Source Code

These source-code files derive from a printout of Luminary 116 (the Apollo 12 Lunar Module guidance computer program), from the personal library of original AGC developer Don Eyles, digitally photographed at archive.org, financially sponsored by Ron Burkey, and transcribed to source code by a team of volunteers. This colorized, syntax-highlighted form was created by assembling that transcribed source code. Note that the full page images are available on the Virtual AGC project page at archive.org, while reduced-size images are presented at the VirtualAGC project website. Report or fix any transcription errors at the Virtual AGC project code repository.

Notations on the program listing read, in part:

	GAP:  ASSEMBLE REVISION 116 OF AGC PROGRAM LUMINARY BY NASA 2021112-071
	19:09 AUG. 11,1969
Note that the date is the date of the printout, not the date of the program revision.

053306,000002:                                                                                                  ## Copyright:   Public domain.
053307,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
053308,000004:                                                                                                  ## Purpose:     A section of Luminary revision 116.
053309,000005:                                                                                                  ##              It is part of the source code for the Lunar Module's (LM) 
053310,000006:                                                                                                  ##              Apollo Guidance Computer (AGC) for Apollo 12.
053311,000007:                                                                                                  ##              This file is intended to be a faithful transcription, except
053312,000008:                                                                                                  ##              that the code format has been changed to conform to the
053313,000009:                                                                                                  ##              requirements of the yaYUL assembler rather than the
053314,000010:                                                                                                  ##              original YUL assembler.
053315,000011:                                                                                                  ## Reference:   pp. 1258-1273
053316,000012:                                                                                                  ## Assembler:   yaYUL
053317,000013:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
053318,000014:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
053319,000015:                                                                                                  ## Mod history: 2017-01-22 MAS  Created from Luminary 99.
053320,000016:                                                                                                  ##              2017-02-09 RRB  Updated for Luminary 116.
053321,000017:                                                                                                  ##              2017-03-14 RSB  Proofed comment text via 3-way diff vs
053322,000018:                                                                                                  ##                              Luminary 99 and 131.
053323,000019:                                                                                                  ##              2017-03-16 RSB  Comment-text fixes identified in 5-way
053324,000020:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
053325,000021: 

Page 1258

053327,000023:                                                                                                  #           THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES. THE TFF ROUTINES NEVER
053328,000024:                                                                                                  #  KNOW WHICH ORIGIN APPLIES. IT IS THE USER WHO KNOWS, AND WHO SUPPLIES  RONE, VONE AND 1/SQRT(MU)  AT THE
053329,000025:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
053330,000026: 
053331,000027:                                                                                                  #        EARTH ORIGIN    POSITION        -29     METERS
053332,000028:                                                                                                  #                        VELOCITY        -7      METERS/CENTISECOND
053333,000029:                                                                                                  #                        1/SQRT(MU)      +17     SQRT(CS SQ/METERS CUBED)
053334,000030: 
053335,000031:                                                                                                  #        MOON ORIGIN     POSITION        -27     METERS
053336,000032:                                                                                                  #                        VELOCITY        -5      METERS/CENTISECONDS
053337,000033:                                                                                                  #                        1/SQRT(MU)      +14     SQRT(CS SQ/METERS CUBED)
053338,000034: 
053339,000035:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE. IN ALL CASES,
053340,000036:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28). PROGRAM  TFF/CONIC  WILL GENERATE VONE/RTMU AND
053341,000037:                                                                                                  #  LEAVE IT IN VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
053342,000038:                                                                                                  #           THE USER MUST STORE THE STATE VECTOR IN  RONE, VONE  AND MU IN  THE FORM 1/SQRT(MU) IN  TFF/RTMU
053343,000039:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING  TFF/CONIC. SINCE  RONE, VONE  ARE IN THE EXTENDED VERB STORAGE AREA,
053344,000040:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
053345,000041:                                                                                                  #           PROGRAMS     CALC/TFF  AND  CALC/TPER  ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
053346,000042:                                                                                                  #  RADIUS. THIS RESTRICTION CAN BE REMOVED BY A  15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
053347,000043: 
053348,000044:                                                                                                  #           THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
053349,000045: 
053350,000046:                                                                                                  #                                        BELOW   E:  IS USED FOR EARTH ORIGIN SCALE
053351,000047:                                                                                                  #                                                M:  IS USED FOR MOON  ORIGIN SCALE
053352,000048: 
053353,000049:                                                                                                  # TFFSW          =       119D    BIT1    0 = CALCTFF             1 = CALCTPER
053354,000050: 10,2213                        TFFDELQ            =        10D                                   #  Q2-Q1                   E: (-16)  M: (-15)
053355,000051: 10,2213                        RMAG1              =        12D                                   #  ABVAL(RN)  M            E: (-29)  M: (-27)
053356,000052:                                                                                                  # RPER           =       14D             PERIGEE RADIUS  M       E: (-29)  M: (-27)
053357,000053: 10,2213                        TFFQ1              =        14D                                   #  R.V / SQRT(MUE)         E: (-16)  M: (-15)
053358,000054:                                                                                                  # SDELF/2                                SIN(THETA) /2
053359,000055: 10,2213                        CDELF/2            =        14D                                   #  COS(THETA) /2
053360,000056:                                                                                                  # RAPO           =       16D             APOGEE RADIUS  M        E: (-29)  M: (-27)
053361,000057: 10,2213                        NRTERM             =        16D                                   #  TERMINAL RADIUS  M      E: (-29+NR)
053362,000058:                                                                                                  #                          M: (-27+NR)
053363,000059: 10,2213                        RTERM              =        18D                                   #  TERMINAL RADIUS  M      E: (-29)  M: (-27)
053364,000060: 10,2213                        TFFVSQ             =        20D                                   #  -(V SQUARED/MU)  1/M    E: (20)   M: (18)
053365,000061: 10,2213                        TFF1/ALF           =        22D                                   #  SEMI MAJ AXIS  M        E: (-22-2 NA)
053366,000062:                                                                                                  #                          M: (-20-2 NA)
053367,000063: 10,2213                        TFFRTALF           =        24D                                   #  SQRT(ALFA)              E:(10+NA) M: (9+NA)
053368,000064: 10,2213                        TFFALFA            =        26D                                   #  ALFA  1/M               E:(26-NR) M: (24-NR)
053369,000065: 10,2213                        TFFNP              =        28D                                   #  SEMI LATUS RECTUM  M    E: (-38+2 NR)
053370,000066:                                                                                                  #                          M: (-36+2 NR)
053371,000067: 10,2213                        TFF/RTMU           =        30D                                   #  1/SQRT(MU)              E: (17)   M: (14)
053372,000068: 10,2213                        NRMAG              =        32D                                   #  PRESENT RADIUS  M       E: (-29+NR)
053373,000069:                                                                                                  #                          M: (-27+NR)
053374,000070: 10,2213                        TFFX               =        34D                                   
053375,000071: 10,2213                        TFFTEM             =        36D                                   #  TEMPORARY

Page 1259

053377,000073:                                                                                                  #                REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
053378,000074:                                                                                                  #                INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES. THEY ARE ESTAB-
053379,000075:                                                                                                  #                LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
053380,000076:                                                                                                  #                SUBROUTINES.
053381,000077:                                                                                                  #                -NR                             C(X1) = NORM COUNT OF RMAG
053382,000078:                                                                                                  #                -NA                             C(X2)= NORM COUNT OF SQRT(ABS(ALFA))
053383,000079: 

Page 1260

053385,000081:                                                                                                  #  SUBROUTINE NAME:     TFFCONIC                                            DATE:    01.29.67
053386,000082:                                                                                                  #  MOD NO:  0                                                               LOG SECTION:    TIME OF FREE FALL
053387,000083:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053388,000084:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE: 11 APR 67
053389,000085:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE: 21 NOV 67       ADD MOON MU.
053390,000086:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE: 21 MAR 68       ACCEPT DIFFERENT EARTH/MOON SCALES
053391,000087:                                                                                                  #  FUNCTIONAL DESCRIPTION:      THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
053392,000088:                                                                                                  #           SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA. THE PARAMETERS ARE LISTED UNDER OUTPUT.
053393,000089:                                                                                                  #           THE EQUATIONS ARE
053394,000090:                                                                                                  #                  -   -  -
053395,000091:                                                                                                  #                  H = RN*VN                                               ANGULAR MOMENTUM
053396,000092:                                                                                                  #                        - -
053397,000093:                                                                                                  #                  LCP = H.H / MU                                          SEMI LATUS RECTUM
053398,000094:                                                                                                  #                                -  -
053399,000095:                                                                                                  #                  ALFA = 2/RN - VN.VN / MU                                RECIPROCAL SEMI MAJ AXIS, SIGNED
053400,000096: 
053401,000097:                                                                                                  #           AND ALFA IS POS FOR ELLIPTIC ORBITS
053402,000098:                                                                                                  #                        0  FOR PARABOLIC ORBITS
053403,000099:                                                                                                  #                       NEG FOR HYPERBOLIC ORBITS.
053404,000100:                                                                                                  #           SUBROUTINE ALSO COMPUTES AND SAVES RMAG.
053405,000101:                                                                                                  #  CALLING SEQUENCE:
053406,000102:                                                                                                  #           TFFCONIC  EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
053407,000103:                                                                                                  #           1/SQRT(MU). PROGRAM WILL SAVE IN  TFF/RTMU  . THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
053408,000104:                                                                                                  #           ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
053409,000105:                                                                                                  #           VONE  AT PROPER SCALE. THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
053410,000106:                                                                                                  #           TFF ROUTINES.
053411,000107:                                                                                                  #           ENTRY POINT  TFFCONMU  EXPECTS THAT  TFF/RTMU  IS ALREADY LOADED.
053412,000108:                                                                                                  #           TO SPECIFY MU:      DLOAD   CALL               IF MU ALREADY STORED:    CALL
053413,000109:                                                                                                  #                                       YOURMU  1/RTMU       E:(17) M:(14)                TFFCONMU
053414,000110:                                                                                                  #                                       TFFCONIC
053415,000111:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
053416,000112: 
053417,000113:                                                                                                  #  SUBROUTINES CALLED:  NONE
053418,000114:                                                                                                  #  NORMAL EXIT MODES:  RVQ
053419,000115:                                                                                                  #  ALARMS:  NONE
053420,000116:                                                                                                  #  OUTPUT:  THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
053421,000117:                                                                                                  #           RMAG1  E:(-29) M:(-27) M  RN, PRESENT RADIUS LENGTH.
053422,000118:                                                                                                  #           NRMAG  E:(-29+NR)      M  RMAG, NORMALIZED
053423,000119:                                                                                                  #                  M:(-27+NR)
053424,000120:                                                                                                  #           X1                     -NR, NORM COUNT
053425,000121:                                                                                                  #           TFFNP  E:(-38+2NR)     M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.       FOR VGAMCALC
053426,000122:                                                                                                  #                  M:(-36+2NR)
053427,000123:                                                                                                  #           TFF/RTMU E:(17)  M:(14)        1/SQRT(MU)
053428,000124:                                                                                                  #           TFFVSQ E:(20)  M:(18) 1/M    -(V SQ/MU): PRESENT VELOCITY,NORMLIZED.    FOR VGAMCALC
053429,000125:                                                                                                  #           TFFALFA  E:(26-NR)    1/M    ALFA, WEIGHTED BY NR
053430,000126:                                                                                                  #                    M:(24-NR)
053431,000127:                                                                                                  #           TFFRTALF  E:(10+NA)   SQRT(ALFA), NORMALIZED
053432,000128:                                                                                                  #                     M:(9+NA)

Page 1261

053434,000130:                                                                                                  #           X2                    -NA, NORMCOUNT
053435,000131:                                                                                                  #           TFF1/ALF  E:(-22-2NA) SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
053436,000132:                                                                                                  #                     M:(-20-2NA)
053437,000133:                                                                                                  #           PUSHLOC AT PDL+0
053438,000134:                                                                                                  #           THE FOLLOWING  IS STORED IN GENERAL ERASABLE
053439,000135:                                                                                                  #           VONE'  E:(10)  M:(9)   V/RT(MU), NORMALIZED VELOCITY
053440,000136:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053441,000137:                                                                                                  #           RONE   E:(-29)  M:(-27)  M      STATE VECTOR                LEFT BY CALLER
053442,000138:                                                                                                  #           VONE   E:(-7)   M:(-5)   M/CS   STATE VECTOR                LEFT BY CALLER
053443,000139:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)      1/RT(CS SQ/M CUBE)            IF ENTER VIA  TFFCONMU.
053444,000140:                                                                                                  #  DEBRIS:  QPRET,    PDL+0 ... PDL+3
053445,000141: 
053446,000142: 33,3762                                           BANK     33                                    
053447,000143: 27,2000                                           SETLOC   TOF-FF                                
053448,000144: 27,2000                                           BANK                                           
053449,000145: 
053450,000146: 27,3360                                           COUNT*   $$/TFF                                
053451,000147: 
053452,000148: 27,3360           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)       E:(17)    M:(14)
053453,000149: 
053454,000150: 27,3361           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
053455,000151: 27,3362           02207                                    RONE                                  #  SAVED RN.  M     E:(-29)   M:(-27)
053456,000152: 27,3363           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
053457,000153: 27,3364           00045                                    36D                                   #  MAGNITUDE
053458,000154: 27,3365           00015                           STORE    RMAG1                                 #  M    E:(-29)    M:(-27)
053459,000155: 
053460,000156: 27,3366           77701                           NORM                                           
053461,000157: 27,3367           00047                                    X1                                    #  -NR
053462,000158: 27,3370           24041                           STOVL    NRMAG                                 #  RMAG  M   E: (-29+NR)  M: (-27+NR)
053463,000159: 27,3371           02215                                    VONE                                  #  SAVED VN.  M/CS   E: (-7)   M: (-5)
053464,000160: 27,3372           77761                           VXSC                                           
053465,000161: 27,3373           00037                                    TFF/RTMU                              #  E: (17)   M: (14)
053466,000162: 27,3374           02170                           STORE    VONE'                                 #  VN/SQRT(MU)   E: (10)   M: (9)
053467,000163: 
053468,000164: 27,3375           47361                           VXSC     VXV                                   
053469,000165: 27,3376           00041                                    NRMAG                                 #  E: (-29+NR)  M: (-27+NR)
053470,000166:                                                                                                  #  UR/2 FROM PDL
053471,000167: 27,3377           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR)  M:(-18+NR)
053472,000168: 27,3400           14035                           STODL    TFFNP                                 #  LC P  M   E:(-38+2NR) M:(-36+2NR)
053473,000169:                                                                                                  #  SAVE ALSO FOR VGAMCALC
053474,000170: 27,3401           06514                                    TFF1/4                                
053475,000171: 27,3402           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M   E:(26-NR)   M:(24-NR)
053476,000172: 27,3403           00041                                    NRMAG                                 #  RMAG  M   E:(-29+NR)  M:(-27+NR)
053477,000173: 27,3404           02170                                    VONE'                                 #  SAVED VN.   E:(10)    M:(9)
053478,000174: 27,3405           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
053479,000175: 27,3406           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)   E:(20)   M:(18)
053480,000176:                                                                                                  #  SAVE FOR VGAMCALC
053481,000177: 27,3407           43257                           SR*      DAD                                   

Page 1262

053483,000179: 27,3410           20573                                    0          -6,1                       #  GET -VSQ/MU   E:(26-NR)  M:(24-NR)
053484,000180: 27,3411           77626                           STADR                                          
053485,000181:                                                                                                  #  2/RMAG   FROM PDL+2
053486,000182: 27,3412           77744                           STORE    TFFALFA                               #  ALFA  1/M  E:(26-NR)   M:(24-NR)
053487,000183: 27,3413           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA   E:(20)    M:(18)
053488,000184: 27,3414           20173                                    0          -6,1                       
053489,000185: 27,3415           75446                           ABS      SQRT                                  #  E:(10)   M:(9)
053490,000186: 27,3416           77701                           NORM                                           
053491,000187: 27,3417           00050                                    X2                                    #  X2 = -NA
053492,000188: 27,3420           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA)   M:(9+NA)
053493,000189: 27,3421           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
053494,000190:                                                                                                  #  ALFA FROM PDL+2   E:(20)   M:(18)
053495,000191: 27,3422           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
053496,000192: 27,3423           57425                                    +2                                    
053497,000193: 27,3424           06514                                    TFF1/4                                
053498,000194: 27,3425           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA   E:(-22-2NA)    M:(-20-2NA)
053499,000195: 27,3426           77616        DUMPCNIC           RVQ                                            
053500,000196: 
053501,000197:                                                                                                  #                                                                                          39 W

Page 1263

053503,000199:                                                                                                  #  SUBROUTINE NAME:      TFFRP/RA                                            DATE:  01.17.67
053504,000200:                                                                                                  #  MOD NO:  0                                                                LOG SECTION:    TIME OF FREE FALL
053505,000201:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053506,000202:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER       DATE: 11 APR 67
053507,000203:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER       DATE: 21 MAR 68       ACCEPT DIFFERENT EARTH/MOON SCALES
053508,000204:                                                                                                  #                                                                            ALSO IMPROVE ACCURACY OF RAPO.
053509,000205: 
053510,000206:                                                                                                  #  FUNCTIONAL DESCRIPTION:          USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
053511,000207:                                                                                                  #           APOGEE RADIUS FOR A GENERAL CONIC.
053512,000208:                                                                                                  #           PROGRAM GIVES PERIGEE RADIUS AS                APOGEE RADIUS IS GIVEN BY
053513,000209:                                                                                                  #                  RP = P/(1+E)                                   RA = (1+E) / ALFA
053514,000210:                                                                                                  #           WHERE   2
053515,000211:                                                                                                  #                  E  = 1 - P ALFA
053516,000212:                                                                                                  #           IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
053517,000213:                                                                                                  #                  1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
053518,000214:                                                                                                  #                  2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
053519,000215:                                                                                                  #                  3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
053520,000216:                                                                                                  #           THIS SUBROUTINE REQUIRES THE SIGNED RECIPROCAL SEMI MAJ AXIS,  ALFA,  AND SEMI LATUS RECTUM AS DATA.
053521,000217:                                                                                                  #  CALLING SEQUENCE:  CALL
053522,000218:                                                                                                  #                            TFFRP/RA
053523,000219:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
053524,000220:                                                                                                  #           C(MPAC) UNSPECIFIED
053525,000221: 
053526,000222:                                                                                                  #  SUBROUTINES CALLED:  NONE
053527,000223:                                                                                                  #  NORMAL EXIT MODE:    RVQ
053528,000224:                                                                                                  #           IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
053529,000225:                                                                                                  #           OTHERWISE, RAPO = POSMAX.
053530,000226:                                                                                                  #  ALARMS:  NONE
053531,000227:                                                                                                  #  OUTPUT:  STORED IN PUSH LIST AREA. SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO  TFF/CONIC.
053532,000228:                                                                                                  #           RPER   E:(-29) M:(-27)   M     PERIGEE RADIUS                  DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
053533,000229:                                                                                                  #           RAPO   E:(-29) M:(-27)   M     APOGEE RADIUS                   WILL BE DESTROYED BY CALCTFF/CALCTPER
053534,000230:                                                                                                  #           PUSHLOC AT PDL+0
053535,000231:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053536,000232:                                                                                                  #           TFFALFA E:(26-NR)      M       1/SEMI MAJ AXIS                 LEFT BY TFFCONIC
053537,000233:                                                                                                  #                   M:(24-NR)
053538,000234:                                                                                                  #           TFFNP  E: (-38+2NR)    M      LC P, SEMI LATUS RECTUM          LEFT BY TFFCONIC
053539,000235:                                                                                                  #                  M: (-36+2NR)
053540,000236:                                                                                                  #           X1                     -NR, NORM COUNT OF RMAG                 LEFT BY TFFCONIC
053541,000237:                                                                                                  #           X2                     -NA, NORM COUNT OF ALFA                 LEFT BY TFFCONIC
053542,000238:                                                                                                  #  DEBRIS:  QPRET,   PDL+0 ... PDL+1
053543,000239: 

Page 1264

053545,000241: 27,3427                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29) M:(-27)
053546,000242: 27,3427                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29) M:(-27)
053547,000243: 
053548,000244: 27,3427           41345        TFFRP/RA           DLOAD    DMP                                   
053549,000245: 27,3430           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR)   M:(24-NR)
053550,000246: 27,3431           00035                                    TFFNP                                 #  LC P  M   E:(-38+2NR)   M:(-36+2NR)
053551,000247: 27,3432           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
053552,000248: 27,3433           20571                                    0          -8D,1                      #  ALFA P  (-4)
053553,000249: 27,3434           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
053554,000250:                                                                                                  #  (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
053555,000251: 27,3435           17765                                    DP2(-4)                               
053556,000252: 27,3436           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA) (-4)
053557,000253: 27,3437           06514                                    TFF1/4                                
053558,000254: 27,3440           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
053559,000255: 27,3441           00035                                    TFFNP                                 #  LCP  M  E:(-38+2NR)  M:(-36+2NR)
053560,000256: 27,3442           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
053561,000257: 27,3443           20601                                    0,1                                   #  X1=-NR
053562,000258: 27,3444           20572                                    0          -7,1                       #  (EFFECTIVE SL)
053563,000259: 27,3445           14017                           STODL    RPER                                  #  PERIGEE RADIUS   M  E:(-29)   M:(-27)
053564,000260:                                                                                                  #  (1+E)  (-2)   FROM PDL+0
053565,000261: 27,3446           41005                           DMP      BOVB                                  
053566,000262: 27,3447           00027                                    TFF1/ALF                              #  E:(-22-2NA)  M:(-20-2NA)
053567,000263: 27,3450           57753                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
053568,000264: 27,3451           53654                           BZE      SL*                                   
053569,000265: 27,3452           57461                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
053570,000266: 27,3453           57603                                    0          -5,2                       #  -5+NA
053571,000267: 27,3454           40057                           SL*      BOV                                   
053572,000268: 27,3455           57576                                    0,2                                   
053573,000269: 27,3456           57461                                    MAXRA                                 #  SET POSMAX IF OVFL.
053574,000270: 27,3457           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
053575,000271: 27,3460           57463                                    +3                                    
053576,000272: 27,3461           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID.  SET RAPO =
053577,000273: 27,3462           17771                                    NEARONE                               #  POSMAX AS A TAG.
053578,000274: 27,3463           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M   E:(-29)    M:(-27)
053579,000275: 27,3464           77616        DUMPRPRA           RVQ                                            
053580,000276: 
053581,000277:                                                                                                  #                                                                30 W

Page 1265

053583,000279:                                                                                                  #  SUBROUTINE NAME:     CALCTPER / CALCTFF                                 DATE:    01.29.67
053584,000280:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
053585,000281:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053586,000282:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE: 21 MAR 67
053587,000283:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE: 14 APR 67
053588,000284:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE: 8 JUL 67       NEAR EARTH MUE AND NEG TFF (GONEPAST)
053589,000285:                                                                                                  #  MOD NO:  4           MOD BY:  RR BAIRNSFATHER      DATE: 21 NOV 67      ADD VARIABLE MU.
053590,000286:                                                                                                  #  MOD NO:  5           MOD BY:  RR BAIRNSFATHER      DATE: 21 MAR 68      ACCEPT DIFFERENT EARTH/MOON SCALES
053591,000287:                                                                                                  #  FUNCTIONAL DESCRIPTION:      PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION  RN  AND
053592,000288:                                                                                                  #           VELOCITY  VN  TO A RADIUS LENGTH SPECIFIED BY  RTERM  , SUPPLIED BY THE USER. THE POSITION VECTOR
053593,000289:                                                                                                  #           RN  MAY BE ON EITHER SIDE OF THE CONIC, BUT  RTERM  IS CONSIDERED ON THE INBOUND SIDE.
053594,000290:                                                                                                  #           THE EQUATIONS ARE
053595,000291: 
053596,000292:                                                                                                  #                  Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)    (INBOUND SIDE))        LEQ +- LCE/SQRT(ALFA)
053597,000293:                                                                                                  #                       -  -
053598,000294:                                                                                                  #                  Q1 = RN.VN / SQRT(MU)                                            LEQ +- LCE/SQRT(ALFA)
053599,000295: 
053600,000296:                                                                                                  #                  Z = NUM / DEN                                                    LEQ +- 1/SQRT(ALFA)
053601,000297: 
053602,000298:                                                                                                  #           WHERE, IF INBOUND
053603,000299:                                                                                                  #                  NUM = RTERM -RN                                                  LEQ +- 2 LCE/ALFA
053604,000300:                                                                                                  #                  DEN = Q2+Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
053605,000301: 
053606,000302:                                                                                                  #           AND, IF OUTBOUND 
053607,000303:                                                                                                  #                  NUM = Q2-Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
053608,000304:                                                                                                  #                  DEN = 2 - ALFA (RTERM + RN) .                                    LEQ +- 2 LCE
053609,000305: 
053610,000306:                                                                                                  #           IF     ALFA ZZ  <  1.0               (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
053611,000307: 
053612,000308:                                                                                                  #           THEN   X = ALFA Z Z
053613,000309:                                                                                                  #           AND    TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
053614,000310: 
053615,000311:                                                                                                  #                  EXCEPT  IF ALFA PNZ, AND IF TFF NEG,
053616,000312:                                                                                                  #                  THEN    TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
053617,000313: 
053618,000314:                                                                                                  #           OR     IF ALFA ZZ GEQ 1.0             (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
053619,000315: 
053620,000316:                                                                                                  #           THEN   X = 1/ALFA Z Z
053621,000317:                                                                                                  #           AND    TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
053622,000318: 
053623,000319:                                                                                                  #           WHERE  T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
053624,000320:                                                                                                  #                             2     3                        2
053625,000321:                                                                                                  #                  1/3 -X/5 +X /7 -X /9 ...                (X   <  1.0)
053626,000322: 
053627,000323:                                                                                                  #  CALLING SEQUENCE:  TIME TO RTERM                           TIME TO PERIGEE
053628,000324:                                                                                                  #                     CALL                                    CALL
053629,000325:                                                                                                  #                             CALCTFF                                CALCTPER
053630,000326:                                                                                                  #                     C(MPAC) = TERMNL RAD M                  C(MPAC) = PERIGEE RAD M
053631,000327:                                                                                                  #           FOR EITHER,   E:(-29)     M:(-27)
053632,000328:                                                                                                  #           FOR EITHER, PUSHLOC = PDL+0, ARBITRARY IF LEQ 8D.

Page 1266

053634,000330: 
053635,000331:                                                                                                  #  SUBROUTINES CALLED:  T(X), VIA RTB
053636,000332:                                                                                                  #  NORMAL EXIT MODE:  RVQ
053637,000333:                                                                                                  #           HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS  IN MPAC. USER MUST STORE.
053638,000334:                                                                                                  #                  A. TFF = FLIGHT TIME. NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
053639,000335:                                                                                                  #                  B. (THIS OPTION IS NO LONGER USED.)
053640,000336:                                                                                                  #                  C. TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
053641,000337:                                                                                                  #                     THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
053642,000338:                                                                                                  #  OUTPUT:  C(MPAC)  (-28)  CS    TIME OF FLIGHT, OR TIME TO PERIGEE
053643,000339:                                                                                                  #           TFFX    (0)           X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
053644,000340:                                                                                                  #           NRTERM  E:(-29+NR)    M  RTERM, WEIGHTED BY NR                LEFT FOR ENTRY DISPLAY TFF ROUTINES
053645,000341:                                                                                                  #                   M:(-27+NR)
053646,000342:                                                                                                  #           TFFTEM  E:(-59+2NR)   LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
053647,000343:                                                                                                  #                   M:(-55+2NR)   LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
053648,000344:                                                                                                  #           NOTE:  TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
053649,000345:                                                                                                  #           RMAG1  E:(-29) M:(-27) PDL 12 NOT TOUCHED.
053650,000346:                                                                                                  #           TFFQ1  E:(-16) M:(-15) PDL 14D
053651,000347:                                                                                                  #           TFFDELQ E:(-16) M:(-15) PDL 10D
053652,000348:                                                                                                  #           PUSHLOC AT PDL+0
053653,000349:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053654,000350:                                                                                                  #           RONE   E:(-29)  M:(-27)  M   STATE VECTOR                      LEFT BY USER
053655,000351:                                                                                                  #           VONE'  E:(+10)  M:(+9)   VN/SQRT(MU)                           LEFT BY TFF/CONIC
053656,000352:                                                                                                  #           RMAG1  E:(-29)  M:(-27)  PRESENT RADIUS,  M                    LEFT BY TFFCONIC
053657,000353:                                                                                                  #           C(MPAC)E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH, M      LEFT BY USER
053658,000354: 
053659,000355:                                                                                                  #           THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
053660,000356:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)  1/SQRT(MU)                           LEFT BY TFFCONIC.
053661,000357:                                                                                                  #           NRMAG  E: (-29+NR)  M  RMAG, NORMALIZED                        LEFT BY TFFCONIC
053662,000358:                                                                                                  #                  M: (-27+NR)
053663,000359:                                                                                                  #           X1                     -NR, NORM COUNT                         LEFT BY TFFCONIC
053664,000360:                                                                                                  #           TFFNP  E: (-38+2NR)  M   LCP, SEMI LATUS RECTUM, WEIGHT NR     LEFT BY TFFCONIC
053665,000361:                                                                                                  #                  M: (-36+2NR)
053666,000362:                                                                                                  #           TFFALFA  E: (26-NR)    1/M  ALFA, WEIGHT NR                    LEFT BY TFFCONIC
053667,000363:                                                                                                  #                    M: (24-NR)
053668,000364:                                                                                                  #           TFFRTALF  E:(10+NA)    SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
053669,000365:                                                                                                  #                     M:(9+NA)
053670,000366:                                                                                                  #           X2                     -NA, NORMCOUNT                          LEFT BY TFFCONIC
053671,000367:                                                                                                  #           TFF1/ALF  E:(-22-2NA)   SIGNED SEMIMAJ AXIS, WEIGHTED BY NA    LEFT BY TFFCONIC
053672,000368:                                                                                                  #                     M:(-20-2NA)
053673,000369:                                                                                                  #  DEBRIS:  QPRET,   PDL+0 ... PDL+3
053674,000370:                                                                                                  #           RTERM  E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH
053675,000371:                                                                                                  #           RAPO   E:(-29)  M:(-27)  PDL 16D  (=NRTERM)
053676,000372:                                                                                                  #           RPER   E:(-29)  M:(-27)  PDL 14D   (=TFFQ1)
053677,000373: 

Page 1267

053679,000375: 27,3465           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER IN MPAC
053680,000376: 27,3466           03436                                    TFFSW                                 
053681,000377: 27,3467           57472                                    +3                                    
053682,000378: 27,3470           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
053683,000379: 27,3471           03676                                    TFFSW                                 
053684,000380: 27,3472           00023                 +3        STORE    RTERM                                 #  E: (-29)  M: (-27)
053685,000381: 27,3473           77657                           SL*                                            
053686,000382: 27,3474           20201                                    0,1                                   #  X1=-NR
053687,000383: 27,3475           00021                           STORE    NRTERM                                #  RTERM  E: (-29+NR)  M: (-27+NR)
053688,000384: 27,3476           44205                           DMP      BDSU                                  
053689,000385: 27,3477           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
053690,000386: 27,3500           06514                                    TFF1/4                                
053691,000387: 27,3501           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
053692,000388: 27,3502           00021                                    NRTERM                                #  E: (-29+NR)  M: (-27+NR)
053693,000389: 27,3503           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
053694,000390:                                                                                                  #  E: (-32+NR)   M: (-30+NR)
053695,000391: 27,3504           00035                                    TFFNP                                 #  LC P  E:(-38+2NR)  M:(-36+2NR)
053696,000392: 27,3505           20573                                    0          -6,1                       #  X1 = -NR
053697,000393: 27,3506           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
053698,000394:                                                                                                  #  RTERM(2-ALFA RTERM) FROM PDL +2
053699,000395:                                                                                                  #  E: (-32+NR)  M: (-30+NR)
053700,000396: 27,3507           77657                           SR*                                            #  LEAVE  E: (-32)  M: (-30)
053701,000397: 27,3510           20601                                    0,1                                   #  X1 = -NR
053702,000398: 27,3511           71214                           BOFF     DLOAD                                 #  CHECK TFF / TPER SWITCH
053703,000399: 27,3512           03756                                    TFFSW                                 
053704,000400: 27,3513           57515                                    +2                                    #  IF TFF, CONTINUE
053705,000401: 27,3514           06524                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
053706,000402: 27,3515           75440                 +2        BMN      SQRT                                  #  E: (-16)  M: (-15)
053707,000403: 
053708,000404: 27,3516           57650                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
053709,000405:                                                                                                  #  RESET PDL, SET TFF=POSMAX, AND EXIT.
053710,000406: 
053711,000407: 27,3517           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
053712,000408: 27,3520           57753                                    TCDANZIG                              #  ANY PORT IN A STORM.
053713,000409: 27,3521           24045                           STOVL    TFFTEM                                #  Q2   E: (-16)  M: (-15)
053714,000410: 27,3522           02170                                    VONE'                                 #  VN/SQRT(MU) E: (10)  M: (9)
053715,000411: 27,3523           52441                           DOT      SL3                                   
053716,000412: 27,3524           02207                                    RONE                                  #  SAVED RN.  E: (-29)  M:(-27)
053717,000413: 27,3525           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
053718,000414:                                                                                                  #  E: (-16)  M: (-15)
053719,000415: 27,3526           44240                           BMN      BDSU                                  
053720,000416: 27,3527           57550                                    INBOUND                               #  USE ALTERNATE Z
053721,000417: 27,3530           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
053722,000418: 
053723,000419:                                                                                                  #  OUTBOUND Z CALC CONTINUES HERE
053724,000420: 
053725,000421: 27,3531           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E: (-16)  M:(-15)
053726,000422: 27,3532           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
053727,000423: 27,3533           44205                           DMP      BDSU                                  

Page 1268

053729,000425: 27,3534           00041                                    NRMAG                                 #  RMAG  E: (-29+NR)  M: (-27+NR)
053730,000426:                                                                                                  #  (2-RTERM ALFA)  (-3) FROM PDL+0
053731,000427: 27,3535           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E: (-3) OR (-16)
053732,000428:                                                                                                  #                M: (-3) OR (-15)
053733,000429: 27,3536           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
053734,000430: 27,3537           17757                                    LIM(-22)                              #  =1.0-B(-22)
053735,000431: 27,3540           57561                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
053736,000432: 27,3541           65345                           DLOAD    PDDL                                  #  SET DEN=0 OTHERWISE
053737,000433: 27,3542           06524                                    TFFZEROS                              
053738,000434:                                                                                                  #  XCH ZERO WITH PDL+0
053739,000435: 27,3543           57545                           DLOAD    DCOMP                                 
053740,000436: 27,3544           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
053741,000437: 27,3545           71240                           BMN      DLOAD                                 #  FOR TPER: Z INDET AT DELE/2=0 AND 90.
053742,000438: 27,3546           57655                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
053743,000439: 
053744,000440:                                                                                                  #  Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
053745,000441: 27,3547           77616        DUMPTFF1           RVQ                                            #  RETURN TFF =0
053746,000442: 
053747,000443:                                                                                                  #  INBOUND Z CALC CONTINUES HERE
053748,000444: 
053749,000445: 27,3550           77745        INBOUND            DLOAD                                          #  RESET PDL+0
053750,000446: 27,3551           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
053751,000447: 27,3552           00023                                    RTERM                                 #  E: (-29)  M: (-27)
053752,000448: 27,3553           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
053753,000449: 27,3554           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E: (-29)  M: (-27)
053754,000450: 27,3555           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
053755,000451: 27,3556           52015                           DAD      GOTO                                  
053756,000452: 27,3557           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
053757,000453: 27,3560           57535                                    SAVEDEN                               #  DEN = Q2+Q1   E: (-16)  M:(-15)
053758,000454: 
053759,000455: 27,3561           65215        TFFXTEST           DAD      PDDL                                  #  (ABS(DEN) TO PDL+2))   E: (-3) OR (-16)
053760,000456:                                                                                                  #                         M: (-3) OR (-15)
053761,000457: 27,3562           17761                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
053762,000458: 27,3563           00043                                    TFFX                                  #  NUM E:(-16) OR (-29)  M:(-15) OR (-27)
053763,000459: 27,3564           53605                           DMP      SR*                                   
053764,000460: 27,3565           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
053765,000461: 27,3566           57201                                    0          -3,2                       #  X2=-NA
053766,000462: 27,3567           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)  E:(-3) OR (-16)
053767,000463:                                                                                                  #                           M:(-3) OR (-15)
053768,000464:                                                                                                  #  ABS(DEN) FROM PDL+2  E:(-3) OR (-16)
053769,000465:                                                                                                  #                       M:(-3) OR (-15)
053770,000466: 27,3570           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
053771,000467: 27,3571           00043                                    TFFX                                  #  NUM  E: (-16) OR (-29)  M: (-15) OR (-27)
053772,000468: 27,3572           57653                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
053773,000469: 
053774,000470:                                                                                                  #  OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
053775,000471: 
053776,000472: 27,3573           45471                           DDV      STADR                                 
053777,000473:                                                                                                  #  DEN FROM PDL+0  E: (-3) OR (-16)
053778,000474:                                                                                                  #                  M: (-3) OR (-15)
053779,000475: 27,3574           77732                           STORE    TFFTEM                                #  Z SAVE FOR SIGN OF SDELF.

Page 1269

053781,000477:                                                                                                  #  E: (-13)  M: (-12)
053782,000478: 27,3575           63406                           PUSH     DSQ                                   #  Z TO PDL+0
053783,000479: 27,3576           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E: (-26)  M: (-24)
053784,000480: 27,3577           00035                                    TFFNP                                 #  LC P  E: (-38+2NR)  M: (-36+2NR)
053785,000481: 27,3600           75261                           SL       SIGN                                  
053786,000482: 27,3601           20206                                    5                                     
053787,000483: 27,3602           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
053788,000484: 27,3603           14045                           STODL    TFFTEM                                #  P ZSQ  E: (-59+2NR)  M: (-55+2NR)
053789,000485:                                                                                                  #  (ARG IS USED IN TFF/TRIG)
053790,000486:                                                                                                  #  ZSQ FROM PDL+2   E: (-26)  M: (-24)
053791,000487: 27,3604           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
053792,000488: 27,3605           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
053793,000489: 27,3606           77657                           SL*                                            
053794,000490: 27,3607           20201                                    0,1                                   #  X1=-NR
053795,000491: 27,3610           00043                           STORE    TFFX                                  #  X
053796,000492: 27,3611           41234                           RTB      DMP                                   
053797,000493: 27,3612           57735                                    T(X)                                  #   POLY
053798,000494:                                                                                                  #  ZSQ FROM PDL+2  E: (-26)  M: (-24)
053799,000495: 27,3613           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E: (-29)  M: (-27)
053800,000496: 27,3614           00023                                    RTERM                                 #  RTERM  E: (-29)  M: (-27)
053801,000497: 27,3615           41215                           DAD      DMP                                   
053802,000498: 27,3616           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
053803,000499:                                                                                                  #  Z FROM PDL+0  E: (-13)  M: (-12)
053804,000500: 27,3617           51042                           SR3      BPL                                   #  TFF SQRT(MU)   E: (-45)  M: (-42)
053805,000501: 27,3620           57641                                    ENDTFF                                #  (NO PUSH UP)
053806,000502: 27,3621           75206                           PUSH     SIGN                                  #  TFF SQRT(MU) TO PDL+0
053807,000503: 27,3622           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
053808,000504: 27,3623           71244                           BPL      DLOAD                                 #  GONE PAST ?
053809,000505: 27,3624           57645                                    NEGTFF                                #  YES. TFF < 0.
053810,000506: 27,3625           00027                                    TFF1/ALF                              #  1/ALFA  E: (-22-2NA)  M: (-20-2NA)
053811,000507: 27,3626           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
053812,000508: 27,3627           57645                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
053813,000509: 
053814,000510:                                                                                                  #  CORRECT FOR ORBITAL PERIOD.
053815,000511: 
053816,000512: 27,3630           77676                           DCOMP                                          #  YES. CORRECT FOR ORB PERIOD.
053817,000513: 27,3631           56205                           DMP      DDV                                   
053818,000514: 27,3632           17755                                    PI/16                                 #  2 PI (-5)
053819,000515: 27,3633           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
053820,000516: 27,3634           53657                           SL*      SL*                                   
053821,000517: 27,3635           57602                                    0          -4,2                       #  X2=-NA
053822,000518: 27,3636           57602                                    0          -4,2                       
053823,000519: 27,3637           43257                           SL*      DAD                                   
053824,000520: 27,3640           57576                                    0,2                                   
053825,000521:                                                                                                  #  TFF SQRT(MU) FROM PDL+0  E:(-45) M:(-42)
053826,000522: 27,3641           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC     E:(-45) M:(-42)
053827,000523: 27,3642           00037                                    TFF/RTMU                              #  E: (17)  M: (14)
053828,000524: 27,3643           57651                                    MAXTFF                                #  SET POSMAX IF OVFL.
053829,000525: 
053830,000526: 27,3644           77616        DUMPTFF2           RVQ                                            #  RETURN TFF   (-28) CS IN MPAC.
053831,000527: 

Page 1270

053833,000529: 27,3645           77745        NEGTFF             DLOAD                                          
053834,000530:                                                                                                  #  TFF SQRT(MU)  FROM PDL+0, NEGATIVE.
053835,000531: 27,3646           77650                           GOTO                                           
053836,000532: 27,3647           57641                                    ENDTFF                                
053837,000533: 
053838,000534: 27,3650           77745        MAXTFF1            DLOAD                                          #  RESET PDL
053839,000535: 27,3651           43545        MAXTFF             DLOAD    RVQ                                   
053840,000536: 27,3652           17771                                    NEARONE                               
053841,000537: 
053842,000538:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
053843,000539: 
053844,000540:                                                                                                  #  NUM FROM TFFX.  E: (-16) OR (-29)
053845,000541:                                                                                                  #                  M: (-15) OR (-27)
053846,000542: 27,3653           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
053847,000543: 27,3654           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
053848,000544:                                                                                                  #  DEN FROM PDL+0 E:(-3)/( 16) M:(-3)/(-15)
053849,000545:                                                                                                  #  N/D TO PDL+0  E:(11) M:(10)
053850,000546: 27,3655           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
053851,000547: 27,3656           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
053852,000548: 27,3657           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
053853,000549: 27,3660           14013                           STODL    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
053854,000550:                                                                                                  #  D/N FROM PDL+0
053855,000551: 27,3661           77626                           STADR                                          
053856,000552: 27,3662           77732                           STORE    TFFTEM                                #  D/N  E: (11)  M: (10)
053857,000553: 27,3663           53605                           DMP      SL*                                   
053858,000554: 27,3664           00027                                    TFF1/ALF                              #  1/ALFA E: (-22-2NA)  M: (-20-2NA)
053859,000555: 27,3665           57576                                    0,2                                   #  1/ALFA Z  E: (-11-NA)  M: (-10-NA)
053860,000556: 27,3666           41206                           PUSH     DMP                                   #  TO PDL+0
053861,000557: 27,3667           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
053862,000558: 27,3670           41057                           SL*      BOVB                                  
053863,000559: 27,3671           57576                                    0,2                                   #  X2= -NA
053864,000560: 27,3672           21713                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
053865,000561: 27,3673           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
053866,000562: 27,3674           41234                           RTB      DMP                                   
053867,000563: 27,3675           57735                                    T(X)                                  #  POLY
053868,000564: 27,3676           00043                                    TFFX                                  
053869,000565: 27,3677           45242                           SR3      DSU                                   
053870,000566: 27,3700           17763                                    DP2(-3)                               
053871,000567: 27,3701           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA  E: (-15-NA)
053872,000568:                                                                                                  #                       M: (-14-NA)
053873,000569:                                                                                                  #  1/ALFA Z FROM PDL+0  E: (-11-NA)
053874,000570:                                                                                                  #                       M: (-10-NA)
053875,000571: 27,3702           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
053876,000572: 27,3703           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
053877,000573: 27,3704           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
053878,000574: 27,3705           43312                           SL2      DAD                                   
053879,000575: 27,3706           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
053880,000576: 27,3707           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z)  =SGN OF SDELF E:(-16) M:(-15
053881,000577: 27,3710           00035                                    TFFNP                                 #  LC P E: (-38+2NR) M: (-36+2NR)
053882,000578: 27,3711           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1271

053884,000580: 27,3712           00027                                    TFF1/ALF                              #  1/ALFA   E:(-22-2NA)  M:(-20-2NA)
053885,000581: 27,3713           57575                                    1,2                                   #  X2=-NA
053886,000582: 27,3714           53765                           SIGN     SL*                                   
053887,000583: 27,3715           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
053888,000584: 27,3716           57576                                    0,2                                   
053889,000585: 27,3717           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR)  M:(-55+2NR)
053890,000586:                                                                                                  #  (ARG FOR USE IN TFF/TRIG)
053891,000587: 27,3720           00027                                    TFF1/ALF                              #  1/ALFA E:(-22-2NA)  M:(-20-2NA)
053892,000588: 27,3721           41366                           SQRT     DMP                                   
053893,000589: 27,3722           17755                                    PI/16                                 #  PI (-4)
053894,000590: 27,3723           77615                           DAD                                            
053895,000591:                                                                                                  #  2(XT(X)-1)/Z ALFA FROM PDL E:(-15-NA)
053896,000592:                                                                                                  #                             M:(-14-NA)
053897,000593: 27,3724           45257                           SL*      DSU                                   
053898,000594: 27,3725           57577                                    0          -1,2                       
053899,000595: 27,3726           00013                                    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
053900,000596: 27,3727           53605                           DMP      SL*                                   
053901,000597: 27,3730           00027                                    TFF1/ALF                              #  1/ALFA   E:(-22-2NA) M:(-20-2NA)
053902,000598: 27,3731           57601                                    0          -3,2                       
053903,000599: 27,3732           52057                           SL*      GOTO                                  
053904,000600: 27,3733           57602                                    0          -4,2                       
053905,000601: 27,3734           57641                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
053906,000602: 

Page 1272

053908,000604:                                                                                                  #  PROGRAM NAME:      T(X)                                                   DATE:    01.17.67
053909,000605:                                                                                                  #  MOD NO:  0                                                                LOG SECTION:    TIME OF FREE FALL
053910,000606:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053911,000607:                                                                                                  #  FUNCTIONAL DESCRIPTION:        THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES  CALCTFF AND
053912,000608:                                                                                                  #           CALCTPER TO APPROXIMATE THE SERIES
053913,000609:                                                                                                  #                             2     3
053914,000610:                                                                                                  #                  1/3 -X/5 +X /7 -X /9 ...
053915,000611: 
053916,000612:                                                                                                  #           WHERE  X = ALFA Z Z            IF ALFA Z Z LEQ 1
053917,000613:                                                                                                  #                  X = 1/(ALFA Z Z)        IF ALFA Z Z G 1
053918,000614: 
053919,000615:                                                                                                  #           ALSO   X IS NEG FOR HYPERBOLIC ORBITS
053920,000616:                                                                                                  #                  X = 0 FOR PARABOLIC ORBITS
053921,000617:                                                                                                  #                  X IS POSITIVE FOR ELLIPTIC ORBITS
053922,000618:                                                                                                  #           FOR FLIGHT 278, THE POLYNOMIAL T(X) IS FITTED OVER THE RANGE  (0,+1) AND HAS A MAXIMUM
053923,000619:                                                                                                  #           DEVIATION FROM THE SERIES OF  2 E-5      (T(X) IS A CHEBYCHEV  TYPE FIT AND WAS OBTAINED USING
053924,000620:                                                                                                  #           MAC PROGRAM AUTCURFIT294RRB  AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE (-.08,+1).)
053925,000621:                                                                                                  #  CALLING SEQUENCE:  RTB
053926,000622:                                                                                                  #                            T(X)
053927,000623:                                                                                                  #           C(MPAC) = X
053928,000624: 
053929,000625:                                                                                                  #  SUBROUTINES CALLED:  NONE
053930,000626:                                                                                                  #  NORMAL EXIT MODE:    TC   DANZIG
053931,000627:                                                                                                  #  ALARMS:  NONE
053932,000628:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
053933,000629:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053934,000630:                                                                                                  #           C(MPAC) = X
053935,000631:                                                                                                  #  DEBRIS:  NONE
053936,000632: 
053937,000633: 27,3735           07225        T(X)               TC       POLY                                  
053938,000634: 27,3736           00004                           DEC      4          B-14                       #  N-1
053939,000635: 27,3737           12525 12525                     2DEC     3.333333333 E-1                        
053940,000636: 
053941,000637: 27,3741           71463 57703                     2DEC*    -1.999819135 E-1*                       
053942,000638: 
053943,000639: 27,3743           04423 17645                     2DEC*    1.418148467 E-1*                       
053944,000640: 
053945,000641: 27,3745           74604 43667                     2DEC*    -1.01310997 E-1*                       
053946,000642: 
053947,000643: 27,3747           01626 37256                     2DEC*    5.609004986 E-2*                       
053948,000644: 
053949,000645: 27,3751           77404 52071                     2DEC*    -1.536156925 E-2*                       
053950,000646: 
053951,000647: 27,3753           06064        ENDT(X)            TC       DANZIG                                
053952,000648: 
053953,000649: 27,3754  27,3753               TCDANZIG           =        ENDT(X)                               
053954,000650: 

Page 1273

053956,000652:                                                                                                  #  TFF CONSTANTS
053957,000653: 
053958,000654: 32,3764                                           BANK     32                                    
053959,000655: 
053960,000656: 27,2000                                           SETLOC   TOF-FF1                               
053961,000657: 27,2000                                           BANK                                           
053962,000658: 
053963,000659:                                                                                                  #                                                NOTE _  NOTE _  ADJUSTED MUE FOR NEAR EARTH TRAJ.
053964,000660:                                                                                                  # MUE            =       3.990815471 E10         M CUBE/CS SQ
053965,000661:                                                                                                  # RTMUE          =       1.997702549 E5 B-18*    MODIFIED EARTH MU
053966,000662: 
053967,000663:                                                                                                  #                                                NOTE _  NOTE _  ADJUSTED MUE FOR NEAR EARTH TRAJ.
053968,000664:                                                                                                  # MUM            =       4.902778 E8             M CUBE/CS SQ
053969,000665:                                                                                                  # RTMUM          2DEC*   2.21422176 E4 B-18*
053970,000666: 
053971,000667: 27,3754           06220 37553  PI/16              2DEC     3.141592653 B-4                        
053972,000668: 
053973,000669: 27,3756           37777 37700  LIM(-22)           2OCT     3777737700                            #  1.0 -B(-22)
053974,000670: 
053975,000671: 27,3760           00000 00100  DP(-22)            2OCT     0000000100                            #  B(-22)
053976,000672: 
053977,000673: 27,3762           04000 00000  DP2(-3)            2DEC     1          B-3                        
053978,000674: 
053979,000675: 27,3764           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
053980,000676: 
053981,000677:                                                                                                  #  RPAD1         2DEC    6373338 B-29            M (-29) = 20909901.57 FT
053982,000678: 
053983,000679: 27,3766  23,2337               RPAD1              =        RPAD                                  
053984,000680: 
053985,000681: 27,3766           00305 11205  R300K              2DEC     6464778    B-29                       #  (-29) M
053986,000682: 
053987,000683: 27,3770           37777 37777  NEARONE            2DEC     .999999999                            
053988,000684: 
053989,000685: 27,3772  23,2523               TFFZEROS           EQUALS   HI6ZEROS                              
053990,000686: 27,3772  23,2513               TFF1/4             EQUALS   HIDP1/4                               
053991,000687: 

End of include-file TIME_OF_FREE_FALL.agc.  Parent file is MAIN.agc