Phase Angle Region

The four impulse coelliptic sequence (CSI, CDH, TPI, and TPF) is the s tandard technique f o r Apollo rendezvous. off problem it can be used throughout the nominal phase angle region. There a r e four independent variables that may be used to shape the s tandard coelliptic sequence: t ime for CSI, t r ans fe r orbi t aps i s at which CDH is performed, t ime of TPI, and elevation angle of the vehicle-to- vehicle l ine-of-sight a t TPI. F o r the lunar rendezvous case the elevation angle is fixed to allow thrusting nearly along the line of sight. of CSI and T P I a r e constrained by the location of the maneuvers to a given t ime o r the given t ime plus a cer ta in number of complete revolutions. This resu l t s in the actual variables used in this study being the revolution in which CSI is performed, the t ransfer orbi t aps i s a t which CDH is performed, and the revolution in which T P I is performed. zontal impulse performed a t the specified t ime and inser t s the active vehicle into the t r ans fe r orbit . of the t r a n s f e r orbi t and inser t s the active vehicle into a coelliptic orbit . The coelliptic orbi t is one in which the apocynthion and pericynthion altitudes differ f r o m the corresponding altitudes of the ta rge t orbi t by the s a m e amount, the coelliptic differential altitude (Ah). The var iables used a r e chosen so that the elevation angle of the line of sight between the two vehicles will be a des i red value a t the specified time of TPI. The third maneuver, TPI, is performed nearly along the line of sight and in se r t s the active vehicle into an orbi t which intercepts the ta rge t vehicle a f te r it has t rave led 130 degrees . The final maneuver, TPF , cancels the relat ive

CSM alone o r with combined maneuvers by both vehicles.

F o r the anytime LM l i f t -

The t imes

CSI is a hori-

CDH is performed at the des i r ed aps is

. velocity at intercept. This sequence can be performed by the LM o r the

6. I. 1 LM-Active rendezvous. - CSI i s performed 50 minutes a f te r LM Dericvnthion on the f i r s t , second, o r third revolution. CDU is pe r - f o r k e d a i t h e first o r second apocynthion crossing (first o r th i rd apsis) after CSI. inser t ion orb i t pericynthion during the f i r s t o r second revolution in the coelliptic orbit .

T P I i s performed when the CSM is 90 degrees west of LM

The selection of the above mentioned parameters for any par t icular

a phase angle is a function of the bounds on coelliptic differential altitude (Ah). This can be seen in F igure 5 which presents the choice of input

13

paramete r s and the resultant Ah fo r the entire nominal phase angle region. At 17. 5 degrees, CSI is performed 50 minutes a f te r insertion, CDH occurs at the f i rs t apocynthion, and TPI is performed during the first revolution in the coelliptic orbi t (when the CSM is 90 degrees west of LM insertion on its second revolution). 10 nautical miles, which is the lower bound on this parameter . As phase angle increases , Ah also increases and reaches i ts upper bound of 20 nautical miles a t about 21. 6 degrees . TPI t ime is increased one CSM period while maintaining CSI t ime a t 50 minutes and CDH a t the f i r s t apocynthion. tant Ah is 8. 5 nautical miles, and Ah remains below 10 nautical miles for phase angles l e s s than about 23. 1 degrees . unacceptable, then it would be necessary to delay LM lift-off by about one-half minute to allow the CSM to move 1. 5 degrees fa r ther ahead of the LM at insertion. 28. 8 degrees at which point CDH can be moved to the third apsis crossing (second apocynthion) while maintaining the previous values for CSI t ime and TPI revolution. 35. 6 degrees which corresponds to Ah variation between the permissible limit of 10 to 20 nautical miles . CSI t ime is maintained at 50 minutes af ter insertion, CDH still occurs a t the third apsis , and TPI t ime i s increased by one CSM revolution.

This resul ts in a value of Ah of

F o r l a rge r phase angles, the

At 21. 6 degrees the resul-

If these values a r e t ru ly

This sequence i s used for phase angles up to

The range for this sequence is f rom 28. 8 to

F r o m 35. 6 degrees to 39. 2 degrees

The four impulse sequence discussed above comprise the basic scheme for using the LM-active coelliptic sequence rendezvous. be seen in Figure 5 that the Ah profile for phase angles between 39. 2 and 60 .9 degrees is a duplicate of the previous profile between 17. 5 and 39.2 degrees . l a te r , and TPI occurs one CSM period la te r . F o r instance, if the in se r - tion phase angle is 41. 3 degrees then CSI occurs a t 168. 9 minutes (one LM period plus 50 minutes) af ter insertion, CDH is performed a t the first apsis , and TPI occurs when the CSM is 90 degrees west of the LM insertion pericynthion on the third CSM revolution. 15 nautical miles, is the same a s for the equivalent sequence performed one revolution ear l ie r at an insertion phase angle of 19. 6 degrees . F o r phase angles between 60. 9 and 78. 5 degrees , the basic sequence repeats once more, in part, by increasing CSI and TPI t imes by one o r more revolutions.

It can

The only difference is that CSI occurs one LM period

The resultant Ah,

The performance and total rendezvous t ime for the LM-active coelliptic sequence a r e presented in F igure 6. CSI, CDH, TPI, and total of a l l four impulses a r e presented in the figure. A comparison of Figures 5 and 6 shows the correlation between AV requirements and Ah. CSI and CDH AV dec reases a s Ah increases , while TPI and total AV increase with Ah. 131 feet per second. lated by adding 9 0 minutes to the TPI t imes of F igure 5. the t ime required to complete terminal phase braking, docking, and crew t ransfer . The maximum time requirement is 587 minutes, which is within the LM ascent stage lifetime of 11. 5 hours .

The AV requirements for

The maximum total impulsive AV is The values for total rendezvous t ime were calcu-

This is about

14

6.1.2 CSM-Active rendezvous. - This sequence is used a s a backup, in case the LM cannot perform CSI at the des i red time. If this happens, the CSM then initiates the sequence by per forming CSI 1 minute after the LM would have done so. CDH i s performed at the f i r s t o r third apsis crossing ( in this case first o r second pericynthion) a f te r CSI. then in an orbit which i s coelliptic with, and above, the LM insertion orbit. west of the insertion pericynthion in whichever revolution TPI i s to occur , F o r any par t icular revolution this t ime i s a constant regardless of phase angle since the LM always s t a r t s at pericynthion.

The CSM i s

The t ime of TPI i s determined by requiring the LM to be 90 degrees

In selecting input parameters for this sequence, the profile e-stablished for the LM-active sequence is followed a s closely a s possible. Thus CSI always occurs 1 minute after the LM-active CSI t ime, CDH occurs at the same apsis crossing, and TPI i s performed during the same coelliptic revolution. Figure 7. for the LM-active sequence. requirements a r e presented in Figure 8. CDH, TPI, and total of a l l four impulses a r e presented in the figure, The relationships between AV and A h discussed in Section 6. 1. 1 a r e also apparent fo r the CSM-active case, 140 feet p e r second. i s a lso shown in the figure. 565 minutes, which is l e s s than the LM ascent stage lifetime of 11. 5 hours.

The input pa rame te r s and the resultant A h a r e presented in It can be seen that A h f o r the CSM-active sequence i s lower than

The performance and total rendezvous t ime The AV requirements for CSI,

The maximum total impulsive AV i s The total rendezvous t ime ( T P I t ime plus 90 minutes)

The maximum t ime requirement i s about

6.1.3 LM-active CSI, CSM-active CDE. - This sequence i s used a s a backup in case the LM performs CSI but i s unable to per form CDH at the desired-time. would have done so. above, the t r ans fe r orbit into which the LM was inser ted at CSI. coelliptic differential altitude generally will be grea te r than for the LM- active case , since the CSM is past apocynthion of the LM t ransfer orbit when CDH is performed. than in the LM-active case a s a result of the l a r g e r differential angular ra te in the coelliptic orbits. and the resultant differential height a r e presented in Figure 9. A com- par ison of Figures 9 and 5 shows the difference in A h mentioned above. The AV for CDH, TPI, and total of the th ree CSM-active impulses a r e p r e sented in Figure 9 (AV for LM-active CSI was presented in Figure 6). can be seen that the maximum total CSM-active impulsive AV requirement i s 137 fee t p e r second. ( F r o m Figure 6 , the maximum LM-active CSI AV is 56 feet p e r second. ) It can also be seen in the figure that the maximum total rendezvous t ime i s about 530 minutes.

The CSM then performs CDH immediately after the LM The resultant CSM orbi t will be coelliptic with, and

The

This will cause TPI to be performed ea r l i e r

The performance and t ime requirements ,

It

6 . 2 Post-Nominal Phase Angle Region

The CSM high apocynthion dwell sequence i s used in the post-nominal phase angle region (78.5 degrees to 325 degrees) . into an elliptical dwell orbit with 60-nautical mile pericynthion altitude and an apocynthion altitude which may be a s great a s 321 nautical miles .

The CSM is inser ted

The I

15

CSM remains in this dwell orbi t One, two, o r th ree revolutions, then recircular izes a t pericynthion. CSM as a result of the increased differential angular ra te between the two orb i t s . coelliptic sequence.

During this t ime the LM has gained on the

Rendezvous i s then completed using the LM-active four impulse

The high apocynthion dwell maneuvers are computed in the RTCC This means that, based on assumptions 6, 12, and 13, the following oper - ations m u s t be performed before the sequence can be initiated. is tracked by MSFN fo r 10 minutes following inser t ion, and i t s o rb i t is determined. Transmission of the maneuver to, and verification by the CSM requires 2 minutes. Preparation f o r the maneuver requires 10 minutes. Thus, a total of 29 minutes will elapse before the f i r s t dwell maneuver can be performed. 60-nautical mile lunar parking orbit . g r e a t e r than 273 degrees, the dwell sequence can be initiated on the f i r s t CSM passage over LM pericynthion. 325 degrees , the sequence will be initiated 29 minutes a f te r LM insertion.

The LM

Maneuver computation in the RTCC requires 7 minutes.

This corresponds to about 87 degrees of CSM t rave l in the Thus, f o r inser t ion phase angles not

F o r phase angles between 273 and

The apocynthion altitude of the dwell orbit is chosen s o that , after

In the des i red zequence, recircular izat ion, the LM can pe r fo rm a coelliptic sequence similar to the one used af ter a lift-off a t the nominal time. CSI occurs 50 minutes a f te r LM pericynthion, CDH i s per formed at the f i r s t aps i s , A h i s 10 nautical mi l e s , and T P I occurs 90 degrees west of LM pericynthion during the f i r s t revolution in the coelliptic orbi t . The input parameters used for computing the dwell sequence and the subsequent LM-active coelliptic sequence a r e presented in Figure 10. angles between 78.5 degrees and 135 degrees the CSM remains in the dwell orbi t one revolution. At 135 degrees the apocynthion altitude of 321 nautical mi l e s requires 300 feet p e r second f o r each impulse, o r 600 feet p e r second total for the dwell sequence. At this point, however, the CSM can remain in the dwell orbi t two revolutions and the required apocynthion altitude drops to 153 nautical miles . used fo r phase angles up to 230 degrees , a t which point the apocynthion altitude i s again up to 321 nautical miles and the total AV requirement i s 600 feet p e r second. F r o m 230 degrees to 325 degrees the th ree revolution sequence i s used. be seen a t 273 degrees as a resul t of the change in location of the dwell maneuvers . t imes of the dwell maneuvers . The t ime of CSI and T P I f o r the LM-active coelliptic sequence are a l so shown in F igure 10.

F o r phase

The two revolution sequence can be

A slight change in slope of the altitude curve can

This effect i s m o r e apparent in the upper graph showing the

The total performance requirements and total rendezvous t ime a r e shown in Figure 11. ment of 600 feet per second. 127 feet p e r second of the LM RCS AV allowance. If CSM rescue is neces- s a r y , this could require an additional 131 fee t p e r second. Thus, the maximum CSM AV requirement f o r the post-nominal phase angle region i s 731 feet p e r second, which i s within the allowance fo r in-plane CSM rescue. The total rendezvous t ime was calculated by adding 90 minutes to the TPI times of Figure 10. The maximum total t ime requirement is 680 minutes , which i s just under the 11. 5-hour (690-minute) LM ascent stage lifetime.

The AV curve shows a maximum CSM SPS require- The LM-active coelliptic sequence requires

16

6 . 3 Pre-Nominal Phase Angle Region

The pre-nominal phase angle region ( - 3 5 degrees to 4-17. 5 deg rees ) i s the most difficult region. second thrust by the LM immediately af ter insertion, raising the apocynthion altitude to about 100 nautical mi l e s , preplanned Hohmann t ransfer to a 20-nautical mile c i rcu lar orbit. F r o m this orbit the CSM per forms the four impulse coelliptic sequence. If the LM cannot thrust af ter insertion, then the CSM will rescue the LM using the five o r six impulse extended coelliptic sequences. sequence will be used for negative phase angles and the s ix impulse sequence for positive phase angles.

The region sequence requires a 100-foot p e r

The CSM then pe r fo rms a

The five impulse

6. 3. 1 Immediately af ter insertion into the 30-nautical mile by 60, 000-foot standard orbi t , the LM pe r fo rms a preplanned 100-foot p e r second positive horizontal thrust . This r a i se s the LM apocynthion altitude to 104 nautical mi les . Ten minutes l a t e r the CSM initiates a Hohmann t ransfer to 20 nautical mi les , circularizing one-half revolution l a t e r at pericynthion. The CSM gains on the LM while in this low orbit . On the second passage over LM pericynthion the CSM per forms CSI, t ransferr ing to an elliptical orbi t with apocynthion altitude grea te r than 20 nautical mi les , It remains in this orbit one revolution and then p e r f o r m s CDH at the second apsis ( f i r s t per i - cynthion). and over LM pericynthion, the resultant A h is always about 1 0 nautical mi les . t ical mi les . i s 90 degrees west of pericynthion.

CSM-active rendezvous following LM thrust at inser t ion. -

Since this maneuver i s always performed at 20 nautical mi les

The CSM coelliptic orbit is always 114 nautical mi les by 20 nau- TPI occurs during the f i r s t coelliptic revolution when the LM

The input parameters and performance requirements for this sequence a r e presented in Figure 12. t r ans fe r a r e preplanned, the only input required a r e the CSI and T P I t imes. constant 383. 1 minutes af ter LM insertion. CSI is shown in Figure 12. -26. 5 degrees (LM ahead) the altitude i s equal to 114 nautical mi les , the apocynthion altitude of the coelliptic orbit . F o r phase angles l e s s than this value, both CSI and CDH a r e positive maneuvers. Since they both occur a t the same altitude and the resultant orbi t i s always the same, then the total AV is a constant. F o r phase angles g rea t e r than - 2 6 . 5 degrees , the CSM gains too much phase angle p r io r to CSI and must go higher than the coelliptic orbit to allow the LM to regain some. CDH maneuver. 625 feet p e r second, which i s within the allocation for in-plane CSM rescue , t r ans fe r is about 473 minutes, well within the LM ascent stage lifetime.

Since the LM thrust and the CSM Hohmann

CSI t ime is a function of insertion phase angle; whereas , TPI is a The apocynthion altitude a f te r

Notice that f o r a phase angle of about

This resul ts in a negative The maximum total CSM AV for all s ix impulses i s about

The total t ime f r o m insertion to completion of docking and crew

6. 3. 2 sequence. - This rescue technique i s used for negative insertion phase angles ( -35 degrees to 0 degree) , i s computed in the RTCC and transmitted to the CSM. the first passage over LM insertion orbi t apocynthion and t r ans fe r s the CSM to a high phasing orbit, putation, and maneuver transmission and verification require a total of

CSM rescue using the five impulse extended coelliptic

The coelliptic phasing maneuver ( C P M ) It i s per formed on

LM postinsertion tracking, maneuver corn--

17

19 minutes. There is sufficient t ime to p e r f o r m these operations before the CSM loses communications with MSFN f o r all candidate landing s i tes . The CSM remains in the phasing orbi t f o r t h ree full revolutions allowing the LM to catch up. the CSM into a 60-nautical mi le by 25-nautical mi l e t r a n s f e r orbit. i s per formed one- ha l f revolution l a t e r and inser t s the CSM into a coelliptic orbit with a A h of 15 nautical mi l e s above the LM orbi t , TPI i s performed during the f i r s t coelliptic revolution when the LM i s 90 degrees west of inser t ion orb i t pericynthion.

CSI is per formed over LM apocynthion and in se r t s CDH

The input parameters and performance requirements f o r th i s sequence are presented in F igure 13. on phase angle, while the CSI and T P I t imes a r e constant at 500 and 587 minutes , respectively. The apocynthion altitude of the phasing orbi t reaches a maximum value of 362 nautical mi les . requirement for CPM, CSI, and CDH i s 748 feet p e r second. However, the CDH AV i s a constant 20 feet p e r second and could be per formed by the RCS. This leaves a maximum CSM SPS AV requirement of 728 feet p e r second. 677 minutes , just within the LM ascent stage l ifetime.

The t ime of the CPM maneuver i s dependent

The maximum total AV

li

The total t ime f rom inser t ion to docking and c rew t r a n s f e r i s

6. 3 . 3 CSM rescue using the s ix impulse extended coelliptic sequence. - T h i s rescue technique i s used for positive insertion phase angles ( 0 to 17.5 degrees) . At the f i r s t passage over LM inser t ion orbit apocynthion the CSM p e r f o r m s a Hohmann t r ans fe r t o a 60-nautical mi l e by 10-nautical mile orbit. The CPM maneuver is computed in the RTCC and t ransmit ted to CSM when it r e sumes contact with MSFN. CPM i s performed at f irst pericynthion of the Hohmann t r ans fe r orb i t which i s s e t to occur over LM insertion pericynthion. phasing orbi t at CPM and remains in this orbi t fo r t h ree and one-half revolutions. formed one-half revolution l a t e r over LM orbi t pericynthion. will then be a coelliptic orbit with a Ah of 10 nautical mi l e s above the LM. T P I occurs during the f i r s t coelliptic revolution when the LM is 90 degrees west of insertion.

The CSM i s inser ted into a low

CSI occurs at apocynthion of the phasing orbit and CDH i s p e r - The CSM

The input pa rame te r s and performance requirements for the s ix impulse sequence a r e presented in F igure 14. t ransfer and CPM maneuvers a r e functions of insertion phase angle. t ime i s near ly constant at 502 minutes , and T P I occurs at 587 minutes , the same as in the five impulse sequence. The apocynthion altitude of the phasing orbi t is as low as 12. 5 nautical mi l e s which is safely above the minimum permissible altitude of 60, 000 feet . The maximum total AV requirement f o r this sequence is 188 feet p e r second which is well below the CSM in-plane rescue AV budget. The total t ime f rom inser t ion to docking and crew t r ans fe r i s 677 minutes , just within the LM ascent s tage lifetime.

The t imes of the Hohmann CSI

18

7. EXAMPLES O F RENDEZVOUS FOLLOWING ANYTIME LIFT-OFF

A se t of detailed examples has been generated to i l lustrate the appli- cation of the anytime lift-off ,rendezvous plan. chosen during the first CSM revolution af ter LM landing. phase angles corresponding to the five lift-off times fall into all three regions of the 360-degree range: two in the nominal region, one in the post-nominal, and two in the pre-nominal. F o r each lift-off t ime, the applicable rendezvous and rescue sequences were generated using a Keplerian Program-. insertion resulting f rom an integrated simulated lift-off f rom Lunar Landing Site 11-P-2 (longitude 34. 0 E , latitude 2. 75 N) on 18 August 1969. The CSM i s in a 58. 27-nautical mile by 58. 04-nautical mile lunar parking orbi t ( referenced to the mean lunar radius). The LM is inser ted into a 28.48-nautical mile by 9. 06-nautical mi l e elliptical orbit. o rb i t s are lower than the corresponding target orbi ts used in the pa ra - m e t r i c analysis of the rendezvous techniques. Therefore, some variation in the geometric, performance, and t i m e pa rame te r s is expected. This i s handled, as it would be i f the sequences were computed in r ea l t ime, by varying the input parameters until an acceptable sequence is computed. The variation in insertion phase angle with lift-off t ime during the f i r s t CSM revolution is shown in Figure 15. The five cases a r e noted in the figure. The p r imary rendezvous technique is documented for each of the five lift-off times. In addition, the CSM-rescue profiles a r e documented f o r the two cases in the pre-nominal region, since they a r e significantly different f r o m the p r imary profiles. Data a r e presented in the form of relative motion, range and range rate versus time, state vectors a f te r each maneuver , and profile timeline showing sunlight/ shadow and communications blackouts for each vehicle.

Five LM lift-off t imes were The insertion

Each case was initialized with s ta te vectors a t LM

These actual

7. 1 Lift-off at Touchdown

LM lift-off a t touchdown results in an insertion phase angle of 23.0 degrees , near the lower l imit of the nominal region. m e t e r s for the LM-active coelliptic sequence can be found in F igure 5. CSI occurs 50 minutes af ter insertion, CDH is at the f i r s t apsis ( f i r s t apocynthion) of the t ransfer orbit , and TPI occurs 260 minutes a f te r i n se r - tion during the second revolution of the coelliptic orbit. and s ta te vectors a f t e r each maneuver are presented in Table I. for each maneuver compare favorably with those in Figure 6. vous t imeline i s presented in Figure 16. communications blackouts a r e shown in the figure. the LM with respect to the CSM i s shown in Figure 17. curve representing about one and one-third revolutions in the coelliptic orbi t i s straight because both vehicles a r e in c i rcu lar orbi ts , thus the altitude difference is constant, The vehicle-to-vehicle range and range ra te are shown in Figure 18 as functions of t ime f rom LM insertion, discontinuities in the range ra te curve a t the maneuver t imes represent the component of AV along the line of sight between vehicles, TPI, the discontinuity i s equal to the magnitude of the impulse presented in Table I.

The input pa ra -

The maneuvers The AV's

The rendez-

The relative motion of The section of the

Data on sunlight/shadow and

The

Thus, a t

19

The input pa rame te r s f o r the CSM-active coelliptic sequence a re found in F igure 7. the LM CSI time. t ransfer orbi t . TPI occurs at about 250 minutes a f t e r insertion. The resultant Ah i s 10 nautical mi les . each maneuver a r e presented in Table 11. The miss ion t imel ines , relative motion, and range and range ra te are near ly identical to those fo r the LM- active case , thus a r e not presented. The only discernible difference i s in the coelliptic portion of the relative motion plot. elliptical, there i s a slight variation (less than to. 5 nautical m i l e ) in the differential altitude around the orbits. the t imel ines and range and range rate plots. The same holds t r u e f o r the case of CSM rescue after a LM-active CSI maneuver. The maneuvers and state vec tors after each maneuver are presented in Table 111. The t ime- l ine, re la t ive motion, and range and range r a t e a r e not shown since they a re near ly identical to the data presented in F igures 16 , 17, and 18.

CSI occurs 51 minutes a f t e r LM inser t ion, one minute af ter CDH i s at the f i r s t aps i s ( f i r s t pericynthion) of the

The maneuvers and state vec tors a f te r

Since the two orbi ts a r e

The re i s negligible difference in

7. 2 Lift-off 17 Minutes af ter Touchdown

LM-lift-off 17 minutes a f te r touchdown resu l t s in an inser t ion phase angle of 74. 6 degrees , nea r the upper l imit of the nominal region. input pa rame te r s f r o m Figure 5 are: inser t ion ( 5 0 minutes a f te r pericynthion on the third revolution), CDH a t the th i rd aps is (second apocynthion), and T P I at about 480 minutes after insertion. The maneuvers and state vec tors after each maneuver are presented in Table IV. F igure 19. The relative motion of the LM with respect to the CSM i s shown in Figure 20. crossings in the LM insertion orbit. in the figure. vehicle-to-vehicle range and range ra te are shown i n F igu re 21 as functions of time f rom insertion. osci l la tory motion seen in the relat ive motion plot. ra te is always negative, that i s , the range is reduced monotonically.

The CSI t ime of 287.9 minutes f r o m

The rendezvous t imeline is presented in

The two peaks p r i o r to CSI represent apocynthion The third aps is CDH i s a lso apparent

The coelliptic differential height is 16 nautical mi l e s , The

The range ra te plot exhibits the same Even so, the range

The input pa rame te r s for the CSM-active coelliptic sequence are found in Figure 7. These pa rame te r s a r e similar to those used in the LM-active sequence. When the sequence was computed for these s ta te vec tors , the resultant Ah was above 15 nautical mi les . The maneuvers and state vec- t o r s af ter each maneuver a r e presented in Table V. case discussed i n Section 7. 1, the rendezvous t imeline, relative motion, and range and range ra te plots are so s imi l a r to those fo r the LM-active sequence that it is unnecessary to present them in this report . This a lso holds t r u e f o r CSM rescue following LM-active CSI. The maneuvers and s ta te vec tors after each maneuver are presented in Table VI fo r this sequence.

As in the previous

20

7. 3 Lift-off 60 Minutes af ter Touchdown

LM lift-off 60 minutes a f te r touchdown resul ts in an insertion phase angle of 205 degrees , near the middle of the post-nominal region. The input pa rame te r s for the CSM-active high apocynthion dwell and the following LM-active coelliptic sequence a r e found in Figure 10. The f i r s t dwell maneuver is performed over LM pericynthion 50 minutes a f t e r i n se r - tion and in se r t s the CSM into a dwell orbi t with an apocynthion altitude of 279 nautical miles . revolutions, then the LM per forms a coelliptic sequence with CSI occurr ing 386 minutes a f te r insertion, CDH at the f i r s t aps i s , and TPI occurr ing a t 478 minutes during the first coelliptic revolution, The predicted Ah would

vectors it is 16 nautical miles. each maneuver a r e presented in Table VII.

Figure 22. shown in F igure 23. CSM, the curvil inear relative motion of the ent i re profile i s meaningless. Therefor'e, the data shown in Figure 23 s t a r t a t 285 minutes af ter i n se r - tion, about 45 minutes before CSM recircularization. The vehicle-to- vehicle range and range ra te a r e shown in Figure 24 as functions of t ime.

The CSM recircular izes af ter two complete dwell

- have been 15 nautical mi l e s below the CSM; however, for these s ta te The maneuvers and state vectors a f te r

The rendezvous timeline with s sunlight/ shadow and MSFN communication blackout t imes i s shown in

The relative motion of the LM with respect to the CSM is Since the LM travels one revolution m o r e than the

In the event of a LM failure during the coelliptic sequence, the CSM can per form the ent i re sequence o r can rescue the LM after the LM-active CSI. of the high apocynthion dwell sequence, the coelliptic sequence rescue data a r e not presented in this report. avail ab1 e.

Since the p r imary purpose of this case i s to i l lustrate the operation

These data have been generated and a r e

7.4 Lift-off 100 Minutes af ter Touchdown

LM lift-off 100 minutes after insertion resul ts in an insertion phase angle of 326.5 degrees ( o r -33.5 degrees) , near the lower l imit of the pre-nominal region. sequence a r e found in Figure 12. The LM per forms a 100-foot p e r second positive horizontal thrust immediately after insertion. This r a i se s the LM apocynthion altitude to about 103 nautical mi les for the given state vectors. The CSM initiates a Hohmann t ransfer to 20 nautical miles 10 minutes l a t e r , and circular izes at the f i r s t pericynthion. The CSM per fo rms a CSI maneuver 236 minutes after insertion, a t the second passage over LM pericynthion. orbi t since CDH i s performed one revolution af ter CSI, again over LM pericynthion. 20 nautical mi les and the LM pericynthion altitude and will be on the o r d e r of 10 nautical miles . f i r s t coelliptic revolution. maneuver are presented in Table VIII. in F igure 25. except Hohmann t r ans fe r circularization. with resDect to the LM is shown in Figure 26.

The input parameters for the p r imary rendezvous

c

The t ransfer orbit between CSI and CDH i s really a phasing

The resultant & is always the difference between

TPI occurs 383. I minutes after insertion, during the The maneuvers and s ta te vectors a f te r each

The rendezvous timeline i s shown

The relative motion of the CSM The CSM i s in contact with MSFN during al l maneuvers

The relative motion ~ ~ I - -

exhibits some oscillation above and below the LM. This i s a resul t of the 0 2 1

relatively high eccentricity of the LM orbit . shown in F igure 27 and also exhibit this oscillation.

The range and range rate are

In case the LM cannot pe r fo rm the required thrust after inser t ion, CSM rescue i s performed using the five impulse extended coelliptic sequence. The input pa rame te r s f o r this sequence a r e found in F igure 13. The coelliptic phasing maneuver , CPM, i s per formed ove r LM apocynthion 71 minutes a f te r insertion. The CSM i s inser ted into a phasing orbi t with an apocynthion altitude of 323 nautical miles. complete revolutions, then pe r fo rms CSI at about 500 minutes after in se r - tion, again over LM apocynthion. pericynthion) and T P I occurs during the f i r s t coelliptic revolution, about 587 minutes after insertion. maneuver are presented in Table IX. The rendezvous t imeline is shown in F igure 28. CPM computation.in the RTCC, and CPM t ransmiss ion and verification before the CSM loses M S F N contact. The relative motion of the CSM with respect to the LM i s shown in F igure 29. orbit i s not shown since presentation in the curvi l inear sys tem is not representat ive of the relative motion. in F igure 30 as functions of t ime.

It s tays in this orbi t t h ree

CDH occurs at the first aps i s (first

The maneuvers and state vec tors after each

There i s sufficient time for LM postinsertion tracking

The m a j o r portion of the phasing

The range and range r a t e are shown

7. 5 Lift-off 116 Minutes after Touchdown

LM lift-off 116 minutes a f te r touchdown resu l t s in an inser t ion phase The angle of 15 degrees , near the upper l imit of the pre-nominal region.

input p a r a m e t e r s for the p r imary rendezvous sequence a r e found in F igure 12. thrust immediately af ter insertion, raising i ts apocynthion altitude to about 103 nautical miles . Ten minutes l a t e r the CSM init iates a Hohmann t ransfer to 20 nautical mi l e s , then c i rcu lar izes at first pericynthion pas - sage. The CSM per forms CSI 2 2 1 minutes after insertion on i t s second passage over LM pericynthion. CDH occurs at the second aps is (first pericynthion) and, a s in Section 7. 4, the resultant Ah i s on the o r d e r of 10 nautical mi les . T P I occurs 383. 1 minutes after insertion, during the f i r s t coelliptic revolution. The maneuvers and s ta te vec tors a f te r each maneuver are presented in Table X. F igure 31. shown in F igure 32. vous technique i s apparent f rom the f igure. and range ra te data of F igure 33.

As in Section 7.4, the LM pe r fo rms a 100-foot p e r second

The rendezvous t imel ine is shown in

The oscil latory motion charac te r i s t ic of this rendez- The relative motion of the CSM with respect to the LM i s

It a lso shows up in the range

If the LM cannot pe r fo rm the required thrust at insertion, CSM rescue is accomplished using the s ix impulse extended coelliptic sequence. input p a r a m e t e r s fo r this sequence are found i n F igure 14. t r ans fe r to a 10-nautical mi le pericynthion altitude occurs 54 minutes after LM insertion, over LM apocynthion. at pericynthion of the Hohmann t r a n s f e r orbit . of the phasing orbit i s 26. 5 nautical mi les . phasing orbi t three and one-half revolutions then, at apocynthion, p e r - f o r m s CSI approximately 502 minutes a f t e r LM insertion. CDH occurs at the f i r s t aps i s ( in this ca se f i r s t pericynthion) and T P I occurs during the f i r s t coelliptic revolution.

The The Hohmann

CPM is per formed 57 minutes later The apocynthion altitude

The CSM remains i n the

The maneuvers and s ta te vec tors after

each maneuver a r e presented in Table XI. . shown in F igure 34. The relative motion of the CSM with respect to the LM is presented in Figure 35, and the vehicle-to-vehicle range and range ra te i s presented in Figure 36. The relative motion appears to indicate that this is not the best possible rendezvous technique. F o r instance, the CSM passes within about 9 nautical mi l e s of the LM 100 minutes af ter insertion, then moves away before completing the rendezvous. It would be possible at this point to inser t the CSM into a stable orbi t with the LM, then per form terminal phase. However, it should be noted that while this could be done for this par t icular phase angle, it could not be performed throughout the pre-nominal phase angle region.

The rendezvous t imeline i s

...

2 3

8. CONCLUSIONS

Rendezvous following LM anytime lift-off can be performed within the cu r ren t performance and t ime constraints. There is CSM rescue capability a f te r a LM fai lure throughout the 360-degree degree phase angle. existing programs. a r e required. miss ion complexity, were discovered during the evaluation of this plan.

The rendezvous techniques used in this plan can be computed on No new systems o r modification of existing sys tems

No problem a r e a s , other than apparently unavoidable

The performance and total time requirements for rendezvous (LM- act ive with CSM assist if specified in the sequence) a r e presented in F igure 37. The independent variable in this ca se is t ime between touchdown and LM lift-off, which is direct ly related to inser t ion phase angle. This f igure is a summary of data presented in F igu res 6, 11, and 12. The maximum CSM SPS impulsive AV requirement of about 625 feet pe r second occur s at the end of the pre-nominal phase angle region (phase angle of 17. 5 degrees) . 131 fee t pe r second occurs at several points in the nominal region. maximum total time to rendezvous of 680 minutes occurs for the three revolution high apocynthion dwell (phase angles f r o m 230 to 325 degrees) .

The maximum LM RCS impulsive AV requirement of The

The performance and total t ime requirements for CSM rescue of a n

This figure is inactive LM a r e presented in Figure 38, again as a function of lift-off t ime during the f i r s t CSM revolution following LM landing. a summary of data presented in Figures 8, 11, 13, and 14. The maximum CSM impulsive AV requirement of 731 fee t pe r second occur s at th ree points in the post-nominal phase angle region (phase angles of 135, 230, and 325 degrees) . as in the LM-active case, occurs throughout the th ree revolution high apocynthion dwell.

The maximum total t ime requirement of 680 minutes,

The multi-impulse rendezvous and rescue techniques used in the p re - nominal region, while satisfying performance and t ime requirements , begin to look l e s s a t t ract ive when studied in detail and compared to waiting until lift-off can occur in the nominal region. show the CSM moving ahead of and behind, and in some cases , above and below the LM. The total time requirement for CSM rescue in this region approaches the 11. 5-hour LM ascent stage lifetime. a r e considerably higher than f o r CSM rescue f r o m the nominal sequence, and the CSM pericynthion altitude goes a s low a s 10 nautical miles . al leviate these problems it is desirable to delay the LM lift-off for a maximum of 18 minutes, allowing it to occur in the nominal region if possible.

The relat ive motion plots

The AV requirements

To

25

2 2 m e 9 . -

Q Q - 4

I ,

. . n m

- I n

0 . 0 o m a m

;i 2 :

- - o m

w w - 4

d d C C - 4

In9 - 0 - * 0 0 g 2 d d

9 . N

I n N

. . - - r~ - - I n - m m 0 0 .

Q I n - -

0

*.I m

0

d

0

m In

I m I u c l

0

N In

Q

0 ?.

tj u

2 2 0.r 9 . d

0 0 9.0 . . I ,

- I n Q N 0.0 m N . . - - 2 z

I ,

9 . v 2 2 w m d d p . r - * -

I n - - m - 0 . o m 0 0 0 0

d d

9 . -

I n * C N

. . - - - -

o r I n N 0 0

4 1 0 . .

0.

9

- r

N In -

H , I u c l

In

?. ?! 9

E c

27

m m

I +-, m .d

0

J k 0 w (I]

a, 5 c Q,

M

28

a

.

:: I d d W

d . n

\ o N m m 2 : o i < 2 -

s a 0 1 d d M

M M - 1 0

I ,

. . - - - I n

010 \ o m M M

-'i 2 7

- - 9 M 0 - m m d d c c - - m a - 0 - d

0 0 8 2 d d

d N

L o w P . N

V I - V I M 00.

I O m

. . - - - - . .

0

m u)

0

d

0

M m

z In2 v c l

0

N

Q m 0

'f.

tj V

m e

r - 0 o m . O N Q 1 0

e - N W

O M 010 - 9 M M

M W Q I O . . - - I ,

e m mom N Q o n :+ N - T - M 0 -

m m d d 2 5

- Q Q O \ o d 0 1 0 0 - 0 0

d d

m w . . V I -

2 : - - - - - M 0.01

I n V I . .

N

i

0'

0.

Lo -

2 m r v - l

0.

0

VI '?. Y. d

E i+

r - Y I - 0

N N 0 0 1 -

i i 5 5

2 2

2 2

m m

0 0 . . I ,

- 0 9 m o m m m . . - -

2 s 0 8

a a 0 0

0 0

c o r n . . 5 5

m a

0 0 0 0 0 0

- - e -

d d

4 N

m d r - P -

m m m m 0 0

. . - m

. -

a- 9'

P-

o o

d

P- N

0

d N

I I n E V J

0

r-

9

m

?. 0

Ir a c

30

L

m o e o - m 9 0 '

c m . .

a m - 0 m a a m . . m m 2 2 I ,

O N - 0 m o . o m . . - - 2 2

Q m 0 - m m d d r - e - - m a g 2 010 0 - 0 0

d d

a Q

m a

Q Q 0 -

m l n

4,. m a

m m

- - - -

r-

hl -

m c

-r

0 N

3 2 v 4

N

ui m - m P

X

N Q m r - m a N Y I

Q t - . .

o m d

o m a 0 m a m m

m m Q Q

. . - - , I

m N m o P O o m

m - . .

2 2

- - m m 0 - m m

d d P t -

* a m a r - - - 0

0 0 d d

P - Q

r - 0 m a 7 6 1

. . - .

2 2 m m u;u;

Q

u) N

m

0

N

m w

B W E v c l

P

0

r-

m

?? -

z &I

o l - 9 0 m - r m - r

O N < G - 2 2 0 . v 7 m

m m a 9

I ,

. . - - - m 90. 0 . 0 ( O N

. . - - 2 ?

- - a m 0 - m m d d I-l- - - r n m

- 9 o r - 0 0 0 0

d d

- r m - 0 m a r - m

m c i m - o m

9 m

. . - .

- .

0

m d

0

0

0

m d

I m I u 4

P

m' ?. r- m -c

;j U

N o . 0.o. 0 0 0 . m m

i o : m r - 4 -

2 % 0 . - - r O

0 0 9 a . . - -

0 ,

m m 0 . 0 . 0 0 N N . . - - m m , ,

- - 9 0 0 0 - m m d d 5 2

- m 0.- d o r - * 0 0 0 0

d d

- m i n ' m m N 9 - - o m

00.

9 r n

d d

- -

N

0 N

m N

0

0 N

I m Z U J

N

N 0

* ?. P

E U n

- 0 O N 0 9 m m

i i N O

d m N O a d m m . . o m a 9

I , - - m m N O . 0 0 V N

- m m ' ;

0 -

0 - m m m m d d 2 5

r - r n 0 - m a

0 0 0 0 m r -

d d

m r n G n ' 0 9 d m

m o o m - 0 . 0 .

- .

;;

9

t- N

0

2

9

m N

P m P u 4

m 9: ?. ?. 0

m

iz I-

o m O d O N o m

do: m m - m

2 2 m b P m

a a I ,

. . m m - - m~

m m r - ' : ' 5

- 0 a 0

- - m m - - m m d d 5 :

O b O b 0 -

0 0 0 - 0 0

d d

P a

r - 7 N b

m a m -

dm' - -

o m . . * m

0

0: m N

0

d

0

0: m hl

3 2 V J

9

m

c?.

- Ln

a

C .d

m N 4

d 4 e .d

U 01

e:

O P P a

P m

Q r N

. a m

0 s ;

f f 0 . m d d . . m m - 4

I ,

m r - c o 0 . N

r - m I -

. . - m m m m m m d d 0 0

c r - - - 0 0 o a 0 0 0 0 . 0 0 0 0

d d

r - 0 d o ' + a N N

m o m - o o

- - - .

a

9 N

0

N -

a 0 N

2 ) : U J

N

m' 0 ?. m

OI

E e

33

N N l - r -

r - d

m o m's'

N

f T m m d d

m m a a . . - -

I ,

m u - a m

< v ;

r - r - 0.-

I r - - a 9 0 0 m m d d r - r - - - 0 0 0 0 0 0 0 0 0 0 0 0

d d

r - N

dm' r - a N N

m m m m 0 0

. -

G.0.

m m 0

N

c N

- d N

E m I U J

m r-'

?.

m m

0.

Lr

w w I c, w .d

0

I4 k 0 w v)

M F: k .d

s k

b 9

a r - I n m 0.6 0.9

N O 9 N

. .

0 m - 0 0 . 0 0 m

O M 9 9 . . * * I ,

- r - a w m N m m

- ' + 5 :

a m 0 - w m d o r - r - - - m r -

o r - O b 0 0

* * * *

d d

0 b

i m ' I n - P . N

V I N I n 0 0 0

9 9

~.

~.

0

0 0 -

0

d

0

0 0 *

m m m u.4

0

N m r- ?

1 d

u 3 cl

O d o a 0 0 0 -

o w . .

m N d

2:: 0 . 0 0 m

o m a .0

I ,

. . * *

r - r -

m N o m - m

i s ' - r -

0 -

- - a m 0 - m m d d -: c

w r - c - 0 - m r - - e 0 0

d d

m v

& i 0 9 N

0 . N M b 0.0

m 9

. .

. .

VI

N VI

m d

m

N m

m m m u - l

0

N VI

9 In -

C

m E

m P vl U

o m

d o '

0 0 O d o m

0 N

2:: 0 . b 0 m

1 0 0 9 9

I ,

. . * *

m r -

:i , e

- w 6 N o m

d

* I

. 0 M 0 - m m . . 0 0 5 :

o r - 0 - 0 - o r - O b 0 0

0 0 . .

N d

& a i -.. 0 . N

m N N 0 0 0 0

I n9

. . - .

m N m

0

d

m hi VI

2 2 u - l

- m ?. m N

E 0

1 m H

a

2 u I

G

0 0 o r - 0 - 0 9

d < m m

2 % 0 . 0 0 m

m m 9 9 . . - - I ,

9 r - r - w l l l N - m

h ; i e 2

- - 9 0 0 - m m d o 2 :

m r -

0 - N e m - ? 0 0

* -

d d

r - b c y1N

9 N - * 0 0

9 9

. . m 2 . . - .

9

9 m

0

d

9

9 m

2 m u - l

-0

VI

m

?.

Li U

- m

r - N 0 - 0

r - m m I n

m - r

. . o m

0 0 - 0

0.- 0 0

m M 9 1 0 . . - -

I ,

m r -

* N m I n 0 . m

i i 2 5

- - 9 0 0 - m m d d c e

\ o r - % = 9 - 0 0 0 0

d d

m - r . . 2 2 0 N

0 0 - 0

9 9

. . m~

. .

- 0 b

9

0:

0.

m' 0

W m u - l

m N

0

e

P T

I U n

3 4

E I - -

$ 2 0 1 0 o o l

N "I 0 ;

W M - 0 e * u - M

e m I \ O

. . d

- N - 0 0 0 m m 0:

r;r;

- - a m 0 - m m d d r;r;

a d f ' s r o

d d - 0

0 .a

I n 9 1 O d

9.0 a -

m m '

- . m m - - \ O m

c

\O 0 M

91

d

c d m

W E u r l

m

T. "I

c In

N

E U

m o l 0 0 d d d o

c 0 " - 2 2 o l d d M

W M \ O I c

I t

. .

r~ m a N O m m . . - - 2 5

- - a m 0 - m m

d d c r ;

m d 2's 2 0 d o 0 0

M a

o m m 9 1 o l d

. .

. . r a m - u - m

m m . .

- d Q m

0

0

- d a m

H m B u - l

CI

4 0 r 0 0

3 U

0.0 o m W N

m m m m

m m

& <

2 g o l d d M

m m \ O \ O . . - *

0 ,

- N - 0 m o \ O m . . - - c - 5

..- a m 0 - m m

d d 2 5

a d M 0's 0 0 d d 0 0

- 9 . . r m

m a r -

N d a d -~ m m m m . .

W

a N

- d

W

N 9'

B m H u - l

In

0 T. 4: - -

2:

V n

35

w w I

.VI

0

G 4 k 0 w VI 1 0 > N a, a I: a,

4 4 k a, c,

2 k r J Y $

o m o m o m o m

do' m o - N

2 2 0 - b b m

m m a a I ,

. . - *

0 -

- N m m m m

N i

b E

- 4

a m 0 - m m d d c c - *

2 5 0 - 0 - O b 0 0

0 0 . .

- b

c ' w - * 0 . N

m N N b - .

m o . - m a

m N m

0

d

m N m

a m P u - l

0

m ?. 0

m d

C 0 a

m

w

- 3 u

U

o m O P O N o m

0 -

m

. . - b m - 0 0 . b b o

o m a a . . - -

I ,

0 - c

O N o m - m

" 4 5 5

- - a m 0 -

m m d d e e * -

% E 0 . - a c 0 - - 0

d o

a b w i m - 9 N

- N N P m o

* a

. . - -

0

b

N m

0

0

m

i m N

W P u - l

VI

c 0 d m

zi U

36

m - m c a m m o

i d m e

m m N O P b m m

o m 9 9 . . - - I ,

- e

b N e m o m

i i 2 :

2 ; ; m m d d 5 2

- -

2 : m - m c b d 0 0

d d

m b . . z 2 O N

0 . N a b 0 0

a a

- . ~.

d c

t-

0

0-

i *

W a u c l

N

01. m

N

?. m

E b

- 0 c c m m o m

d d 0 0 N N

N m 0 0

2 2 2 2 . .

m m

0 8

9 c

N N m L n m m

ii c c - - - - o m * - m m d d e c

E 2 - - c c

d o b b 0 0

0 . b

dm' 4 -

N N

N N b b 0 0

- .

.n-G

0

m N

m

m N

m - -

a m a u - l

N

d ?. 0 0.

h a h

0

s x i,( > 2 3

o m o m m m 010 o m m e O Q 0 0 1 00. o m 0 9 o c

m e m m e - - o w - du; do: 69 '

m N m~

o m o m N - h i ; 5 2 r ;c ;

0 0 m o - 0 0 0 . .

a m 0 - m m

0 0 c e - - m d Q -

0 0

m d

6 2 d d

Q Q

- m - - r m d

C Q 0 -

. . - . m m . . m m

Q

Q d

0

d

Q

9' Y

E 25:

0 * ?. 'I! d

m

o m m m r - - m o - 0 o m o r - m m d < m ' < : Y W

O N O N - 0 0 0 m o 0 0 r O W N W . . . .

- - 0 - Q m 0 . m 0 - 0 - m m m m

et- r - c d d d d - - - -

61 0 . -

0 0 0

0 0 0

4 S S - d d o

0 . 0

i d - -

37

w U Z 3 U

I! o-

0 U

w

W v)

I-

-I -I W

W v) -I 3 n 2 - lx 3 2

F

w

I- > U

-

2 -I

Ln w U Z 3 0

W

w v)

m 3

9 ! Z w e w 3 s;'

h

(3 x u

W 4 (3 Z a W

n : Z Q

z I- ce W Ln

rn Q)

H a, 5 u rn

2 9 a

rn 3 0

a, a s

.rl M

2

38

n

- .

3 9

4

- J

a, a

w 0

cr)

a, k 5 M sz

4 1

7-

Figure 4. Decision Flow Logic for Rendezvous Following Anytime Lift -off

-

W A N D C S M W I H l f C I N T U C K I N G AS SOON AS CONTACT I S 1STAlLISHtD

M S f N CfIflUINIS TIM1 O i CSI. T H l t OF TQl. ANDCDH APSIS. AND l # A N Y I T S lHul TO

AND IN IHt 1TCC IAMS P@OGRWI

42

Q t

THE LM PERFORMS A 100-FPS "CANNED" MANEUVER IMMEDIATELY AFTER INSERTION.

I I

IO-MIN POSTMANEUVER TRACKING BY MSFN. LM ORBIT DETERMINATION.

t

MANEUVER A N D IS INSERTED INTO

MANEUVER A N D CIRCULARIZES AT PERICYNTHION.

I I

MSFN CHOOSES TIMES O F CSI A N D TPI SO THAT CSI OCCURS OVER LM PERICYN- THION A N D TPI OCCURS 450 DEG LATER.

I 1

COMPUTE THE CSM-ACTIVE CSI MANEUVER ON BOARD THE CSM KOLOSSUS P32). I

THE CSM PERFORMS CSI OVER I LM PERICYNTHION. I COMPUTE CDH MANEUVER ON BOARD THE CSM KOLOSSUS P331. .

THE CSM PERFORMS CDH OVER LM PERICYNTHION, ONE REVOLUTION

OVER THE LM APOCYNTHION. THE CSM 1s INSERTED INTO A 60-N MI BY 10-N MI ORBIT.

i

1

COMPUTE THE CSM-ACTIVE CPM MANEUVER IN THE RTCC (ARRS), A N D TRANSMIT I T TO THE CSM.

THE CSM PERFORMS CPM OVER THE LM APOCYNTHION. THE CSM WILL REMAIN IN THIS HIGH PHASING ORBIT FOR THREE REVOLUTIONS.

I

COMPUTE THE CSM-ACTIVE CSI MANEUVER ONBOARD THE CSM (COLOSSUS P32).

THE CSM PERFORMS CPM OVER THE LM PERICYNTHION. THE CSM WILL REMAIN IN THIS LOW PHASING ORBIT FOR 3.5 REVOLUTIONS.

1 LM APOCYNThlON.

COMWTE THE CSM-ACTIVE CDH MANEUVER ONBOARD THE CSM (COLOSSUS P33).

THE CSM PERFORMS CDH OVER LM PERICYNTHION.

THE LM IS POWERED UP, IF POSSIBLE.

I

I t

COMPUTE LM-ACTIVE TPI MANEUVER OD., BOARD THE LM (LUMINARY P34).

I 1

COMPUTE CSM-ACTIVE TPI MANEUVER TO OCCUR AFTER THE LM MANEUVER TIME (COLOSSUS P34).

Figure 4. Decision Flow Logic for Rendezvous Following Anytime Lift -off (Continued)

I THE MIDCOJRSE CORRECTION A N D B R A C h G MANEUVERS WILL BE PERFORMED BY THE LM WHENEVER POSSIBLE. THE CSM WILL ACT AS

=UP O N L Y , I

4 3

I-

d

22

20

18

16

14

12

IO

8

6

APSIS CROSSING AT WHICH CDH IS PERFORMED

TIME FROM INSERTION TO THE CSI MANEUVER (MINI

PHASE ANGLE AT CM INSERTION (DEG)

Figure 5. Input P a r a m e t e r s and Resultant Coelliptic Differential Altitude for the LM-Active Four Impulse Coelliptic Sequence

44

..

5 a

2 30 10 20 30 40 50 60 70 80

PHASE ANGLE AT LM INSERTION (DEG)

Figure 6. Per formance and Time Requirements f o r the LM- Active Four Impulse Coellipti c Sequence

45

-7

t-1+3+l+3+~-t3i

APSIS CROSSING AT WHICH CDH IS PERFORMED

TIME FROM INSERTION TO THE CSI MANEUVER ( M I N )

20

18

16

14

12

10

8

6

4

2

Figure 7. Input P a r a m e t e r s and Resultant Coelliptic Differential Altitude f o r the CSM- Active Four Impulse Coelliptic Sequence

46

Z 0

z c PI Y VI

VI 0 Y - E i5 9 PI > 2

2 P

>

VI n. LL I

U n LL

9

9

n I 3

W

PI

>

n I 3

Y

9 PI >

I60

I50

140

I30

I 20

I IO

100

10 20 30 40 50 60 70 80

PHASE ANGLE AT LM INSERTION

F i g u r e 8. Per formance and Time Requirements for the CSM-Active Four Impulse Coellipt ic Sequence

47

IO 20 30 40 50 60 70 80 PHASE ANGLE AT Lh4 INSERTION PEG)

Figure 9. Performance, Time and Coelliptic Differential Altitude f o r

48 LM-Active CSI, CSM Rescue

600

500 z v) W

s 400 OL W

> 3 300 Z Q s -I 200

0

TIME OF TPI MANEUVER (MIN)

= 350 5

300 t Fl

2 F 250 2 0 200 E

B 2 100

Z

f 150 V

- m &

50

60 EO 100 170 140 160 180 900 720 240 260 380 300 320 340 INSERTION PHASE ANGLE (DEG)

NOTES: ( 1 ) CSI IS PERFORMED 50 MIN AFTER

LM PERICYNTHION, (2) COELLIPTIC DIFFERENTIAL ALTITUDE

IS 15 N MI. (3 ) TPI I S PERFORMED 90 DEG WEST OF

LM PERICYNTHION.

F i g u r e 10. Input P a r a m e t e r s f o r the CSM High Apocynthion Dwell Followed by LM- Active Coelliptic Sequence

49

1-46 568 & 68O--l

TOTAL RENDEZVOUS

TIME (MIN)

t-1+2+3+ DWELL

REVOLUTIONS

700

v, a! w > 3 500 Z Q 3 400

W

-4 -4 W

2 300

200 > Q

0 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

INSERTION PHASE ANGLE (DEG)

REQUIRES 127 FPS 2) CSM RESCUE REQUIRES

Figure 11. Performance and Time Requirements fo r the CSM High Apocynthion Dwell Followed by LM-Active Coelliptic Sequence

50

400 c.- v) Q

5 300

D Z Q -100

- 200 -40 -30 - 20 -10 0 10 20

240 z ’ - 230 - z 6 220

i= 210

LLI

2

700

600

-I

300 5

200 P

100


NOTES: (1) THE LM PERFORMS A 1OO-fPS HORIZONTAL

(2) THE CSM INITIATES A HOHMANN TRANSFER MANEUVER IMMEDIATELY AFTER INSERTION.

TO A 20-N MI CIRCULAR ORBIT 10 MIN AFTER THE LM MANEUVER.

(3) THE CSI MANEUVER I S PERFORMED AT THE SECOND PASSAGE OVER LM PERICYNTHION.

(4) THE CDH MANEUVER I S PERFORMED AT THE , . , . . . - - SECOND APSIS.

(5) THE COELLIPTIC DIFFERENTIAL ALTITUDE Is IO N MI.

AFTER INSERTION. (6) THE TPI MANEUVER IS PERFORMED 383.1 MIN

Figure 12. Input Pa rame te r s and Per formance Requirements for CSM- Active Rendezvous Following a Planned LM Thrust at Insertion

5 1

- 80

2 2

z 70

- L U

8 60 w 2 F 50

Z Q 380

Z- cs 360

oz %E 340 +n st 0= 320 04 z 2 300

g 750

>

E

-3

I a - U v

a 700

2 J

9 650

-340

A

Lo a u. -360

> ‘.I

v

- -380

-400

360

5; 340 a L L v

> \, 320 2 a

300

28 0 .40 -30 - 20 -10 0

LM AHEAD INSERTION PHASE ANGLE IDEG)

INSERTION 2) TPI OCCURS 587 M I N AFTER LM

INSERTION 31 TOTAL RENDEZVOUS TIME I S - I -

677 MIN 4) CDH AV = -20 FPS 5) Ah = 15 N M I I

F igure 13. Input P a r a m e t e r s and Pe r fo rmance Requirements for the CSM-Active F ive Impulse Extended Coelliptic Sequence ,

5 2

120 - U Z O r w-I15

22 v

110

200

c; 180

$ 160

Q U v

-J

;r Q 140

120

- -30 L 2 -50

5 n V -70

VI n

0 5 10 15 20


NOTES: I ) CSM HOHMANN TRANSFER ORBIT IS

3) CSI OCCURS 502MlN AFTER LM INSERTION 4) CSI AV = 14 FPS 5 ) TPI OCCURS 586 M IN AFTER LM INSERTION 6 ) TOTAL RENDEZVOUS TIME I S 677 MIN 7) A h = I O N M I

60 N M1/10 N MI 2) HOHMANN TRANSFER AV = -69 FPS

F i g u r e 14. Input P a r a m e t e r s and Performance Requirements fo r the CSM- Active Six Impulse Extended Coelliptic Sequence

5 3

360

330

300

270

-7

L

h w lA

2 w

$ 150 6 w lA

90

60

30

0 0 20 40 60 80 100

TIME FROM LM TOUCHDOWN TO LIFT-OFF (MIN)

1 20

Figure 15. Insertion Phase Angle as a Function of Lif t -off T ime

54

a c Q,

P;

55

8 d

0 v) c)

0 5 0 m pc;

M d

.r(

6( n Z I m

- w

0 0 v)

0 0 0 R c) w 0

M0139 Wl ( I W N) l N 3 W 3 3 V l d S l a lV311t13A t1V3NIl IA8i l3

56

400

w 2

2 200

? 9

I Y

I Y -I

u 100 I > Y

0 0 50 100 150 200 250 300 350

ELAPSED TIME FROM LM INSERTION (MIN)

Figure 18. Range and Range Rate During Rendezvous Following Lift-off at L M Touchdown

57

- z--

3 4

Y 0--

rn a,

b r(

w w I 0

el j"

B 0 d d 0 cr

a; d

a, k 5

a

a

& CZI .d

58

.

0 0 M o l 3 8 W l - 0

hl 0 c3

0 Tf

( I W N) lN3W33VldSla lV'311V3A VV'3NIlIAVn3

59

0 0 Tf -

0 0 hl c

0 0 0 -

0 0 03

0 0 9

0 0 Tf

0 0 -n

Z I m

- w

2 -1

0

W J

I!

? 400 I W

I W J

I! $ 600

1200

1000

h - 3

800 W

(3 Z 25 W -1

9 600 r W

? P W

400 I w >

200

0 0 100 200 300 400 500

ELAPSED TIME FROM LM INSERTION (MIN)

600

Figure 21. Range and Range Rate During Rendezvous Following Lift-off 17 Minutes After LM Touchdown

6 0

a

a

w w 0 I

1 0 > N

a, k 1 M

a 6 1

0 0 0 0 0 UJ M o l 3 9 W l Ir,

( I W N) lN3W33V ldS Ia iV311t13A t1V3NlGAdn3

a3

0 0 h

0 0 9

0 0 0

0 0 *

0 0 c3

0 0 64

0 0 -n

Z I m

- W

2 --I

0

.

6 2

a

0

0

100

200

300

400

500

600

7 00

800

900

lo00

600

500

400

300

200

100

0 300 350 400 450 500 55 0

ELAPSED TIME FROM INSERTION (MIN)

Figure 24. Range and Range Rate During Rendezvous Following Lif t -off 60 Minutes After L M Touchdown

6 3

a I3

4 c k a,

42 w rd m a,

42 1 F1 2 0 0 d

3 0

p;' k 0 w a, F:

.r(

a

a 64

a .

w > U

v

s 3

3 3 w m

z v) v

100 0 100 200 300 400 500 600 700 CSM AHEAD CSM BEHIND

CURVILINEAR HORIZONTAL DISPLACEMENT (N M I )

Figure 26. Relative Motion (Curvilinear, LM- Centered) During Rendezvous Following Lift-off 100 Minutes After LM Touchdown

6 5

600

400

200

0

200

400

600

800

1000

c4 - 2 Z

(3 Z

v

w

s w -I u I w > t, I- I

w -J V I > - w

700

600

5 00

400

300

200

100

0 0

F i g u r e 27. Range and Range Rate During Rendezvous Following Lift-off 100 Minutes After LM Touchdown

66

1 00 200 300 400


500

a NO lt L IIGHTIIIC, C COMMLINICAllON5 C PM

I I

CI1

I I

CDH I I

T P I I I

I P I

. Figure 28. Timeline for CSM Rescue Following Lift-off 100 Minutes

af ter LM Touchdown

0 67

2 3 A O W WS3 0 0 0 0 0 N 2 -

( I W N) l N 3 W 3 3 V l d S l a lV31113A 1 V I N I l I A 1 n 3

68

a

a .

w -I u I Y

? 400

w -I

2 I > Y

600

800

1000

800

604

400

200

0 400 45 0 500 550 600 650

ELAPSED TIME FROM LM INSERTION WIN)

Figure 30. Range and Range Rate During CSM Rescue Following Lift-off 100 Minutes After LM Touchdown

69

- u - - u - I w. U

c a h -- I - u -

- 3

0 .” a

0 !3

a, w 2

N Q, 5 c, a, P; k 0 w a, d

.A 4

.A E H

.

e

.

70

a

a

.,

a

0

z

7 1

lo00

800

600

400

200

0

200

400

600

800

1000

1 200

900

800

h - 2 700

$ 600 5.

5 w 500 I! w 400

-1

I

? e ,,’, 300

I! I UJ 200 >

-1

100

0 0 100 X)O 300 400 500

ELAPSED TIME FROM INSERTION

Figure 3 3 . Range and Range Rate During Rendezvous Following Li f t - 116 Minutes After LM Touchdown

off

7 2

c

N O T E 1 LlGHllNG C COMMUNICATIONS

INSERTION I I

C SM nOnMANN MINEUVER

I 1

iiMt FROM ToucnmwN I H R MINI

C PM

I I

C S I C DH 1:' , I I I I I I

1 CSM ~1

I P F

Figure 34. Timeline for CSM Rescue Following Lift-off 116 Minutes af ter L M Touchdown

e 7 3

0 v)

n Z

m

- 5

0

z= *Z V-

w

w z U

0 0 m

0 0 0 0 m * O m rn 0 -

3AOBV W S 3 Mol38 WS3 ( I W N) l N 3 W 3 3 V l d S l a lV311t13A t1V3NlllAt1n3

M C .rl

B

k

0

0 4 4

a,

z r/l u M C k

.rl

d

a' h

.

74

(I))

f' 150 r z - s 2 Z

w 100 - 4

P Y -I u w 50 >

0 0 100 200 300 400 500 600 700


F i g u r e 36. Range and Range Rate During CSM Rescue Following Lift-off I 1 6 Minutes After LM Touchdown

7 5

800

7 00

600

500

400

300

300

100

0

800

700

600

500

400

300

200

100

0

. , . , & . . ( , .. . ......,..,. *.* .... ( . ..,. - . . * .... ... ,. . . a . . - - . . . _ _ , . . . . I .,... I . , A e . . & .... * . - . 4 ..__.

0 10 '20 30 40 50 60 70 80 90 100 110 120

TIME FROM TOUCHDOWN TO LIFT-OFF (MIN)

.

Figure 37. Per formance and Time Requirements fo r Rendezvous Fol lowing Anytime LM Lift -off.

.

8 00

7 00

600

5 00

406

300

200

100

0

8 00

7 00

0 10 20 30 40 50 60 70 80 90 100 110 120

TIME FROM TOUCHDOWN TO LIFT-OFF (MIN)

Figure 38. Performance and Time Requirements for CSM Rescue Following Anytime LM Lift-off

77

REFERENCES

1.

2.

. 4.

Lloyd, E . , Diamond, R. M. , et a l . , "Paramet r ic Analysis of Lunar Orbi t P h a s e Abort and Rescue Techniques, 31 July 1968.

MSC IN 68 -FM- 185,

Diamond, R. M. , "Evaluation of CSM Rescue for the Lunar Mission Using the M i r r o r Image Coelliptic Sequence with Maneuver Timing and Velocity Biases , I ' TRW Letter 3421.7-169, 17 October 1968.

Tindall, H. W., J r . , "G Rendezvous Mission Techniques, I ' MSC Memorandum 68-PA-T-202A, 23 September 1968.

"Task Agreement fo r the Development of Lunar Orbi t P h a s e Abort and Rescue Procedures , Task MSCITRW A-159, Amendment No. 2, ' I

17 September 1968.

79

n.:.:.:.:.:.:.:.:.:.:. ;;;e- - ibibliothe lm ascent and rendezvous profiles are being continually...

Documents