Source Code

This is a reconstructed version of Luminary 130, the initial AGC program released in November 1969 for the Apollo 13 LM. Three more releases followed before the flown revision was finally manufactured in February 1970.

This reconstruction was created from a previous transcription of the original listing of Luminary 131, combined with Luminary memo #129 which describes the small difference between the Luminary 130 and 131. The reconstructed source code was verified by matching memory-bank checksums to those listed for Luminary 130 in drawing 2021152G.

In this source code, program comments from the original (Luminary 131) code are prefixed with '#', while those added later by the Virtual AGC project are prefixed with '##'.

053331,000002:                                                                                                  ## Copyright:   Public domain.
053332,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
053333,000004:                                                                                                  ## Purpose:     A section of the reconstructed source code for Luminary 130.
053334,000005:                                                                                                  ##              This was the original program released for the Apollo 13 LM,
053335,000006:                                                                                                  ##              although several more revisions would follow. It has been
053336,000007:                                                                                                  ##              reconstructed from a listing of Luminary 131, from which it
053337,000008:                                                                                                  ##              differs on only two lines in P70-P71. The difference is
053338,000009:                                                                                                  ##              described in detail in Luminary memo #129, which was used
053339,000010:                                                                                                  ##              to perform the reconstruction. This file is intended to be a
053340,000011:                                                                                                  ##              faithful reconstruction, except that the code format has been
053341,000012:                                                                                                  ##              changed to conform to the requirements of the yaYUL assembler
053342,000013:                                                                                                  ##              rather than the original YUL assembler.
053343,000014:                                                                                                  ## Reference:   pp. 1260-1275
053344,000015:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
053345,000016:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
053346,000017:                                                                                                  ## Mod history: 06/03/03 RSB.   Began transcribing.
053347,000018:                                                                                                  ##              05/14/05 RSB    Corrected website reference above
053348,000019:                                                                                                  ##              2010-10-25 JL   Indentation fixes.
053349,000020:                                                                                                  ##              2017-01-06 RSB  Page numbers now agree with those on the
053350,000021:                                                                                                  ##                              original hardcopy, as opposed to the PDF page
053351,000022:                                                                                                  ##                              numbers in 1701.pdf.
053352,000023:                                                                                                  ##              2017-02-27 RSB  Proofed comment text using octopus/ProoferComments.
053353,000024:                                                                                                  ##              2017-03-14 RSB  Comment-text fixes noted in proofing Luminary 116.
053354,000025:                                                                                                  ##              2017-03-16 RSB  Comment-text fixes identified in 5-way
053355,000026:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
053356,000027:                                                                                                  ##              2018-09-04 MAS  Copied from Luminary 131 for Luminary 130.
053357,000028: 

Page 1260

053359,000030:                                                                                                  #  THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES.  THE TFF ROUTINES NEVER
053360,000031:                                                                                                  #  KNOW WHICH ORIGIN APPLIES.  IT IS THE USER WHO KNOWS, AND WHO SUPPLIES RONE, VONE AND 1/SQRT(MU) AT THE
053361,000032:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
053362,000033: 
053363,000034:                                                                                                  #        EARTH ORIGIN    POSITION        -29     METERS
053364,000035:                                                                                                  #                        VELOCITY        -7      METERS/CENTISECOND
053365,000036:                                                                                                  #                        1/SQRT(MU)      +17     SQRT(CS SQ/METERS CUBED)
053366,000037: 
053367,000038:                                                                                                  #        MOON ORIGIN     POSITION        -27     METERS
053368,000039:                                                                                                  #                        VELOCITY        -5      METERS/CENTISECONDS
053369,000040:                                                                                                  #                        1/SQRT(MU)      +14     SQRT(CS SQ/METERS CUBED)
053370,000041: 
053371,000042:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE.  IN ALL CASES,
053372,000043:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28).  PROGRAM TFF/CONIC WILL GENERATE VONE/RTMU AND
053373,000044:                                                                                                  #  LEAVE IT IN VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
053374,000045: 
053375,000046:                                                                                                  #  THE USER MUST STORE THE STATE VECTOR IN RONE, VONE AND MU IN THE FORM 1/SQRT(MU) IN TFF/RTMU
053376,000047:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING TFF/CONIC.  SINCE RONE, VONE ARE IN THE EXTENDED VERB STORAGE AREA,
053377,000048:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
053378,000049: 
053379,000050:                                                                                                  #  PROGRAMS CALC/TFF AND CALC/TPER ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
053380,000051:                                                                                                  #  RADIUS.  THIS RESTRICTION CAN BE REMOVED BY A 15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
053381,000052: 
053382,000053:                                                                                                  #  THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
053383,000054: 
053384,000055:                                                                                                  #                                        BELOW   E:  IS USED FOR EARTH ORIGIN SCALE
053385,000056:                                                                                                  #                                                M:  IS USED FOR MOON  ORIGIN SCALE
053386,000057: 
053387,000058:                                                                                                  # TFFSW          =       119D            BIT1    0 = CALCTFF             1 = CALCTPER
053388,000059: 10,2213                        TFFDELQ            =        10D                                   #  Q2-Q1                 E: (-16)  M: (-15)
053389,000060: 10,2213                        RMAG1              =        12D                                   #  ABVAL(RN)  M          E: (-29)  M: (-27)
053390,000061:                                                                                                  # RPER           =       14D             PERIGEE RADIUS  M       E: (-29)  M: (-27)
053391,000062: 10,2213                        TFFQ1              =        14D                                   #  R.V / SQRT(MUE)               E: (-16)  M: (-15)
053392,000063:                                                                                                  # SDELF/2                                SIN(THETA) /2
053393,000064: 10,2213                        CDELF/2            =        14D                                   #  COS(THETA) /2
053394,000065:                                                                                                  # RAPO           =       16D             APOGEE RADIUS  M        E: (-29)  M: (-27)
053395,000066: 10,2213                        NRTERM             =        16D                                   #  TERMINAL RADIUS  M    E: (-29+NR)
053396,000067:                                                                                                  #                                  M: (-27+NR)
053397,000068: 10,2213                        RTERM              =        18D                                   #  TERMINAL RADIUS  M    E: (-29)  M: (-27)
053398,000069: 10,2213                        TFFVSQ             =        20D                                   #  -(V SQUARED/MU)  1/M  E: (20)   M: (18)
053399,000070: 10,2213                        TFF1/ALF           =        22D                                   #  SEMI MAJ AXIS  M      E: (-22-2 NA)
053400,000071:                                                                                                  #                                  M: (-20-2 NA)
053401,000072: 10,2213                        TFFRTALF           =        24D                                   #  SQRT(ALFA)            E:(10+NA) M: (9+NA)
053402,000073: 10,2213                        TFFALFA            =        26D                                   #  ALFA  1/M             E:(26-NR) M: (24-NR)
053403,000074: 10,2213                        TFFNP              =        28D                                   #  SEMI LATUS RECTUM  M  E: (-38+2 NR)
053404,000075:                                                                                                  #                                  M: (-36+2 NR)
053405,000076: 10,2213                        TFF/RTMU           =        30D                                   #  1/SQRT(MU)            E: (17)   M: (14)
053406,000077: 10,2213                        NRMAG              =        32D                                   #  PRESENT RADIUS  M     E: (-29+NR)
053407,000078:                                                                                                  #                                  M: (-27+NR)
053408,000079: 10,2213                        TFFX               =        34D                                   
053409,000080: 10,2213                        TFFTEM             =        36D                                   #  TEMPORARY

Page 1261

053411,000082:                                                                                                  #                REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
053412,000083:                                                                                                  #                INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES.  THEY ARE ESTAB-
053413,000084:                                                                                                  #                LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
053414,000085:                                                                                                  #                SUBROUTINES.
053415,000086:                                                                                                  #                -NR                             C(X1) = NORM COUNT OF RMAG
053416,000087:                                                                                                  #                -NA                             C(X2) = NORM COUNT OF SQRT(ABS(ALFA))
053417,000088: 

Page 1262

053419,000090:                                                                                                  #  SUBROUTINE NAME:  TFFCONIC                    DATE:  01.29.67
053420,000091:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
053421,000092:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053422,000093:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
053423,000094:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD MOON MU.
053424,000095:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
053425,000096: 
053426,000097:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
053427,000098:                                                                                                  #        SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA.  THE PARAMETERS ARE LISTED UNDER OUTPUT.
053428,000099:                                                                                                  #        THE EQUATIONS ARE
053429,000100:                                                                                                  #                -   -  -
053430,000101:                                                                                                  #                H = RN*VN                       ANGULAR MOMENTUM
053431,000102:                                                                                                  #                      - -
053432,000103:                                                                                                  #                LCP = H.H / MU                  SEMI LATUS RECTUM
053433,000104:                                                                                                  #                              -  -
053434,000105:                                                                                                  #                ALFA = 2/RN - VN.VN / MU        RECIPROCAL SEMI MAJ AXIS, SIGNED
053435,000106: 
053436,000107:                                                                                                  #        AND ALFA IS POS FOR ELLIPTIC ORBITS
053437,000108:                                                                                                  #                      0 FOR PARABOLIC ORBITS
053438,000109:                                                                                                  #                    NEG FOR HYPERBOLIC ORBITS.
053439,000110:                                                                                                  #        SUBROUTINE ALSO COMPUTES AND SAVES RMAG.
053440,000111: 
053441,000112:                                                                                                  #  CALLING SEQUENCE:
053442,000113:                                                                                                  #        TFFCONIC EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
053443,000114:                                                                                                  #        1/SQRT(MU).  PROGRAM WILL SAVE IN TFF/RTMU  . THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
053444,000115:                                                                                                  #        ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
053445,000116:                                                                                                  #        VONE AT PROPER SCALE.  THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
053446,000117:                                                                                                  #        TFF ROUTINES.
053447,000118: 
053448,000119:                                                                                                  #        ENTRY POINT TFFCONMU EXPECTS THAT TFF/RTMU IS ALREADY LOADED.
053449,000120: 
053450,000121:                                                                                                  #        TO SPECIFY MU:  DLOAD   CALL            IF MU ALREADY STORED:           CALL
053451,000122:                                                                                                  #                                YOURMU          1/RTMU E:(17) M:(14)                    TFFCONMU
053452,000123:                                                                                                  #                                TFFCONIC
053453,000124:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
053454,000125: 
053455,000126:                                                                                                  #  SUBROUTINES CALLED:  NONE
053456,000127: 
053457,000128:                                                                                                  #  NORMAL EXIT MODES:  RVQ
053458,000129: 
053459,000130:                                                                                                  #  ALARMS:  NONE
053460,000131: 
053461,000132:                                                                                                  #  OUTPUT:       THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
053462,000133:                                                                                                  #                RMAG1           E:(-29) M:(-27)         M  RN, PRESENT RADIUS LENGTH.
053463,000134:                                                                                                  #                NRMAG           E:(-29+NR)              M  RMAG, NORMALIZED
053464,000135:                                                                                                  #                                M:(-27+NR)
053465,000136:                                                                                                  #                X1                                      -NR, NORM COUNT
053466,000137:                                                                                                  #                TFFNP           E:(-38+2NR)             M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.  FOR VGAMCALC
053467,000138:                                                                                                  #                                M:(-36+2NR)
053468,000139:                                                                                                  #                TFF/RTMU        E:(17) M:(14)           1/SQRT(MU)
053469,000140:                                                                                                  #                TFFVSQ          E:(20) M:(18)           1/M  -(V SQ/MU):  PRESENT VELOCITY, NORMLIZED.  FOR VGAMCALC
053470,000141:                                                                                                  #                TFFALFA         E:(26-NR)               1/M  ALFA, WEIGHTED BY NR
053471,000142:                                                                                                  #                                M:(24-NR)
053472,000143:                                                                                                  #                TFFRTALF        E:(10+NA)               SQRT(ALFA), NORMALIZED
053473,000144:                                                                                                  #                                M:(9+NA)

Page 1263

053475,000146:                                                                                                  #                X2                                      -NA, NORMCOUNT
053476,000147:                                                                                                  #                TFF1/ALF        E:(-22-2NA)             SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
053477,000148:                                                                                                  #                                M:(-20-2NA)
053478,000149:                                                                                                  #                PUSHLOC AT PDL+0
053479,000150: 
053480,000151:                                                                                                  #        THE FOLLOWING IS STORED IN GENERAL ERASABLE
053481,000152:                                                                                                  #                VONE'           E:(10) M:(9)            V/RT(MU), NORMALIZED VELOCITY
053482,000153: 
053483,000154:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053484,000155:                                                                                                  #                RONE            E:(-29) M:(-27)         M  STATE VECTOR         LEFT BY CALLER
053485,000156:                                                                                                  #                VONE            E:(-7) M:(-5)           M/CS  STATE VECTOR      LEFT BY CALLER
053486,000157:                                                                                                  #                TFF/RTMU        E:(17) M:(14)           1/RT(CS SQ/M CUBE)      IF ENTER VIA TFFCONMU.
053487,000158: 
053488,000159:                                                                                                  #  DEBRIS:       QPRET,          PDL+0 ... PDL+3
053489,000160: 
053490,000161: 33,3760                                           BANK     33                                    
053491,000162: 27,2000                                           SETLOC   TOF-FF                                
053492,000163: 27,2000                                           BANK                                           
053493,000164: 
053494,000165: 27,3361                                           COUNT*   $$/TFF                                
053495,000166: 
053496,000167: 27,3361           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)    E:(17) M:(14)
053497,000168: 
053498,000169: 27,3362           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
053499,000170: 27,3363           02207                                    RONE                                  #  SAVED RN.  M  E:(-29) M:(-27)
053500,000171: 27,3364           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
053501,000172: 27,3365           00045                                    36D                                   #  MAGNITUDE
053502,000173: 27,3366           00015                           STORE    RMAG1                                 #  M  E:(-29) M:(-27)
053503,000174: 
053504,000175: 27,3367           77701                           NORM                                           
053505,000176: 27,3370           00047                                    X1                                    #  -NR
053506,000177: 27,3371           24041                           STOVL    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
053507,000178: 27,3372           02215                                    VONE                                  #  SAVED VN.  M/CS  E:(-7) M:(-5)
053508,000179: 27,3373           77761                           VXSC                                           
053509,000180: 27,3374           00037                                    TFF/RTMU                              #  E:(17) M:(14)
053510,000181: 27,3375           02170                           STORE    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
053511,000182: 
053512,000183: 27,3376           47361                           VXSC     VXV                                   
053513,000184: 27,3377           00041                                    NRMAG                                 #  E:(-29+NR) M:(-27+NR)
053514,000185:                                                                                                  #  UR/2 FROM PDL
053515,000186: 27,3400           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR) M:(-18+NR)
053516,000187: 27,3401           14035                           STODL    TFFNP                                 #  LC P  M  E:(-38+2NR) M:(-36+2NR)
053517,000188:                                                                                                  #  SAVE ALSO FOR VGAMCALC
053518,000189: 27,3402           06514                                    TFF1/4                                
053519,000190: 27,3403           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M  E:(26-NR) M:(24-NR)
053520,000191: 27,3404           00041                                    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
053521,000192: 27,3405           02170                                    VONE'                                 #  SAVED VN.  E:(10) M:(9)
053522,000193: 27,3406           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
053523,000194: 27,3407           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)  E:(20) M:(18)
053524,000195:                                                                                                  #  SAVE FOR VGAMCALC
053525,000196: 27,3410           43257                           SR*      DAD                                   

Page 1264

053527,000198: 27,3411           20573                                    0          -6,1                       #  GET -VSQ/MU  E:(26-NR) M:(24-NR)
053528,000199: 27,3412           77626                           STADR                                          
053529,000200:                                                                                                  #  2/RMAG  FROM PDL+2
053530,000201: 27,3413           77744                           STORE    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
053531,000202: 27,3414           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA  E:(20) M:(18)
053532,000203: 27,3415           20173                                    0          -6,1                       
053533,000204: 27,3416           75446                           ABS      SQRT                                  #  E:(10) M:(9)
053534,000205: 27,3417           77701                           NORM                                           
053535,000206: 27,3420           00050                                    X2                                    #  X2 = -NA
053536,000207: 27,3421           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA) M:(9+NA)
053537,000208: 27,3422           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
053538,000209:                                                                                                  #  ALFA FROM PDL+2  E:(20) M:(18)
053539,000210: 27,3423           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
053540,000211: 27,3424           57426                                    +2                                    
053541,000212: 27,3425           06514                                    TFF1/4                                
053542,000213: 27,3426           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053543,000214: 27,3427           77616        DUMPCNIC           RVQ                                            
053544,000215: 
053545,000216:                                                                                                  #                        39 W

Page 1265

053547,000218:                                                                                                  #  SUBROUTINE NAME:  TFFRP/RA                    DATE: 01.17.67
053548,000219:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
053549,000220:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053550,000221:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
053551,000222:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
053552,000223:                                                                                                  #                                                                        ALSO IMPROVE ACCURACY OF RAPO.
053553,000224: 
053554,000225:                                                                                                  #  FUNCTIONAL DESCRIPTION:  USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
053555,000226:                                                                                                  #        APOGEE RADIUS FOR A GENERAL CONIC.
053556,000227:                                                                                                  #        PROGRAM GIVES PERIGEE RADIUS AS         APOGEE RADIUS IS GIVEN BY
053557,000228:                                                                                                  #                RP = P/(1+E)                            RA = (1+E) / ALFA
053558,000229:                                                                                                  #        WHERE    2
053559,000230:                                                                                                  #                E  = 1 - P ALFA
053560,000231:                                                                                                  #        IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
053561,000232:                                                                                                  #                1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
053562,000233:                                                                                                  #                2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
053563,000234:                                                                                                  #                3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
053564,000235: 
053565,000236:                                                                                                  #        THIS SUBROUTINE REQUIRES THE SIGNED RECIPROCAL SEMI MAJ AXIS, ALFA, AND SEMI LATUS RECTUM AS DATA.
053566,000237: 
053567,000238:                                                                                                  #  CALLING SEQUENCE:     CALL
053568,000239:                                                                                                  #                                TFFRP/RA
053569,000240:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
053570,000241:                                                                                                  #        C(MPAC) UNSPECIFIED
053571,000242: 
053572,000243:                                                                                                  #  SUBROUTINES CALLED:   NONE
053573,000244: 
053574,000245:                                                                                                  #  NORMAL EXIT MODE:     RVQ
053575,000246:                                                                                                  #        IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
053576,000247:                                                                                                  #        OTHERWISE, RAPO = POSMAX.
053577,000248: 
053578,000249:                                                                                                  #  ALARMS:       NONE
053579,000250: 
053580,000251:                                                                                                  #  OUTPUT:       STORED IN PUSH LIST AREA.  SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO TFF/CONIC.
053581,000252:                                                                                                  #        RPER    E:(-29) M:(-27)         M       PERIGEE RADIUS          DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
053582,000253:                                                                                                  #        RAPO    E:(-29) M:(-27)         M       APOGEE RADIUS           WILL BE DESTROYED BY CALCTFF/CALCTPER
053583,000254:                                                                                                  #        PUSHLOC AT PDL+0
053584,000255: 
053585,000256:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053586,000257:                                                                                                  #        TFFALFA E:(26-NR)               M       1/SEMI MAJ AXIS         LEFT BY TFFCONIC
053587,000258:                                                                                                  #                M:(24-NR)
053588,000259:                                                                                                  #        TFFNP   E:(-38+2NR)             M       LC P, SEMI LATUS RECTUM LEFT BY TFFCONIC
053589,000260:                                                                                                  #                M:(-36+2NR)
053590,000261:                                                                                                  #        X1                              -NR, NORM COUNT OF RMAG         LEFT BY TFFCONIC
053591,000262:                                                                                                  #        X2                              -NA, NORM COUNT OF ALFA         LEFT BY TFFCONIC
053592,000263: 
053593,000264:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+1
053594,000265: 

Page 1266

053596,000267: 27,3430                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29) M:(-27)
053597,000268: 27,3430                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29) M:(-27)
053598,000269: 
053599,000270: 27,3430           41345        TFFRP/RA           DLOAD    DMP                                   
053600,000271: 27,3431           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
053601,000272: 27,3432           00035                                    TFFNP                                 #  LC P  M E:(-38+2NR) M:(-36+2NR)
053602,000273: 27,3433           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
053603,000274: 27,3434           20571                                    0          -8D,1                      #  ALFA P (-4)
053604,000275: 27,3435           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
053605,000276:                                                                                                  #  (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
053606,000277: 27,3436           17766                                    DP2(-4)                               
053607,000278: 27,3437           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA) (-4)
053608,000279: 27,3440           06514                                    TFF1/4                                
053609,000280: 27,3441           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
053610,000281: 27,3442           00035                                    TFFNP                                 #  LCP  M  E:(-38+2NR) M:(-36+2NR)
053611,000282: 27,3443           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
053612,000283: 27,3444           20601                                    0,1                                   #  X1=-NR
053613,000284: 27,3445           20572                                    0          -7,1                       #  (EFFECTIVE SL)
053614,000285: 27,3446           14017                           STODL    RPER                                  #  PERIGEE RADIUS  M  E:(-29) M:(-27)
053615,000286:                                                                                                  #  (1+E)  (-2)  FROM PDL+0
053616,000287: 27,3447           41005                           DMP      BOVB                                  
053617,000288: 27,3450           00027                                    TFF1/ALF                              #  E:(-22-2NA) M:(-20-2NA)
053618,000289: 27,3451           57754                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
053619,000290: 27,3452           53654                           BZE      SL*                                   
053620,000291: 27,3453           57462                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
053621,000292: 27,3454           57603                                    0          -5,2                       #  -5+NA
053622,000293: 27,3455           40057                           SL*      BOV                                   
053623,000294: 27,3456           57576                                    0,2                                   
053624,000295: 27,3457           57462                                    MAXRA                                 #  SET POSMAX IF OVFL.
053625,000296: 27,3460           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
053626,000297: 27,3461           57464                                    +3                                    
053627,000298: 27,3462           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID.  SET RAPO =
053628,000299: 27,3463           17772                                    NEARONE                               #  POSMAX AS A TAG.
053629,000300: 27,3464           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M  E:(-29) M:(-27)
053630,000301: 27,3465           77616        DUMPRPRA           RVQ                                            
053631,000302: 
053632,000303:                                                                                                  #                        30 W
053633,000304: 

Page 1267

053635,000306:                                                                                                  #  SUBROUTINE NAME:  CALCTPER / CALCTFF          DATE:  01.29.67
053636,000307:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
053637,000308:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053638,000309:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 67
053639,000310:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 14 APR 67
053640,000311:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 8 JUL 67          NEAR EARTH MUE AND NEG TFF (GONEPAST)
053641,000312:                                                                                                  #  MOD NO:  4    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD VARIABLE MU.
053642,000313:                                                                                                  #  MOD NO:  5    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
053643,000314: 
053644,000315:                                                                                                  #  FUNCTIONAL DESCRIPTION:  PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION RN AND
053645,000316:                                                                                                  #        VELOCITY VN TO A RADIUS LENGTH SPECIFIED BY RTERM, SUPPLIED BY THE USER.  THE POSITION VECTOR
053646,000317:                                                                                                  #        RN MAY BE ON EITHER SIDE OF THE CONIC, BUT RTERM IS CONSIDERED ON THE INBOUND SIDE.
053647,000318:                                                                                                  #        THE EQUATIONS ARE
053648,000319: 
053649,000320:                                                                                                  #                Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)  (INBOUND SIDE)) LEQ +- LCE/SQRT(ALFA)
053650,000321:                                                                                                  #                     -  -
053651,000322:                                                                                                  #                Q1 = RN.VN / SQRT(MU)                                   LEQ +- LCE/SQRT(ALFA)
053652,000323: 
053653,000324:                                                                                                  #                Z = NUM / DEN                                           LEQ +- 1/SQRT(ALFA)
053654,000325: 
053655,000326:                                                                                                  #        WHERE, IF INBOUND
053656,000327:                                                                                                  #                NUM = RTERM -RN                                         LEQ +- 2 LCE/ALFA
053657,000328:                                                                                                  #                DEN = Q2+Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
053658,000329: 
053659,000330:                                                                                                  #        AND, IF OUTBOUND
053660,000331:                                                                                                  #                NUM = Q2-Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
053661,000332:                                                                                                  #                DEN = 2 - ALFA (RTERM + RN).                            LEQ +- 2 LCE
053662,000333: 
053663,000334:                                                                                                  #        IF      ALFA ZZ < 1.0           (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
053664,000335:                                                                                                  #        THEN    X = ALFA Z Z
053665,000336:                                                                                                  #        AND     TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
053666,000337:                                                                                                  #                EXCEPT  IF ALFA PNZ, AND IF TFF NEG,
053667,000338:                                                                                                  #                THEN    TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
053668,000339:                                                                                                  #        OR      IF ALFA ZZ GEQ 1.0      (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
053669,000340:                                                                                                  #        THEN    X = 1/ALFA Z Z
053670,000341:                                                                                                  #        AND     TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
053671,000342:                                                                                                  #        WHERE   T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
053672,000343:                                                                                                  #                             2      3             2
053673,000344:                                                                                                  #                1/3 - X/5 + X /7 - X /9 ...     (X  < 1.0)
053674,000345: 
053675,000346:                                                                                                  #  CALLING SEQUENCE:     TIME TO RTERM                   TIME TO PERIGEE
053676,000347:                                                                                                  #                        CALL                            CALL
053677,000348:                                                                                                  #                                CALCTFF                         CALCTPER
053678,000349:                                                                                                  #                        C(MPAC) = TERMNL RAD M          C(MPAC) = PERIGEE RAD M
053679,000350:                                                                                                  #        FOR EITHER, E:(-29) M:(-27)
053680,000351:                                                                                                  #        FOR EITHER, PUSHLOC = PDL+0, ARBITRARY IF LEQ 8D.

Page 1268

053682,000353: 
053683,000354:                                                                                                  #  SUBROUTINES CALLED:   T(X), VIA RTB
053684,000355: 
053685,000356:                                                                                                  #  NORMAL EXIT MODE:     RVQ
053686,000357:                                                                                                  #        HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS IN MPAC.  USER MUST STORE.
053687,000358:                                                                                                  #                A. TFF = FLIGHT TIME.  NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
053688,000359:                                                                                                  #                B. (THIS OPTION IS NO LONGER USED.)
053689,000360:                                                                                                  #                C. TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
053690,000361:                                                                                                  #                   THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
053691,000362: 
053692,000363:                                                                                                  #  OUTPUT:       C(MPAC)         (-28) CS        TIME OF FLIGHT, OR TIME TO PERIGEE
053693,000364:                                                                                                  #                TFFX            (0)             X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
053694,000365:                                                                                                  #                NRTERM          E:(-29+NR) M    RTERM, WEIGHTED BY NR                   LEFT FOR ENTRY DISPLAY TFF ROUTINES
053695,000366:                                                                                                  #                                M:(-27+NR)
053696,000367:                                                                                                  #                TFFTEM          E:(-59+2NR)     LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
053697,000368:                                                                                                  #                                M:(-55+2NR)     LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
053698,000369:                                                                                                  #                NOTE:   TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
053699,000370:                                                                                                  #                RMAG1           E:(-29) M:(-27) PDL 12 NOT TOUCHED.
053700,000371:                                                                                                  #                TFFQ1           E:(-16) M:(-15) PDL 14D
053701,000372:                                                                                                  #                TFFDELQ         E:(-16) M:(-15) PDL 10D
053702,000373:                                                                                                  #                PUSHLOC AT PDL+0
053703,000374: 
053704,000375:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053705,000376:                                                                                                  #                RONE            E:(-29) M:(-27) M  STATE VECTOR                         LEFT BY USER
053706,000377:                                                                                                  #                VONE'           E:(+10) M:(+9)  VN/SQRT(MU)                             LEFT BY TFF/CONIC
053707,000378:                                                                                                  #                RMAG1           E:(-29) M:(-27) PRESENT RADIUS, M                       LEFT BY TFFCONIC
053708,000379:                                                                                                  #                C(MPAC)         E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH, M        LEFT BY USER
053709,000380: 
053710,000381:                                                                                                  #                THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
053711,000382:                                                                                                  #                TFF/RTMU        E:(17) M:(14)   1/SQRT(MU)                              LEFT BY TFFCONIC.
053712,000383:                                                                                                  #                NRMAG           E:(-29+NR)      M  RMAG, NORMALIZED                     LEFT BY TFFCONIC
053713,000384:                                                                                                  #                                M:(-27+NR)
053714,000385:                                                                                                  #                X1                              -NR, NORM COUNT                         LEFT BY TFFCONIC
053715,000386:                                                                                                  #                TFFNP           E:(-38+2NR)     M  LCP, SEMI LATUS RECTUM, WEIGHT NR    LEFT BY TFFCONIC
053716,000387:                                                                                                  #                                M:(-36+2NR)
053717,000388:                                                                                                  #                TFFALFA         E:(26-NR)       1/M  ALFA, WEIGHT NR                    LEFT BY TFFCONIC
053718,000389:                                                                                                  #                                M:(24-NR)
053719,000390:                                                                                                  #                TFFRTALF        E:(10+NA)       SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
053720,000391:                                                                                                  #                                M:(9+NA)
053721,000392:                                                                                                  #                X2                              -NA, NORMCOUNT                          LEFT BY TFFCONIC
053722,000393:                                                                                                  #                TFF1/ALF        E:(-22-2NA)     SIGNED SEMIMAJ AXIS, WEIGHTED BY NA     LEFT BY TFFCONIC
053723,000394:                                                                                                  #                                M:(-20-2NA)
053724,000395: 
053725,000396:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+3
053726,000397:                                                                                                  #                RTERM           E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH
053727,000398:                                                                                                  #                RAPO            E:(-29) M:(-27) PDL 16D (=NRTERM)
053728,000399:                                                                                                  #                RPER            E:(-29) M:(-27) PDL 14D (=TFFQ1)
053729,000400: 

Page 1269

053731,000402: 27,3466           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER IN MPAC
053732,000403: 27,3467           03436                                    TFFSW                                 
053733,000404: 27,3470           57473                                    +3                                    
053734,000405: 27,3471           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
053735,000406: 27,3472           03676                                    TFFSW                                 
053736,000407: 27,3473           00023                 +3        STORE    RTERM                                 #  E:(-29) M:(-27)
053737,000408: 27,3474           77657                           SL*                                            
053738,000409: 27,3475           20201                                    0,1                                   #  X1=-NR
053739,000410: 27,3476           00021                           STORE    NRTERM                                #  RTERM  E:(-29+NR) M:(-27+NR)
053740,000411: 27,3477           44205                           DMP      BDSU                                  
053741,000412: 27,3500           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
053742,000413: 27,3501           06514                                    TFF1/4                                
053743,000414: 27,3502           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
053744,000415: 27,3503           00021                                    NRTERM                                #  E:(-29+NR) M:(-27+NR)
053745,000416: 27,3504           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
053746,000417:                                                                                                  #  E:(-32+NR) M:(-30+NR)
053747,000418: 27,3505           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
053748,000419: 27,3506           20573                                    0          -6,1                       #  X1 = -NR
053749,000420: 27,3507           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
053750,000421:                                                                                                  #  RTERM(2-ALFA RTERM) FROM PDL +2
053751,000422:                                                                                                  #  E:(-32+NR) M:(-30+NR)
053752,000423: 27,3510           77657                           SR*                                            #  LEAVE  E:(-32) M:(-30)
053753,000424: 27,3511           20601                                    0,1                                   #  X1 = -NR
053754,000425: 27,3512           71214                           BOFF     DLOAD                                 #  CHECK TFF /TPER SWITCH
053755,000426: 27,3513           03756                                    TFFSW                                 
053756,000427: 27,3514           57516                                    +2                                    #  IF TFF, CONTINUE
053757,000428: 27,3515           06524                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
053758,000429: 27,3516           75440                 +2        BMN      SQRT                                  #  E:(-16) M:(-15)
053759,000430: 27,3517           57651                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
053760,000431:                                                                                                  #  RESET PDL, SET TFF=POSMAX, AND EXIT.
053761,000432: 
053762,000433: 27,3520           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
053763,000434: 27,3521           57754                                    TCDANZIG                              #  ANY PORT IN A STORM.
053764,000435: 27,3522           24045                           STOVL    TFFTEM                                #  Q2  E:(-16) M:(-15)
053765,000436: 27,3523           02170                                    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
053766,000437: 27,3524           52441                           DOT      SL3                                   
053767,000438: 27,3525           02207                                    RONE                                  #  SAVED RN.  E:(-29) M:(-27)
053768,000439: 27,3526           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
053769,000440:                                                                                                  #  E:(-16) M:(-15)
053770,000441: 27,3527           44240                           BMN      BDSU                                  
053771,000442: 27,3530           57551                                    INBOUND                               #  USE ALTERNATE Z
053772,000443: 27,3531           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
053773,000444: 
053774,000445:                                                                                                  #  OUTBOUND Z CALC CONTINUES HERE
053775,000446: 
053776,000447: 27,3532           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E:(-16) M:(-15)
053777,000448: 27,3533           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
053778,000449: 27,3534           44205                           DMP      BDSU                                  

Page 1270

053780,000451: 27,3535           00041                                    NRMAG                                 #  RMAG  E:(-29+NR) M:(-27+NR)
053781,000452:                                                                                                  #  (2-RTERM ALFA)  (-3) FROM PDL+0
053782,000453: 27,3536           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E:(-3) OR (-16)
053783,000454:                                                                                                  #                M:(-3) OR (-15)
053784,000455: 27,3537           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
053785,000456: 27,3540           17760                                    LIM(-22)                              #  =1.0-B(-22)
053786,000457: 27,3541           57562                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
053787,000458: 27,3542           65345                           DLOAD    PDDL                                  #  SET DEN=0 OTHERWISE
053788,000459: 27,3543           06524                                    TFFZEROS                              
053789,000460:                                                                                                  #  XCH ZERO WITH PDL+0
053790,000461: 27,3544           57545                           DLOAD    DCOMP                                 
053791,000462: 27,3545           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
053792,000463: 27,3546           71240                           BMN      DLOAD                                 #  FOR TPER:  Z INDET AT DELE/2=0 AND 90.
053793,000464: 27,3547           57656                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
053794,000465: 
053795,000466:                                                                                                  #  Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
053796,000467: 27,3550           77616        DUMPTFF1           RVQ                                            #  RETURN TFF =0
053797,000468: 
053798,000469:                                                                                                  #  INBOUND Z CALC CONTINUES HERE
053799,000470: 
053800,000471: 27,3551           77745        INBOUND            DLOAD                                          #  RESET PDL+0
053801,000472: 27,3552           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
053802,000473: 27,3553           00023                                    RTERM                                 #  E:(-29) M:(-27)
053803,000474: 27,3554           00015                                    RMAG1                                 #  E:(-29) M:(-27)
053804,000475: 27,3555           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E:(-29) M:(-27)
053805,000476: 27,3556           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
053806,000477: 27,3557           52015                           DAD      GOTO                                  
053807,000478: 27,3560           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
053808,000479: 27,3561           57536                                    SAVEDEN                               #  DEN = Q2+Q1  E:(-16) M:(-15)
053809,000480: 
053810,000481: 27,3562           65215        TFFXTEST           DAD      PDDL                                  #  (ABS(DEN) TO PDL+2))  E:(-3) OR (-16)
053811,000482:                                                                                                  #                        M:(-3) OR (-15)
053812,000483: 27,3563           17762                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
053813,000484: 27,3564           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
053814,000485: 27,3565           53605                           DMP      SR*                                   
053815,000486: 27,3566           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
053816,000487: 27,3567           57201                                    0          -3,2                       #  X2=-NA
053817,000488: 27,3570           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)       E:(-3) OR (-16)
053818,000489:                                                                                                  #                                M:(-3) OR (-15)
053819,000490:                                                                                                  #  ABS(DEN) FROM PDL+2   E:(-3) OR (-16)
053820,000491:                                                                                                  #                        M:(-3) OR (-15)
053821,000492: 27,3571           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
053822,000493: 27,3572           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
053823,000494: 27,3573           57654                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
053824,000495: 
053825,000496:                                                                                                  #  OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
053826,000497: 
053827,000498: 27,3574           45471                           DDV      STADR                                 
053828,000499:                                                                                                  #  DEN FROM PDL+0        E:(-3) OR (-16)
053829,000500:                                                                                                  #                        M:(-3) OR (-15)
053830,000501: 27,3575           77732                           STORE    TFFTEM                                #  Z SAVE FOR SIGN OF SDELF.

Page 1271

053832,000503:                                                                                                  #  E:(-13) M:(-12)
053833,000504: 27,3576           63406                           PUSH     DSQ                                   #  Z TO PDL+0
053834,000505: 27,3577           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E:(-26) M:(-24)
053835,000506: 27,3600           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
053836,000507: 27,3601           75261                           SL       SIGN                                  
053837,000508: 27,3602           20206                                    5                                     
053838,000509: 27,3603           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
053839,000510: 27,3604           14045                           STODL    TFFTEM                                #  P ZSQ  E:(-59+2NR) M:(-55+2NR)
053840,000511:                                                                                                  #  (ARG IS USED IN TFF/TRIG)
053841,000512:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
053842,000513: 27,3605           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
053843,000514: 27,3606           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
053844,000515: 27,3607           77657                           SL*                                            
053845,000516: 27,3610           20201                                    0,1                                   #  X1=-NR
053846,000517: 27,3611           00043                           STORE    TFFX                                  #  X
053847,000518: 27,3612           41234                           RTB      DMP                                   
053848,000519: 27,3613           57736                                    T(X)                                  #  POLY
053849,000520:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
053850,000521: 27,3614           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E:(-29) M:(-27)
053851,000522: 27,3615           00023                                    RTERM                                 #  RTERM  E:(-29) M:(-27)
053852,000523: 27,3616           41215                           DAD      DMP                                   
053853,000524: 27,3617           00015                                    RMAG1                                 #  E:(-29) M:(-27)
053854,000525:                                                                                                  #  Z FROM PDL+0  E:(-13) M:(-12)
053855,000526: 27,3620           51042                           SR3      BPL                                   #  TFF SQRT(MU)  E:(-45) M:(-42)
053856,000527: 27,3621           57642                                    ENDTFF                                #  (NO PUSH UP)
053857,000528: 27,3622           75206                           PUSH     SIGN                                  #  TFF SQRT(MU) TO PDL+0
053858,000529: 27,3623           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
053859,000530: 27,3624           71244                           BPL      DLOAD                                 #  GONE PAST ?
053860,000531: 27,3625           57646                                    NEGTFF                                #  YES. TFF < 0.
053861,000532: 27,3626           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053862,000533: 27,3627           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
053863,000534: 27,3630           57646                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
053864,000535: 
053865,000536:                                                                                                  #  CORRECT FOR ORBITAL PERIOD.
053866,000537: 
053867,000538: 27,3631           77676                           DCOMP                                          #  YES.  CORRECT FOR ORB PERIOD.
053868,000539: 27,3632           56205                           DMP      DDV                                   
053869,000540: 27,3633           17756                                    PI/16                                 #  2 PI (-5)
053870,000541: 27,3634           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
053871,000542: 27,3635           53657                           SL*      SL*                                   
053872,000543: 27,3636           57602                                    0          -4,2                       #  X2=-NA
053873,000544: 27,3637           57602                                    0          -4,2                       
053874,000545: 27,3640           43257                           SL*      DAD                                   
053875,000546: 27,3641           57576                                    0,2                                   
053876,000547:                                                                                                  #  TFF SQRT(MU) FROM PDL+0       E:(-45) M:(-42)
053877,000548: 27,3642           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC          E:(-45) M:(-42)
053878,000549: 27,3643           00037                                    TFF/RTMU                              #  E:(17) M:(14)
053879,000550: 27,3644           57652                                    MAXTFF                                #  SET POSMAX IF OVFL.
053880,000551: 
053881,000552: 27,3645           77616        DUMPTFF2           RVQ                                            #  RETURN TFF (-28) CS IN MPAC.
053882,000553: 

Page 1272

053884,000555: 27,3646           77745        NEGTFF             DLOAD                                          
053885,000556:                                                                                                  #  TFF SQRT(MU) FROM PDL+0, NEGATIVE.
053886,000557: 27,3647           77650                           GOTO                                           
053887,000558: 27,3650           57642                                    ENDTFF                                
053888,000559: 
053889,000560: 27,3651           77745        MAXTFF1            DLOAD                                          #  RESET PDL
053890,000561: 27,3652           43545        MAXTFF             DLOAD    RVQ                                   
053891,000562: 27,3653           17772                                    NEARONE                               
053892,000563: 
053893,000564:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
053894,000565: 
053895,000566:                                                                                                  #  NUM FROM TFFX.        E:(-16) OR (-29)
053896,000567:                                                                                                  #                        M:(-15) OR (-27)
053897,000568: 27,3654           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
053898,000569: 27,3655           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
053899,000570:                                                                                                  #  DEN FROM PDL+0  E:(-3)/( 16)  M:(-3)/(-15)
053900,000571:                                                                                                  #  N/D TO PDL+0  E:(11) M:(10)
053901,000572: 27,3656           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
053902,000573: 27,3657           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
053903,000574: 27,3660           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
053904,000575: 27,3661           14013                           STODL    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
053905,000576:                                                                                                  #  D/N FROM PDL+0
053906,000577: 27,3662           77626                           STADR                                          
053907,000578: 27,3663           77732                           STORE    TFFTEM                                #  D/N  E:(11) M:(10)
053908,000579: 27,3664           53605                           DMP      SL*                                   
053909,000580: 27,3665           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053910,000581: 27,3666           57576                                    0,2                                   #  1/ALFA Z  E:(-11-NA) M:(-10-NA)
053911,000582: 27,3667           41206                           PUSH     DMP                                   #  TO PDL+0
053912,000583: 27,3670           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
053913,000584: 27,3671           41057                           SL*      BOVB                                  
053914,000585: 27,3672           57576                                    0,2                                   #  X2= -NA
053915,000586: 27,3673           21713                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
053916,000587: 27,3674           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
053917,000588: 27,3675           41234                           RTB      DMP                                   
053918,000589: 27,3676           57736                                    T(X)                                  #  POLY
053919,000590: 27,3677           00043                                    TFFX                                  
053920,000591: 27,3700           45242                           SR3      DSU                                   
053921,000592: 27,3701           17764                                    DP2(-3)                               
053922,000593: 27,3702           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA   E:(-15-NA)
053923,000594:                                                                                                  #                        M:(-14-NA)
053924,000595:                                                                                                  #  1/ALFA Z FROM PDL+0   E:(-11-NA)
053925,000596:                                                                                                  #                        M:(-10-NA)
053926,000597: 27,3703           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
053927,000598: 27,3704           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
053928,000599: 27,3705           00015                                    RMAG1                                 #  E:(-29) M:(-27)
053929,000600: 27,3706           43312                           SL2      DAD                                   
053930,000601: 27,3707           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
053931,000602: 27,3710           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z) =SGN OF SDELF  E:(-16) M:(-15
053932,000603: 27,3711           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
053933,000604: 27,3712           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1273

053935,000606: 27,3713           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053936,000607: 27,3714           57575                                    1,2                                   #  X2=-NA
053937,000608: 27,3715           53765                           SIGN     SL*                                   
053938,000609: 27,3716           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
053939,000610: 27,3717           57576                                    0,2                                   
053940,000611: 27,3720           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR) M:(-55+2NR)
053941,000612:                                                                                                  #  (ARG FOR USE IN TFF/TRIG)
053942,000613: 27,3721           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053943,000614: 27,3722           41366                           SQRT     DMP                                   
053944,000615: 27,3723           17756                                    PI/16                                 #  PI (-4)
053945,000616: 27,3724           77615                           DAD                                            
053946,000617:                                                                                                  #  2(XT(X)-1)/Z ALFA FROM PDL    E:(-15-NA)
053947,000618:                                                                                                  #                                M:(-14-NA)
053948,000619: 27,3725           45257                           SL*      DSU                                   
053949,000620: 27,3726           57577                                    0          -1,2                       
053950,000621: 27,3727           00013                                    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
053951,000622: 27,3730           53605                           DMP      SL*                                   
053952,000623: 27,3731           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
053953,000624: 27,3732           57601                                    0          -3,2                       
053954,000625: 27,3733           52057                           SL*      GOTO                                  
053955,000626: 27,3734           57602                                    0          -4,2                       
053956,000627: 27,3735           57642                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
053957,000628: 

Page 1274

053959,000630:                                                                                                  #  PROGRAM NAME:  T(X)                           DATE:  01.17.67
053960,000631:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
053961,000632:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
053962,000633: 
053963,000634:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES CALCTFF AND
053964,000635:                                                                                                  #        CALCTPER TO APPROXIMATE THE SERIES
053965,000636:                                                                                                  #                           2     3
053966,000637:                                                                                                  #                1/3 -X/5 +X /7 -X /9 ...
053967,000638: 
053968,000639:                                                                                                  #        WHERE   X = ALFA Z Z            IF ALFA Z Z LEQ 1
053969,000640:                                                                                                  #                X = 1/(ALFA Z Z)        IF ALFA Z Z G 1
053970,000641: 
053971,000642:                                                                                                  #        ALSO    X IS NEG FOR HYPERBOLIC ORBITS
053972,000643:                                                                                                  #                X = 0 FOR PARABOLIC ORBITS
053973,000644:                                                                                                  #                X IS POSITIVE FOR ELLIPTIC ORBITS
053974,000645: 
053975,000646:                                                                                                  #        FOR FLIGHT 278, THE POLYNOMIAL T(X) IS FITTED OVER THE RANGE (0,+1) AND HAS A MAXIMUM
053976,000647:                                                                                                  #        DEVIATION FROM THE SERIES OF 2 E-5   (T(X) IS A CHEBYCHEV TYPE FIT AND WAS OBTAINED USING
053977,000648:                                                                                                  #        MAC PROGRAM AUTCURFIT294RRB AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE (-.08,+1).)
053978,000649: 
053979,000650:                                                                                                  #  CALLING SEQUENCE:     RTB
053980,000651:                                                                                                  #                                T(X)
053981,000652:                                                                                                  #        C(MPAC) = X
053982,000653: 
053983,000654:                                                                                                  #  SUBROUTINES CALLED:  NONE
053984,000655: 
053985,000656:                                                                                                  #  NORMAL EXIT MODE:  TC DANZIG
053986,000657: 
053987,000658:                                                                                                  #  ALARMS:  NONE
053988,000659: 
053989,000660:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
053990,000661: 
053991,000662:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
053992,000663:                                                                                                  #        C(MPAC) = X
053993,000664: 
053994,000665:                                                                                                  #  DEBRIS:  NONE
053995,000666: 
053996,000667: 27,3736           07225        T(X)               TC       POLY                                  
053997,000668: 27,3737           00004                           DEC      4          B-14                       #  N-1
053998,000669: 27,3740           12525 12525                     2DEC     3.333333333 E-1                        
053999,000670: 27,3742           71463 57703                     2DEC*    -1.999819135 E-1*                       
054000,000671: 27,3744           04423 17645                     2DEC*    1.418148467 E-1*                       
054001,000672: 27,3746           74604 43667                     2DEC*    -1.01310997 E-1*                       
054002,000673: 27,3750           01626 37256                     2DEC*    5.609004986 E-2*                       
054003,000674: 27,3752           77404 52071                     2DEC*    -1.536156925 E-2*                       
054004,000675: 
054005,000676: 27,3754           06064        ENDT(X)            TC       DANZIG                                
054006,000677: 
054007,000678: 27,3755  27,3754               TCDANZIG           =        ENDT(X)                               
054008,000679: 

Page 1275

054010,000681:                                                                                                  #  TFF CONSTANTS
054011,000682: 
054012,000683: 32,3751                                           BANK     32                                    
054013,000684: 
054014,000685: 27,2000                                           SETLOC   TOF-FF1                               
054015,000686: 27,2000                                           BANK                                           
054016,000687: 
054017,000688:                                                                                                  #                                                NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
054018,000689:                                                                                                  # MUE            =       3.990815471 E10         M CUBE/CS SQ
054019,000690:                                                                                                  # RTMUE          =       1.997702549 E5 B-18*    MODIFIED EARTH MU
054020,000691: 
054021,000692:                                                                                                  #                                                NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
054022,000693:                                                                                                  # MUM            =       4.902778 E8             M CUBE/CS SQ
054023,000694:                                                                                                  # RTMUM          2DEC*   2.21422176 E4 B-18*
054024,000695: 27,3755           06220 37553  PI/16              2DEC     3.141592653 B-4                        
054025,000696: 27,3757           37777 37700  LIM(-22)           2OCT     3777737700                            #  1.0 -B(-22)
054026,000697: 27,3761           00000 00100  DP(-22)            2OCT     0000000100                            #  B(-22)
054027,000698: 27,3763           04000 00000  DP2(-3)            2DEC     1          B-3                        
054028,000699: 27,3765           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
054029,000700: 
054030,000701:                                                                                                  #  RPAD1         2DEC    6373338 B-29            M (-29) = 20909901.57 FT
054031,000702: 27,3767  23,2337               RPAD1              =        RPAD                                  
054032,000703: 
054033,000704: 27,3767           00305 11205  R300K              2DEC     6464778    B-29                       #  (-29) M
054034,000705: 27,3771           37777 37777  NEARONE            2DEC     .999999999                            
054035,000706: 27,3773  23,2523               TFFZEROS           EQUALS   HI6ZEROS                              
054036,000707: 27,3773  23,2513               TFF1/4             EQUALS   HIDP1/4                               
054037,000708: 

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