Source Code

These source-code files were derived from scans of the Colossus 237 (Apollo 8 Command Module) program listing from the private collection of original AGC developer Fred Martin. Scanning was by Ron Burkey. Pre-existing Colossus 249 (Apollo 9 CM) source files were used as a template, and changes between Colossus 249 and Colossus 237 were manually transcribed by a team of volunteers. Note that the page images presented online are of reduced quality, and that additional images are available. Report any conversion errors or legibility problems in page images to info@sandroid.org. Notations on the program listing read, in part:

	GAP: ASSEMBLE REVISION 237 OF AGC PROGRAM COLOSSUS 
	BY NASA 2021111-031  1:17 AUG. 24, 1968
Note that the date is the date of the printout, not the date of the program revision.

056830,000002:                                                                                                  ## Copyright:   Public domain.
056831,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
056832,000004:                                                                                                  ## Purpose:     Part of the source code for Colossus build 237.
056833,000005:                                                                                                  ##              This is for the Command Module's (CM) Apollo Guidance
056834,000006:                                                                                                  ##              Computer (AGC), for Apollo 8.
056835,000007:                                                                                                  ## Assembler:   yaYUL
056836,000008:                                                                                                  ## Contact:     Jim Lawton <jim DOT lawton AT gmail DOT com>
056837,000009:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
056838,000010:                                                                                                  ## Page Scans:  www.ibiblio.org/apollo/ScansForConversion/Colossus237/
056839,000011:                                                                                                  ## Mod history: 2011-04-17 JL   Adapted from corresponding Colossus 249 file.
056840,000012:                                                                                                  ##              2011-04-17 JL   Removed temporary line.
056841,000013:                                                                                                  ##              2016-11-02 RSB  Typo (various offset-references +2 and +3 not indented).
056842,000014:                                                                                                  ##              2017-01-01 RSB  Proofed comment text using octopus/ProoferComments,
056843,000015:                                                                                                  ##                              and fixed errors found.
056844,000016:                                                                                                  ##              2017-01-20 RSB  Fixed comment-text errors noted while diff'ing
056845,000017:                                                                                                  ##                              vs Colossus 249.
056846,000018:                                                                                                  ##              2017-03-14 RSB  Comment-text fixes noted in proofing Luminary 116.
056847,000019: 

Page 1337

056849,000021:                                                                                                  #           THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES. THE TFF ROUTINES NEVER
056850,000022:                                                                                                  #  KNOW WHICH ORIGIN APPLIES. IT IS THE USER WHO KNOWS, AND WHO SUPPLIES  RONE, VONE AND 1/SQRT(MU)  AT THE
056851,000023:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
056852,000024: 
056853,000025:                                                                                                  #           EARTH ORIGIN           POSITION      -29       METERS
056854,000026:                                                                                                  #                                  VELOCITY      -7        METERS/CENTISECOND
056855,000027:                                                                                                  #                                  1/SQRT(MU)    +17       SQRT(CS SQ/METERS CUBED)
056856,000028: 
056857,000029:                                                                                                  #           MOON ORIGIN            POSITION      -27       METERS
056858,000030:                                                                                                  #                                  VELOCITY      -5        METERS/CENTISECONDS
056859,000031:                                                                                                  #                                  1/SQRT(MU)    +14       SQRT(CS SQ/METERS CUBED)
056860,000032: 
056861,000033:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE. IN ALL CASES,
056862,000034:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28). PROGRAM  TFF/CONIC  WILL GENERATE VONE/RTMU  AND
056863,000035:                                                                                                  #  LEAVE IT IN  VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
056864,000036:                                                                                                  #           THE USER MUST STORE THE STATE VECTOR IN  RONE, VONE  AND MU IN  THE FORM 1/SQRT(MU) IN  TFF/RTMU
056865,000037:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING  TFF/CONIC. SINCE  RONE, VONE  ARE IN THE EXTENDED VERB STORAGE AREA,
056866,000038:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
056867,000039:                                                                                                  #           PROGRAMS     CALC/TFF  AND  CALC/TPER  ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
056868,000040:                                                                                                  #  RADIUS. THIS RESTRICTION CAN BE REMOVED BY A  15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
056869,000041: 
056870,000042:                                                                                                  #           THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
056871,000043: 
056872,000044: 
056873,000045:                                                                                                  #                                                               BELOW      E:   IS USED FOR EARTH ORIGIN SCALE
056874,000046:                                                                                                  #                                                                          M:   IS USED FOR MOON  ORIGIN SCALE
056875,000047: 
056876,000048:                                                                                                  #  TFFSW         =       119D  BIT1      0 = CALCTFF        1 = CALCTPER
056877,000049: 23,3725                        TFFDELQ            =        10D                                   #  Q2-Q1              E: (-16)  M: (-15)
056878,000050: 23,3725                        RMAG1              =        12D                                   #  ABVAL(RN)  M       E: (-29)  M: (-27)
056879,000051:                                                                                                  #  RPER          =       14D             PERIGEE RADIUS M   E: (-29)  M: (-27)
056880,000052: 23,3725                        TFFQ1              =        14D                                   #  R.V / SQRT(MUE)    E: (-16)  M: (-15)
056881,000053:                                                                                                  #  SDELF/2                               SIN(THETA) /2
056882,000054: 23,3725                        CDELF/2            =        14D                                   #  COS(THETA) /2
056883,000055:                                                                                                  #  RAPO          =       16D             APOGEE RADIUS  M   E: (-29)  M: (-27)
056884,000056: 23,3725                        NRTERM             =        16D                                   #  TERMINAL RADIUS M  E: (-29+NR)
056885,000057:                                                                                                  #                     M: (-27+NR)
056886,000058: 23,3725                        RTERM              =        18D                                   #  TERMINAL RADIUS M  E: (-29)  M: (-27)
056887,000059: 23,3725                        TFFVSQ             =        20D                                   #  -(V SQUARED/MU)  1/M  E: (20)  M: (18)
056888,000060: 23,3725                        TFF1/ALF           =        22D                                   #  SEMI MAJ AXIS  M  E: (-22-2 NA)
056889,000061:                                                                                                  #                    M: (-20-2 NA)
056890,000062: 23,3725                        TFFRTALF           =        24D                                   #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
056891,000063: 23,3725                        TFFALFA            =        26D                                   #  ALFA  1/M   E: (26-NR)  M: (24-NR)
056892,000064: 23,3725                        TFFNP              =        28D                                   #  SEMI LATUS RECTUM  M  E: (-38+2 NR)
056893,000065:                                                                                                  #                        M: (-36+2 NR)
056894,000066: 23,3725                        TFF/RTMU           =        30D                                   #  1/SQRT(MU)         E: (17)   M: (14)
056895,000067: 23,3725                        NRMAG              =        32D                                   #  PRESENT RADIUS  M  E: (-29+NR)
056896,000068:                                                                                                  #                     M: (-27+NR)
056897,000069: 23,3725                        TFFX               =        34D                                   
056898,000070: 23,3725                        TFFTEM             =        36D                                   #  TEMPORARY

Page 1338

056900,000072:                                                                                                  #                                          REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
056901,000073:                                                                                                  #                                          INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES. THEY ARE ESTAB-
056902,000074:                                                                                                  #                                          LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
056903,000075:                                                                                                  #                                          SUBROUTINES.
056904,000076:                                                                                                  #                                          -NR                             C(X1) = NORM COUNT OF RMAG
056905,000077:                                                                                                  #                                          -NA                             C(X2)= NORM COUNT OF SQRT(ABS(ALFA))
056906,000078: 

Page 1339

056908,000080: 
056909,000081: 
056910,000082:                                                                                                  #  SUBROUTINE NAME:     TFFCONIC                                           DATE:    01.29.67
056911,000083:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
056912,000084:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
056913,000085:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  11 APR 67
056914,000086:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  21 NOV 67     ADD MOON MU.
056915,000087:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
056916,000088:                                                                                                  #  FUNCTIONAL DESCRIPTION:      THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
056917,000089:                                                                                                  #           SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA. THE PARAMETERS ARE LISTED UNDER OUTPUT.
056918,000090:                                                                                                  #           THE EQUATIONS ARE
056919,000091:                                                                                                  #                  -   -  -
056920,000092:                                                                                                  #                  H = RN*VN                                               ANGULAR MOMENTUM
056921,000093:                                                                                                  #                        - -
056922,000094:                                                                                                  #                  LCP = H.H / MU                                          SEMI LATUS RECTUM
056923,000095:                                                                                                  #                                -  -
056924,000096:                                                                                                  #                  ALFA = 2/RN - VN.VN / MU                                RECIPROCAL SEMI MAJ AXIS, SIGNED
056925,000097: 
056926,000098:                                                                                                  #           AND ALFA IS POS FOR ELLIPTIC  ORBITS
056927,000099:                                                                                                  #                        0  FOR PARABOLIC ORBITS
056928,000100:                                                                                                  #                       NEG FOR HYPERBOLIC ORBITS.
056929,000101:                                                                                                  #           SUBROUTINE ALSO COMPUTES AND SAVES  RMAG.
056930,000102:                                                                                                  #  CALLING SEQUENCE:
056931,000103:                                                                                                  #           TFFCONIC  EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
056932,000104:                                                                                                  #           1/SQRT(MU). PROGRAM WILL SAVE IN  TFF/RTMU  . THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
056933,000105:                                                                                                  #           ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
056934,000106:                                                                                                  #           VONE  AT PROPER SCALE. THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
056935,000107:                                                                                                  #           TFF ROUTINES.
056936,000108:                                                                                                  #           ENTRY POINT  TFFCONMU  EXPECTS THAT  TFF/RTMU  IS ALREADY LOADED.
056937,000109:                                                                                                  #           TO SPECIFY MU:      DLOAD  CALL                IF MU ALREADY STORED:    CALL
056938,000110:                                                                                                  #                                      YOURMU       1/RTMU   E: (17)  M: (14)              TFFCONMU
056939,000111:                                                                                                  #                                      TFFCONIC
056940,000112:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
056941,000113: 
056942,000114:                                                                                                  #  SUBROUTINES CALLED:  NONE
056943,000115:                                                                                                  #  NORMAL EXIT MODES:   RVQ
056944,000116:                                                                                                  #  ALARMS:  NONE
056945,000117:                                                                                                  #  OUTPUT:  THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
056946,000118:                                                                                                  #           RMAG1  E:(-29) M:(-27) M  RN, PRESENT RADIUS LENGTH.
056947,000119:                                                                                                  #           NRMAG  E: (-29+NR)     M  RMAG, NORMALIZED
056948,000120:                                                                                                  #                  M: (-27+NR)
056949,000121:                                                                                                  #           X1                        -NR, NORM COUNT
056950,000122:                                                                                                  #           TFFNP  E: (-38+2NR)    M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.       FOR VGAMCALC
056951,000123:                                                                                                  #                  M: (-36+2NR)
056952,000124:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)       1/SQRT(MU)
056953,000125:                                                                                                  #           TFFVSQ E:(20)  M:(18)  1/M   -(V SQ/MU): PRESENT VELOCITY,NORMLIZED.    FOR VGAMCALC
056954,000126:                                                                                                  #           TFFALFA  E: (26-NR)    1/M   ALFA, WEIGHTED BY NR
056955,000127:                                                                                                  #                    M: (24-NR)
056956,000128:                                                                                                  #           TFFRTALF  E: (10+NA)   SQRT(ALFA), NORMALIZED
056957,000129:                                                                                                  #                     M: (9+NA)

Page 1340

056959,000131:                                                                                                  #           X2                     -NA, NORMCOUNT
056960,000132:                                                                                                  #           TFF1/ALF  E: (-22-2NA) SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
056961,000133:                                                                                                  #                     M: (-20-2NA)
056962,000134:                                                                                                  #           PUSHLOC AT PDL+0
056963,000135:                                                                                                  #           THE FOLLOWING  IS STORED IN GENERAL ERASABLE
056964,000136:                                                                                                  #           VONE'  E:(10)  M:(9)   V/RT(MU), NORMALIZED VELOCITY
056965,000137:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
056966,000138:                                                                                                  #           RONE   E:(-29)  M:(-27)  M      STATE VECTOR                   LEFT BY CALLER
056967,000139:                                                                                                  #           VONE   E:(-7)   M:(-5)   M/CS   STATE VECTOR                   LEFT BY CALLER
056968,000140:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)      1/RT(CS SQ/M CUBE)               IF ENTER VIA TFFCONMU.
056969,000141:                                                                                                  #  DEBRIS:  QPRET,    PDL+0 ... PDL+3
056970,000142: 
056971,000143: 
056972,000144: 
056973,000145: 33,3773                                           BANK     33                                    
056974,000146: 27,2000                                           SETLOC   TOF-FF                                
056975,000147: 27,2000                                           BANK                                           
056976,000148: 
056977,000149: 27,2721                                           COUNT*   $$/TFF                                
056978,000150: 
056979,000151: 27,2721           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)       E: (17)   M: (14)
056980,000152: 
056981,000153: 27,2722           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
056982,000154: 27,2723           02327                                    RONE                                  #  SAVED RN.  M     E: (-29)  M: (-27)
056983,000155: 27,2724           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
056984,000156: 27,2725           00045                                    36D                                   #  MAGNITUDE
056985,000157: 27,2726           00015                           STORE    RMAG1                                 #  M    E: (-29)   M: (-27)
056986,000158: 
056987,000159: 27,2727           77701                           NORM                                           
056988,000160: 27,2730           00047                                    X1                                    #  -NR
056989,000161: 27,2731           24041                           STOVL    NRMAG                                 #  RMAG  M   E: (-29+NR)  M: (-27+NR)
056990,000162: 27,2732           02335                                    VONE                                  #  SAVED VN.  M/CS   E: (-7)   M: (-5)
056991,000163: 27,2733           77761                           VXSC                                           
056992,000164: 27,2734           00037                                    TFF/RTMU                              #  E: (17)   M: (14)
056993,000165: 27,2735           02372                           STORE    VONE'                                 #  VN/SQRT(MU)   E: (10)   M: (9)
056994,000166: 
056995,000167: 27,2736           47361                           VXSC     VXV                                   
056996,000168: 27,2737           00041                                    NRMAG                                 #  E: (-29+NR)  M: (-27+NR)
056997,000169:                                                                                                  #                                          UR/2 FROM PDL
056998,000170: 27,2740           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR)  M:(-18+NR)
056999,000171: 27,2741           14035                           STODL    TFFNP                                 #  LC P  M   E:(-38+2NR)  M:(-36+2NR)
057000,000172:                                                                                                  #                                          SAVE ALSO FOR VGAMCALC
057001,000173: 27,2742           15322                                    TFF1/4                                
057002,000174: 27,2743           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M   E:(26-NR)   M:(24-NR)
057003,000175: 27,2744           00041                                    NRMAG                                 #  RMAG  M   E:(-29+NR)  M:(-27+NR)
057004,000176: 27,2745           02372                                    VONE'                                 #  SAVED VN.   E: (10)   M: (9)
057005,000177: 27,2746           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
057006,000178: 27,2747           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)   E:(20)   M:(18)
057007,000179:                                                                                                  #                                          SAVE FOR VGAMCALC
057008,000180: 27,2750           43257                           SR*      DAD                                   

Page 1341

057010,000182: 27,2751           20573                                    0          -6,1                       #  GET -VSQ/MU   E:(26-NR)   M:(24-NR)
057011,000183: 27,2752           77626                           STADR                                          
057012,000184:                                                                                                  #                                          2/RMAG   FROM PDL+2
057013,000185: 27,2753           77744                           STORE    TFFALFA                               #  ALFA  1/M   E:(26-NR)   M:(24-NR)
057014,000186: 27,2754           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA    E:(20)   M:(18)
057015,000187: 27,2755           20173                                    0          -6,1                       
057016,000188: 27,2756           75446                           ABS      SQRT                                  #  E:(10)   M:(9)
057017,000189: 27,2757           77701                           NORM                                           
057018,000190: 27,2760           00050                                    X2                                    #  X2 = -NA
057019,000191: 27,2761           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA)   M:(9+NA)
057020,000192: 27,2762           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
057021,000193:                                                                                                  #                                          ALFA FROM PDL+2   E:(20)   M:(18)
057022,000194: 27,2763           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
057023,000195: 27,2764           56766                                    +2                                    
057024,000196: 27,2765           15322                                    TFF1/4                                
057025,000197: 27,2766           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA   E:(-22-2NA)   M:(-20-2NA)
057026,000198: 27,2767           77616        DUMPCNIC           RVQ                                            
057027,000199:                                                                                                  #                                                                 39 W
057028,000200: 

Page 1342

057030,000202:                                                                                                  #  SUBROUTINE NAME:     TFFRP/RA                                           DATE:  01.17.67
057031,000203:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
057032,000204:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
057033,000205:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  11 APR 67
057034,000206:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
057035,000207:                                                                                                  #                                                                          ALSO IMPROVE ACCURACY OF RAPO.
057036,000208:                                                                                                  #  FUNCTIONAL DESCRIPTION:         USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
057037,000209:                                                                                                  #           APOGEE RADIUS FOR A GENERAL CONIC.
057038,000210:                                                                                                  #           PROGRAM GIVES PERIGEE RADIUS AS               APOGEE RADIUS IS GIVEN BY
057039,000211:                                                                                                  #                  RP = P /(1+E)                                 RA = (1+E) / ALFA
057040,000212:                                                                                                  #           WHERE   2
057041,000213:                                                                                                  #                  E  = 1 - P ALFA
057042,000214:                                                                                                  #           IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
057043,000215:                                                                                                  #                  1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
057044,000216:                                                                                                  #                  2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
057045,000217:                                                                                                  #                  3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
057046,000218:                                                                                                  #           THIS SUBROUTINE REQUIRES THE SIGNED  RECIPROCAL SEMI MAJ AXIS,  ALFA,  AND SEMI LATUS RECTUM AS DATA.
057047,000219:                                                                                                  #  CALLING SEQUENCE:  CALL
057048,000220:                                                                                                  #                            TFFRP/RA
057049,000221:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
057050,000222:                                                                                                  #           C(MPAC) UNSPECIFIED
057051,000223: 
057052,000224:                                                                                                  #  SUBROUTINES CALLED:  NONE
057053,000225:                                                                                                  #  NORMAL EXIT MODE:    RVQ
057054,000226:                                                                                                  #           IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
057055,000227:                                                                                                  #           OTHERWISE, RAPO = POSMAX.
057056,000228:                                                                                                  #  ALARMS:  NONE
057057,000229:                                                                                                  #  OUTPUT:  STORED IN PUSH LIST AREA. SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO  TFF/CONIC.
057058,000230:                                                                                                  #           RPER   E:(-29)  M:(-27)  M     PERIGEE RADIUS                  DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
057059,000231:                                                                                                  #           RAPO   E:(-29)  M:(-27)  M     APOGEE  RADIUS                  WILL BE DESTROYED BY CALCTFF/CALCTPER
057060,000232:                                                                                                  #           PUSHLOC AT PDL+0
057061,000233:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
057062,000234:                                                                                                  #           TFFALFA E:(26-NR)      M   1/SEMI MAJ AXIS                     LEFT BY TFFCONIC
057063,000235:                                                                                                  #                   M:(24-NR)
057064,000236:                                                                                                  #           TFFNP  E: (-38+2NR)    M  LC P, SEMI LATUS RECTUM              LEFT BY TFFCONIC
057065,000237:                                                                                                  #                  M: (-36+2NR)
057066,000238:                                                                                                  #           X1                     -NR, NORM COUNT OF RMAG                 LEFT BY TFFCONIC
057067,000239:                                                                                                  #           X2                     -NA, NORM COUNT OF ALFA                 LEFT BY TFFCONIC
057068,000240:                                                                                                  #  DEBRIS:  QPRET,    PDL+0 ... PDL+1
057069,000241: 

Page 1343

057071,000243: 
057072,000244: 27,2770                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29)  M:(-27)
057073,000245: 27,2770                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29)  M:(-27)
057074,000246: 
057075,000247: 27,2770           41345        TFFRP/RA           DLOAD    DMP                                   
057076,000248: 27,2771           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR)   M:(24-NR)
057077,000249: 27,2772           00035                                    TFFNP                                 #  LC P  M   E:(-38+2NR)   M:(-36+2NR)
057078,000250: 27,2773           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
057079,000251: 27,2774           20571                                    0          -8D,1                      #  ALFA P  (-4)
057080,000252: 27,2775           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
057081,000253:                                                                                                  #                                          (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
057082,000254: 27,2776           17330                                    DP2(-4)                               
057083,000255: 27,2777           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA)   (-4)
057084,000256: 27,3000           15322                                    TFF1/4                                
057085,000257: 27,3001           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
057086,000258: 27,3002           00035                                    TFFNP                                 #  LCP  M  E:(-38+2NR)   M:(-36+2NR)
057087,000259: 27,3003           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
057088,000260: 27,3004           20601                                    0,1                                   #  X1=-NR
057089,000261: 27,3005           20572                                    0          -7,1                       #  (EFFECTIVE SL)
057090,000262: 27,3006           14017                           STODL    RPER                                  #  PERIGEE RADIUS  M   E:(-29)   M:(-27)
057091,000263:                                                                                                  #                                          (1+E)  (-2)   FROM PDL+0
057092,000264: 27,3007           41005                           DMP      BOVB                                  
057093,000265: 27,3010           00027                                    TFF1/ALF                              #  E:(-22-2NA)  M:(-20-2NA)
057094,000266: 27,3011           57314                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
057095,000267: 27,3012           53654                           BZE      SL*                                   
057096,000268: 27,3013           57022                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
057097,000269: 27,3014           57603                                    0          -5,2                       #  -5+NA
057098,000270: 27,3015           40057                           SL*      BOV                                   
057099,000271: 27,3016           57576                                    0,2                                   
057100,000272: 27,3017           57022                                    MAXRA                                 #  SET POSMAX IF OVFL.
057101,000273: 27,3020           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
057102,000274: 27,3021           57024                                    +3                                    
057103,000275: 27,3022           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID. SET RAPO =
057104,000276: 27,3023           17334                                    NEARONE                               #  POSMAX AS A TAG.
057105,000277: 27,3024           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M   E:(-29)   M:(-27)
057106,000278: 27,3025           77616        DUMPRPRA           RVQ                                            
057107,000279: 
057108,000280:                                                                                                  #                                                                  30 W
057109,000281: 

Page 1344

057111,000283:                                                                                                  #  SUBROUTINE NAME:     CALCTPER  /  CALCTFF                               DATE:    01.29.67
057112,000284:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
057113,000285:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
057114,000286:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 67
057115,000287:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  14 APR 67
057116,000288:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE:  8JUL 67       NEAR EARTH MUE AND NEG TFF (GONEPAST)
057117,000289:                                                                                                  #  MOD NO:  4           MOD BY:  RR BAIRNSFATHER      DATE:  21 NOV 67     ADD VARIABLE MU.
057118,000290:                                                                                                  #  MOD NO:  5           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
057119,000291:                                                                                                  #  FUNCTIONAL DESCRIPTION:      PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION  RN  AND
057120,000292:                                                                                                  #           VELOCITY  VN  TO A RADIUS LENGTH SPECIFIED BY  RTERM  , SUPPLIED BY THE USER. THE POSITION VECTOR
057121,000293:                                                                                                  #           RN  MAY BE ON EITHER SIDE OF THE CONIC, BUT  RTERM  IS CONSIDERED ON THE INBOUND SIDE.
057122,000294:                                                                                                  #           THE EQUATIONS ARE
057123,000295: 
057124,000296:                                                                                                  #                  Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)    (INBOUND SIDE))        LEQ +- LCE/SQRT(ALFA)
057125,000297:                                                                                                  #                       -  -
057126,000298:                                                                                                  #                  Q1 = RN.VN / SQRT(MU)                                            LEQ +- LCE/SQRT(ALFA)
057127,000299: 
057128,000300:                                                                                                  #                  Z = NUM / DEN                                                    LEQ +- 1/SQRT(ALFA)
057129,000301: 
057130,000302:                                                                                                  #           WHERE, IF INBOUND
057131,000303:                                                                                                  #                  NUM = RTERM -RN                                                  LEQ +- 2 LCE/ALFA
057132,000304:                                                                                                  #                  DEN = Q2+Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
057133,000305: 
057134,000306:                                                                                                  #           AND, IF OUTBOUND
057135,000307:                                                                                                  #                  NUM = Q2-Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
057136,000308:                                                                                                  #                  DEN = 2 - ALFA (RTERM + RN) .                                    LEQ +- 2 LCE
057137,000309: 
057138,000310:                                                                                                  #           IF     ALFA ZZ  <  1.0               (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
057139,000311: 
057140,000312:                                                                                                  #           THEN   X = ALFA Z Z
057141,000313:                                                                                                  #           AND    TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
057142,000314: 
057143,000315:                                                                                                  #                  EXCEPT IF ALFA PNZ, AND IF TFF NEG,
057144,000316:                                                                                                  #                  THEN   TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
057145,000317: 
057146,000318:                                                                                                  #           OR IF  ALFA ZZ  GEQ  1.0             (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
057147,000319: 
057148,000320:                                                                                                  #           THEN   X = 1/ALFA Z Z
057149,000321:                                                                                                  #           AND    TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
057150,000322: 
057151,000323:                                                                                                  #           WHERE  T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
057152,000324:                                                                                                  #                               2      3                     2
057153,000325:                                                                                                  #                  1/3 - X/5 + X /7 - X /9 ...             (X   <  1.0)
057154,000326: 
057155,000327:                                                                                                  #  CALLING SEQUENCE:  TIME TO RTERM                           TIME TO PERIGEE
057156,000328:                                                                                                  #                     CALL                                    CALL
057157,000329:                                                                                                  #                            CALCTFF                                 CALCTPER
057158,000330:                                                                                                  #                     C(MPAC) = TERMNL RAD  M                 C(MPAC) = PERIGEE RAD  M
057159,000331:                                                                                                  #           FOR EITHER,   E: (-29)    M: (-27)
057160,000332:                                                                                                  #           FOR EITHER, PUSHLOC = PDL+0 , ARBITRARY IF LEQ 8D.

Page 1345

057162,000334:                                                                                                  #  SUBROUTINES CALLED:  T(X),  VIA RTB
057163,000335:                                                                                                  #  NORMAL EXIT MODE:  RVQ
057164,000336:                                                                                                  #           HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS IN MPAC. USER MUST STORE.
057165,000337:                                                                                                  #                  A.  TFF= FLIGHT TIME. NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
057166,000338:                                                                                                  #                  B.  (THIS OPTION IS NO LONGER USED.)
057167,000339:                                                                                                  #                  C.  TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
057168,000340:                                                                                                  #                      THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
057169,000341:                                                                                                  #  OUTPUT:  C(MPAC)  (-28)  CS     TIME OF FLIGHT, OR TIME TO PERIGEE
057170,000342:                                                                                                  #           TFFX    (0)            X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
057171,000343:                                                                                                  #           NRTERM  E: (-29+NR)    M  RTERM, WEIGHTED BY NR                LEFT FOR ENTRY DISPLAY TFF ROUTINES
057172,000344:                                                                                                  #                   M: (-27+NR)
057173,000345:                                                                                                  #           TFFTEM  E: (-59+2NR)   LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
057174,000346:                                                                                                  #                   M: (-55+2NR)   LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
057175,000347:                                                                                                  #           NOTE:  TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
057176,000348:                                                                                                  #           RMAG1  E:(-29)  M:(-27)  PDL 12 NOT TOUCHED.
057177,000349:                                                                                                  #           TFFQ1  E:(-16)  M:(-15)  PDL 14D
057178,000350:                                                                                                  #           TFFDELQ E:(-16) M:(-15)  PDL 10D
057179,000351:                                                                                                  #           PUSHLOC AT PDL+0
057180,000352:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
057181,000353:                                                                                                  #           RONE   E:(-29)  M:(-27)  M    STATE VECTOR                     LEFT BY USER
057182,000354:                                                                                                  #           VONE'  E:(+10)  M:(+9)   VN/SQRT(MU)                           LEFT BY TFF/CONIC
057183,000355:                                                                                                  #           RMAG1  E:(-29)  M:(-27)  PRESENT RADIUS,  M                    LEFT BY TFFCONIC
057184,000356:                                                                                                  #           C(MPAC)E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH, M      LEFT BY USER
057185,000357: 
057186,000358:                                                                                                  #           THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
057187,000359:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)  1/SQRT(MU)                           LEFT BY TFFCONIC.
057188,000360:                                                                                                  #           NRMAG  E: (-29+NR)  M  RMAG, NORMALIZED                        LEFT BY TFFCONIC
057189,000361:                                                                                                  #                  M: (-27+NR)
057190,000362:                                                                                                  #           X1                     -NR, NORM COUNT                         LEFT BY TFFCONIC
057191,000363:                                                                                                  #           TFFNP  E: (-38+2NR)  M   LCP, SEMI LATUS RECTUM, WEIGHT  NR    LEFT BY TFFCONIC
057192,000364:                                                                                                  #                  M: (-36+2NR)
057193,000365:                                                                                                  #           TFFALFA  E: (26-NR)    1/M  ALFA, WEIGHT  NR                   LEFT BY TFFCONIC
057194,000366:                                                                                                  #                    M: (24-NR)
057195,000367:                                                                                                  #           TFFRTALF  E:(10+NA)    SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
057196,000368:                                                                                                  #                     M:(9+NA)
057197,000369:                                                                                                  #           X2                     -NA, NORM COUNT                         LEFT BY TFFCONIC
057198,000370:                                                                                                  #           TFF1/ALF  E: (-22-2NA)  SIGNED SEMIMAJ AXIS, WEIGHTED BY NA    LEFT BY TFFCONIC
057199,000371:                                                                                                  #                     M: (-20-2NA)
057200,000372:                                                                                                  #  DEBRIS:  QPRET,   PDL+0 ... PDL+3
057201,000373:                                                                                                  #           RTERM  E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH
057202,000374:                                                                                                  #           RAPO   E:(-29)  M:(-27)  PDL 16D  (=NRTERM)
057203,000375:                                                                                                  #           RPER   E:(-29)  M:(-27)  PDL 14D   (=TFFQ1)
057204,000376: 

Page 1346

057206,000378: 27,3026           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER  IN MPAC
057207,000379: 27,3027           03436                                    TFFSW                                 
057208,000380: 27,3030           57033                                    +3                                    
057209,000381: 27,3031           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
057210,000382: 27,3032           03676                                    TFFSW                                 
057211,000383: 27,3033           00023                 +3        STORE    RTERM                                 #  E: (-29)  M: (-27)
057212,000384: 27,3034           77657                           SL*                                            
057213,000385: 27,3035           20201                                    0,1                                   #  X1=-NR
057214,000386: 27,3036           00021                           STORE    NRTERM                                #  RTERM  E: (-29+NR)  M: (-27+NR)
057215,000387: 27,3037           44205                           DMP      BDSU                                  
057216,000388: 27,3040           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
057217,000389: 27,3041           15322                                    TFF1/4                                
057218,000390: 27,3042           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
057219,000391: 27,3043           00021                                    NRTERM                                #  E: (-29+NR)  M: (-27+NR)
057220,000392: 27,3044           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
057221,000393:                                                                                                  #                                          E: (-32+NR)   M: (-30+NR)
057222,000394: 27,3045           00035                                    TFFNP                                 #  LC P  E:(-38+2NR)  M:(-36+2NR)
057223,000395: 27,3046           20573                                    0          -6,1                       #  X1 = -NR
057224,000396: 27,3047           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
057225,000397:                                                                                                  #                                          RTERM(2-ALFA RTERM) FROM PDL +2
057226,000398:                                                                                                  #                                          E: (-32+NR)  M: (-30+NR)
057227,000399: 27,3050           77657                           SR*                                            #  LEAVE  E: (-32)  M: (-30)
057228,000400: 27,3051           20601                                    0,1                                   #  X1 = -NR
057229,000401: 27,3052           71214                           BOFF     DLOAD                                 #  CHECK TFF / TPER SWITCH
057230,000402: 27,3053           03756                                    TFFSW                                 
057231,000403: 27,3054           57056                                    +2                                    #  IF TFF, CONTINUE
057232,000404: 27,3055           15332                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
057233,000405: 27,3056           75440                 +2        BMN      SQRT                                  #  E: (-16)  M: (-15)
057234,000406: 
057235,000407: 27,3057           57211                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
057236,000408:                                                                                                  #                                          RESET PDL, SET TFF=POSMAX, AND EXIT.
057237,000409: 
057238,000410: 27,3060           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
057239,000411: 27,3061           57314                                    TCDANZIG                              #  ANY PORT IN A STORM.
057240,000412: 27,3062           24045                           STOVL    TFFTEM                                #  Q2   E: (-16)  M: (-15)
057241,000413: 27,3063           02372                                    VONE'                                 #  VN/SQRT(MU) E: (10)  M: (9)
057242,000414: 27,3064           52441                           DOT      SL3                                   
057243,000415: 27,3065           02327                                    RONE                                  #  SAVED RN.  E: (-29)  M: (-27)
057244,000416: 27,3066           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
057245,000417:                                                                                                  #                                          E: (-16)  M: (-15)
057246,000418: 27,3067           44240                           BMN      BDSU                                  
057247,000419: 27,3070           57111                                    INBOUND                               #  USE ALTERNATE Z
057248,000420: 27,3071           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
057249,000421: 
057250,000422:                                                                                                  #                                          OUTBOUND  Z CALC CONTINUES HERE
057251,000423: 
057252,000424: 27,3072           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E: (-16)  M: (-15)
057253,000425: 27,3073           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
057254,000426: 27,3074           44205                           DMP      BDSU                                  

Page 1347

057256,000428: 27,3075           00041                                    NRMAG                                 #  RMAG  E: (-29+NR)  M: (-27+NR)
057257,000429:                                                                                                  #                                          (2-RTERM ALFA)  (-3) FROM PDL+0
057258,000430: 27,3076           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E:(-3) OR (-16)
057259,000431:                                                                                                  #                                                        M:(-3) OR (-15)
057260,000432: 27,3077           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
057261,000433: 27,3100           17322                                    LIM(-22)                              #  =1.0-B(-22)
057262,000434: 27,3101           57122                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
057263,000435: 27,3102           65345                           DLOAD    PDDL                                  #  SET DEN=0 OTHERWISE
057264,000436: 27,3103           15332                                    TFFZEROS                              
057265,000437:                                                                                                  #                                          XCH ZERO WITH PDL+0
057266,000438: 27,3104           57545                           DLOAD    DCOMP                                 
057267,000439: 27,3105           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
057268,000440: 27,3106           71240                           BMN      DLOAD                                 #  FOR TPER: Z INDET AT DELE/2=0 AND 90.
057269,000441: 27,3107           57216                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
057270,000442: 
057271,000443:                                                                                                  #                                          Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
057272,000444: 27,3110           77616        DUMPTFF1           RVQ                                            #  RETURN  TFF =0
057273,000445: 
057274,000446:                                                                                                  #                                          INBOUND  Z  CALC CONTINUES HERE
057275,000447: 27,3111           77745        INBOUND            DLOAD                                          #  RESET PDL+0
057276,000448: 27,3112           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
057277,000449: 27,3113           00023                                    RTERM                                 #  E: (-29)  M: (-27)
057278,000450: 27,3114           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
057279,000451: 27,3115           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E: (-29)  M: (-27)
057280,000452: 27,3116           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
057281,000453: 27,3117           52015                           DAD      GOTO                                  
057282,000454: 27,3120           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
057283,000455: 27,3121           57076                                    SAVEDEN                               #  DEN = Q2+Q1   E: (-16)  M: (-15)
057284,000456: 
057285,000457: 27,3122           65215        TFFXTEST           DAD      PDDL                                  #   (ABS(DEN) TO PDL+2))  E: (-3) OR (-16)
057286,000458:                                                                                                  #                                                                 M: (-3) OR (-15)
057287,000459: 27,3123           17324                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
057288,000460: 27,3124           00043                                    TFFX                                  #  NUM E:(-16) OR (-29)  M:(-15) OR (-27)
057289,000461: 27,3125           53605                           DMP      SR*                                   
057290,000462: 27,3126           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
057291,000463: 27,3127           57201                                    0          -3,2                       #  X2=-NA
057292,000464: 27,3130           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)  E:(-3) OR (-16)
057293,000465:                                                                                                  #                                                                   M:(-3) OR (-15)
057294,000466:                                                                                                  #                                          ABS(DEN) FROM PDL+2  E:(-3) OR (-16)
057295,000467:                                                                                                  #                                                               M:(-3) OR (-15)
057296,000468: 27,3131           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
057297,000469: 27,3132           00043                                    TFFX                                  #  NUM  E: (-16) OR (-29)  M:(-15) OR (-27)
057298,000470: 27,3133           57214                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
057299,000471: 
057300,000472:                                                                                                  #                                          OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
057301,000473: 
057302,000474: 27,3134           45471                           DDV      STADR                                 
057303,000475:                                                                                                  #                                          DEN FROM PDL+0   E: (-3) OR (-16)
057304,000476:                                                                                                  #                                                           M: (-3) OR (-15)
057305,000477: 27,3135           77732                           STORE    TFFTEM                                #  Z  SAVE FOR SIGN OF SDELF.

Page 1348

057307,000479:                                                                                                  #                                          E: (-13)  M: (-12)
057308,000480: 27,3136           63406                           PUSH     DSQ                                   #  Z TO PDL+0
057309,000481: 27,3137           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E: (-26)  M: (-24)
057310,000482: 27,3140           00035                                    TFFNP                                 #  LC P  E: (-38+2NR)  M: (-36+2NR)
057311,000483: 27,3141           75261                           SL       SIGN                                  
057312,000484: 27,3142           20206                                    5                                     
057313,000485: 27,3143           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
057314,000486: 27,3144           14045                           STODL    TFFTEM                                #  P ZSQ  E: (-59+2NR)  M: (-55+2NR)
057315,000487:                                                                                                  #                                          (ARG IS USED IN TFF/TRIG)
057316,000488:                                                                                                  #                                          ZSQ FROM PDL+2   E: (-26)  M: (-24)
057317,000489: 27,3145           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
057318,000490: 27,3146           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
057319,000491: 27,3147           77657                           SL*                                            
057320,000492: 27,3150           20201                                    0,1                                   #  X1=-NR
057321,000493: 27,3151           00043                           STORE    TFFX                                  #  X
057322,000494: 27,3152           41234                           RTB      DMP                                   
057323,000495: 27,3153           57276                                    T(X)                                  #   POLY
057324,000496:                                                                                                  #                                          ZSQ FROM PDL+2  E: (-26)  M: (-24)
057325,000497: 27,3154           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E: (-29)  M: (-27)
057326,000498: 27,3155           00023                                    RTERM                                 #  RTERM  E: (-29)  M: (-27)
057327,000499: 27,3156           41215                           DAD      DMP                                   
057328,000500: 27,3157           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
057329,000501:                                                                                                  #                                          Z FROM PDL+0  E: (-13)  M: (-12)
057330,000502: 27,3160           51042                           SR3      BPL                                   #  TFF SQRT(MU)   E: (-45)  M: (-42)
057331,000503: 27,3161           57202                                    ENDTFF                                #  (NO PUSH UP)
057332,000504: 27,3162           75206                           PUSH     SIGN                                  #  TFF SQRT(MU) TO PDL+0
057333,000505: 27,3163           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
057334,000506: 27,3164           71244                           BPL      DLOAD                                 #  GONE PAST ?
057335,000507: 27,3165           57206                                    NEGTFF                                #  YES. TFF < 0 .
057336,000508: 27,3166           00027                                    TFF1/ALF                              #  1/ALFA  E: (-22-2NA)  M: (-20-2NA)
057337,000509: 27,3167           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
057338,000510: 27,3170           57206                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
057339,000511: 
057340,000512:                                                                                                  #                                          CORRECT FOR ORBITAL PERIOD.
057341,000513: 
057342,000514: 27,3171           77676                           DCOMP                                          #  YES. CORRECT FOR ORB PERIOD.
057343,000515: 27,3172           56205                           DMP      DDV                                   
057344,000516: 27,3173           17320                                    PI/16                                 #  2 PI (-5)
057345,000517: 27,3174           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
057346,000518: 27,3175           53657                           SL*      SL*                                   
057347,000519: 27,3176           57602                                    0          -4,2                       #  X2=-NA
057348,000520: 27,3177           57602                                    0          -4,2                       
057349,000521: 27,3200           43257                           SL*      DAD                                   
057350,000522: 27,3201           57576                                    0,2                                   
057351,000523:                                                                                                  #                                          TFF SQRT(MU) FROM PDL+0  E:(-45) M:(-42)
057352,000524: 27,3202           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC     E:(-45) M:(-42)
057353,000525: 27,3203           00037                                    TFF/RTMU                              #  E: (17)  M: (14)
057354,000526: 27,3204           57212                                    MAXTFF                                #  SET POSMAX IF OVFL.
057355,000527: 
057356,000528: 27,3205           77616        DUMPTFF2           RVQ                                            #  RETURN  TFF   (-28) CS IN MPAC.

Page 1349

057358,000530: 27,3206           77745        NEGTFF             DLOAD                                          
057359,000531:                                                                                                  #                                          TFF SQRT(MU)  FROM PDL+0, NEGATIVE.
057360,000532: 27,3207           77650                           GOTO                                           
057361,000533: 27,3210           57202                                    ENDTFF                                
057362,000534: 
057363,000535: 27,3211           77745        MAXTFF1            DLOAD                                          #  RESET PDL
057364,000536: 27,3212           43545        MAXTFF             DLOAD    RVQ                                   
057365,000537: 27,3213           17334                                    NEARONE                               
057366,000538: 
057367,000539:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
057368,000540: 
057369,000541:                                                                                                  #                                          NUM FROM TFFX.  E: (-16) OR (-29)
057370,000542:                                                                                                  #                                                          M: (-15) OR (-27)
057371,000543: 27,3214           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
057372,000544: 27,3215           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
057373,000545:                                                                                                  #                                          DEN FROM PDL+0 E:(-3)/( 16) M:(-3)/(-15)
057374,000546:                                                                                                  #                                          N/D TO PDL+0  E: (11)  M: (10)
057375,000547: 27,3216           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
057376,000548: 27,3217           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
057377,000549: 27,3220           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
057378,000550: 27,3221           14013                           STODL    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
057379,000551:                                                                                                  #                                          D/N FROM PDL+0
057380,000552: 27,3222           77626                           STADR                                          
057381,000553: 27,3223           77732                           STORE    TFFTEM                                #  D/N  E: (11)  M: (10)
057382,000554: 27,3224           53605                           DMP      SL*                                   
057383,000555: 27,3225           00027                                    TFF1/ALF                              #  1/ALFA E: (-22-2NA)  M: (-20-2NA)
057384,000556: 27,3226           57576                                    0,2                                   #  1/ALFA Z  E: (-11-NA)  M: (-10-NA)
057385,000557: 27,3227           41206                           PUSH     DMP                                   #  TO PDL+0
057386,000558: 27,3230           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
057387,000559: 27,3231           41057                           SL*      BOVB                                  
057388,000560: 27,3232           57576                                    0,2                                   #  X2= -NA
057389,000561: 27,3233           45707                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
057390,000562: 27,3234           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
057391,000563: 27,3235           41234                           RTB      DMP                                   
057392,000564: 27,3236           57276                                    T(X)                                  #  POLY
057393,000565: 27,3237           00043                                    TFFX                                  
057394,000566: 27,3240           45242                           SR3      DSU                                   
057395,000567: 27,3241           17326                                    DP2(-3)                               
057396,000568: 27,3242           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA  E: (-15-NA)
057397,000569:                                                                                                  #                                                               M: (-14-NA)
057398,000570:                                                                                                  #                                          1/ALFA Z FROM PDL+0  E: (-11-NA)
057399,000571:                                                                                                  #                                                               M: (-10-NA)
057400,000572: 27,3243           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
057401,000573: 27,3244           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
057402,000574: 27,3245           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
057403,000575: 27,3246           43312                           SL2      DAD                                   
057404,000576: 27,3247           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
057405,000577: 27,3250           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z)  =SGN OF SDELF E:(-16) M:(-15
057406,000578: 27,3251           00035                                    TFFNP                                 #  LC P E: (-38+2NR) M: (-36+2NR)
057407,000579: 27,3252           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1350

057409,000581: 27,3253           00027                                    TFF1/ALF                              #  1/ALFA   E:(-22-2NA)  M:(-20-2NA)
057410,000582: 27,3254           57575                                    1,2                                   #  X2=-NA
057411,000583: 27,3255           53765                           SIGN     SL*                                   
057412,000584: 27,3256           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
057413,000585: 27,3257           57576                                    0,2                                   
057414,000586: 27,3260           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR)  M:(-55+2NR)
057415,000587:                                                                                                  #                                          (ARG FOR USE IN TFF/TRIG)
057416,000588: 27,3261           00027                                    TFF1/ALF                              #  1/ALFA E:(-22-2NA)  M:(-20-2NA)
057417,000589: 27,3262           41366                           SQRT     DMP                                   
057418,000590: 27,3263           17320                                    PI/16                                 #  PI (-4)
057419,000591: 27,3264           77615                           DAD                                            
057420,000592:                                                                                                  #                                          2(XT(X)-1)/Z ALFA FROM PDL E:(-15-NA)
057421,000593:                                                                                                  #                                                                     M:(-14-NA)
057422,000594: 27,3265           45257                           SL*      DSU                                   
057423,000595: 27,3266           57577                                    0          -1,2                       
057424,000596: 27,3267           00013                                    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
057425,000597: 27,3270           53605                           DMP      SL*                                   
057426,000598: 27,3271           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA)  M:(-20-2NA)
057427,000599: 27,3272           57601                                    0          -3,2                       
057428,000600: 27,3273           52057                           SL*      GOTO                                  
057429,000601: 27,3274           57602                                    0          -4,2                       
057430,000602: 27,3275           57202                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
057431,000603: 

Page 1351

057433,000605:                                                                                                  #  PROGRAM NAME:      T(X)                                                 DATE:    01.17.67
057434,000606:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
057435,000607:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
057436,000608:                                                                                                  #  FUNCTIONAL DESCRIPTION:      THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES  CALCTFF AND
057437,000609:                                                                                                  #           CALCTPER TO APPROXIMATE THE SERIES
057438,000610:                                                                                                  #                             2     3
057439,000611:                                                                                                  #                  1/3 -X/5 +X /7 -X /9 ...
057440,000612: 
057441,000613:                                                                                                  #           WHERE  X = ALFA Z Z       IF ALFA Z Z  LEQ 1
057442,000614:                                                                                                  #                  X = 1/(ALFA Z Z )  IF ALFA Z Z   G  1
057443,000615: 
057444,000616:                                                                                                  #           ALSO   X IS NEG FOR HYPERBOLIC ORBITS
057445,000617:                                                                                                  #                  X = 0 FOR PARABOLIC ORBITS
057446,000618:                                                                                                  #                  X IS POSITIVE FOR ELLIPTIC ORBITS
057447,000619:                                                                                                  #           FOR FLIGHT 278, THE POLYNOMIAL  T(X) IS FITTED OVER THE RANGE  (0,+1)  AND HAS A MAXIMUM
057448,000620:                                                                                                  #           DEVIATION FROM THE SERIES OF  2 E-5       (T(X) IS A CHEBYCHEV  TYPE FIT AND WAS OBTAINED USING
057449,000621:                                                                                                  #           MAC PROGRAM AUTCURFIT294RRB  AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE  (-.08,+1). )
057450,000622:                                                                                                  #  CALLING SEQUENCE:  RTB
057451,000623:                                                                                                  #                            T(X)
057452,000624:                                                                                                  #           C(MPAC) = X
057453,000625: 
057454,000626:                                                                                                  #  SUBROUTINES CALLED:  NONE
057455,000627:                                                                                                  #  NORMAL EXIT MODE:    TC   DANZIG
057456,000628:                                                                                                  #  ALARMS:  NONE
057457,000629:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
057458,000630:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
057459,000631:                                                                                                  #           C(MPAC)  =  X
057460,000632:                                                                                                  #  DEBRIS:  NONE
057461,000633: 
057462,000634: 27,3276           07171        T(X)               TC       POLY                                  
057463,000635: 27,3277           00004                           DEC      4          B-14                       #  N-1
057464,000636: 27,3300           12525 12525                     2DEC     3.333333333 E-1                        
057465,000637: 27,3302           71463 57703                     2DEC*    -1.999819135 E-1*                       
057466,000638: 27,3304           04423 17645                     2DEC*    1.418148467 E-1*                       
057467,000639: 27,3306           74604 43667                     2DEC*    -1.01310997 E-1*                       
057468,000640: 27,3310           01626 37256                     2DEC*    5.609004986 E-2*                       
057469,000641: 27,3312           77404 52071                     2DEC*    -1.536156925 E-2*                       
057470,000642: 27,3314           06030        ENDT(X)            TC       DANZIG                                
057471,000643: 
057472,000644: 27,3315  27,3314               TCDANZIG           =        ENDT(X)                               
057473,000645: 

Page 1352

057475,000647:                                                                                                  #  TFF CONSTANTS
057476,000648: 32,3776                                           BANK     32                                    
057477,000649: 
057478,000650: 27,2000                                           SETLOC   TOF-FF1                               
057479,000651: 27,2000                                           BANK                                           
057480,000652: 
057481,000653:                                                                                                  #                                                               NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
057482,000654: 
057483,000655:                                                                                                  #  MUE           =       3.990 815 471 E10  M CUBE/CS SQ
057484,000656:                                                                                                  #  RTMUE         =       1.997702549 E5 B-18*     MODIFIED EARTH MU
057485,000657: 
057486,000658: 27,3315           24775 30424  1/RTMU             2DEC*    .5005750271 E-5        B17*            #  MODIFIED EARTH MU
057487,000659:                                                                                                  #                                                               NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
057488,000660: 
057489,000661:                                                                                                  #  MUM           =       4.902 778  E8     M CUBE /CS SQ
057490,000662: 
057491,000663:                                                                                                  #  RTMUM         2DEC*   2.21422176 E4 B-18*
057492,000664: 27,3317           06220 37553  PI/16              2DEC     3.141592653 B-4                        
057493,000665: 27,3321           37777 37700  LIM(-22)           2OCT     37777      37700                      #  1.0 -B(-22)
057494,000666: 27,3323           00000 00100  DP(-22)            2OCT     00000      00100                      #  B(-22)
057495,000667: 27,3325           04000 00000  DP2(-3)            2DEC     1          B-3                        
057496,000668: 27,3327           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
057497,000669:                                                                                                  #  RPAD1    2DEC   6373338 B-29    M  (-29)  =20 909 901.57 FT
057498,000670: 
057499,000671: 27,3331  22,3310               RPAD1              =        RPAD                                  
057500,000672: 27,3331           00305 11205  R300K              2DEC     6464778    B-29                       #   (-29) M
057501,000673: 27,3333           37777 37777  NEARONE            2DEC     .999999999                            
057502,000674: 27,3335  26,3331               TFFZEROS           EQUALS   HI6ZEROS                              
057503,000675: 27,3335  26,3321               TFF1/4             EQUALS   HIDP1/4                               

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