Source Code

These source-code files were from the printout at the MIT Museum, with many thanks to Deborah Douglas, the Museum's Curator of Science and Technology, for releasing it to us. The printout was digitally photographed by Paul Fjeld. A team of volunteers transcribed the source code manually from these images or, where appropriate, modified already-transcribed but similar source Colossus 249 (Apollo 9) source code to agree with the images from the printout. Note that the page images presented online are of reduced quality, and that higher-quality 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 055 OF AGC PROGRAM COMANCHE BY NASA 2021113-051
	10:28 APR.  1,1969
Note that the date is the date of the printout, not the date of the program revision.

059754,000002:                                                                                                  ## Copyright:   Public domain.
059755,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
059756,000004:                                                                                                  ## Purpose:     Part of the source code for Colossus 2A, AKA Comanche 055.
059757,000005:                                                                                                  ##              It is part of the source code for the Command Module's (CM)
059758,000006:                                                                                                  ##              Apollo Guidance Computer (AGC), for Apollo 11.
059759,000007:                                                                                                  ## Assembler:   yaYUL
059760,000008:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
059761,000009:                                                                                                  ## Website:     www.ibiblio.org/apollo.
059762,000010:                                                                                                  ## Pages:       1373-1388
059763,000011:                                                                                                  ## Mod history: 2009-05-10 SN   (Sergio Navarro). Started adapting
059764,000012:                                                                                                  ##                              from the Colossus249/ file of the same
059765,000013:                                                                                                  ##                              name, using Comanche055 page images.
059766,000014:                                                                                                  ##              2010-08-29 JL   Fixed indentation, whitespace.
059767,000015:                                                                                                  ##              2016-12-22 RSB  Proofed comment text using octopus/ProoferComments
059768,000016:                                                                                                  ##                              and corrected the errors found.
059769,000017:                                                                                                  ##              2017-01-20 RSB  Fixed comment-text errors noted while diff'ing
059770,000018:                                                                                                  ##                              vs Colossus 249.
059771,000019:                                                                                                  ##              2017-03-14 RSB  Comment-text fixes noted in proofing Luminary 116.
059772,000020: 
059773,000021:                                                                                                  ## This source code has been transcribed or otherwise adapted from digitized
059774,000022:                                                                                                  ## images of a hardcopy from the MIT Museum.  The digitization was performed
059775,000023:                                                                                                  ## by Paul Fjeld, and arranged for by Deborah Douglas of the Museum.  Many
059776,000024:                                                                                                  ## thanks to both.  The images (with suitable reduction in storage size and
059777,000025:                                                                                                  ## consequent reduction in image quality as well) are available online at
059778,000026:                                                                                                  ## www.ibiblio.org/apollo.  If for some reason you find that the images are
059779,000027:                                                                                                  ## illegible, contact me at info@sandroid.org about getting access to the
059780,000028:                                                                                                  ## (much) higher-quality images which Paul actually created.
059781,000029:                                                                                                  ##
059782,000030:                                                                                                  ## Notations on the hardcopy document read, in part:
059783,000031:                                                                                                  ##
059784,000032:                                                                                                  ##    Assemble revision 055 of AGC program Comanche by NASA
059785,000033:                                                                                                  ##    2021113-051.  10:28 APR. 1, 1969 
059786,000034:                                                                                                  ##
059787,000035:                                                                                                  ##    This AGC program shall also be referred to as
059788,000036:                                                                                                  ##            Colossus 2A
059789,000037: 

Page 1373

059791,000039:                                                                                                  #  THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES.  THE TFF ROUTINES NEVER
059792,000040:                                                                                                  #  KNOW WHICH ORIGIN APPLIES.  IT IS THE USER WHO KNOWS, AND WHO SUPPLIES RONE, VONE AND 1/SQRT(MU) AT THE
059793,000041:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
059794,000042: 
059795,000043:                                                                                                  #        EARTH ORIGIN    POSITION        -29     METERS
059796,000044:                                                                                                  #                        VELOCITY        -7      METERS/CENTISECOND
059797,000045:                                                                                                  #                        1/SQRT(MU)      +17     SQRT(CS SQ/METERS CUBED)
059798,000046: 
059799,000047:                                                                                                  #        MOON ORIGIN     POSITION        -27     METERS
059800,000048:                                                                                                  #                        VELOCITY        -5      METERS/CENTISECONDS
059801,000049:                                                                                                  #                        1/SQRT(MU)      +14     SQRT(CS SQ/METERS CUBED)
059802,000050: 
059803,000051:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE.  IN ALL CASES,
059804,000052:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28).  PROGRAM TFF/CONIC WILL GENERATE VONE/RTMU AND
059805,000053:                                                                                                  #  LEAVE IT IN VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
059806,000054: 
059807,000055:                                                                                                  #  THE USER MUST STORE THE STATE VECTOR IN RONE, VONE  AND MU IN THE FORM 1/SQRT(MU) IN TFF/RTMU
059808,000056:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING TFF/CONIC.  SINCE RONE, VONE ARE IN THE EXTENDED VERB STORAGE AREA,
059809,000057:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
059810,000058: 
059811,000059:                                                                                                  #  PROGRAMS CALC/TFF AND CALC/TPER ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
059812,000060:                                                                                                  #  RADIUS.  THIS RESTRICTION CAN BE REMOVED BY A 15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
059813,000061: 
059814,000062:                                                                                                  #  THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
059815,000063: 
059816,000064:                                                                                                  #                                        BELOW   E:  IS USED FOR EARTH ORIGIN SCALE
059817,000065:                                                                                                  #                                                M:  IS USED FOR MOON  ORIGIN SCALE
059818,000066: 
059819,000067:                                                                                                  # TFFSW          =       119D            BIT1    0 = CALCTFF             1 = CALCTPER
059820,000068: 23,3772                        TFFDELQ            =        10D                                   #        Q2-Q1                   E: (-16)  M: (-15)
059821,000069: 23,3772                        RMAG1              =        12D                                   #        ABVAL(RN)  M            E: (-29)  M: (-27)
059822,000070:                                                                                                  # RPER           =       14D             PERIGEE RADIUS  M       E: (-29)  M: (-27)
059823,000071: 23,3772                        TFFQ1              =        14D                                   #        R.V / SQRT(MUE)         E: (-16)  M: (-15)
059824,000072:                                                                                                  # SDELF/2                                SIN(THETA) /2
059825,000073: 23,3772                        CDELF/2            =        14D                                   #        COS(THETA) /2
059826,000074:                                                                                                  # RAPO           =       16D             APOGEE RADIUS  M        E: (-29)  M: (-27)
059827,000075: 23,3772                        NRTERM             =        16D                                   #        TERMINAL RADIUS  M      E: (-29+NR)
059828,000076:                                                                                                  #                                          M: (-27+NR)
059829,000077: 23,3772                        RTERM              =        18D                                   #        TERMINAL RADIUS  M      E: (-29)  M: (-27)
059830,000078: 23,3772                        TFFVSQ             =        20D                                   #        -(V SQUARED/MU)  1/M    E: (20)   M: (18)
059831,000079: 23,3772                        TFF1/ALF           =        22D                                   #        SEMI MAJ AXIS  M        E: (-22-2 NA)
059832,000080:                                                                                                  #                                          M: (-20-2 NA)
059833,000081: 23,3772                        TFFRTALF           =        24D                                   #        SQRT(ALFA)              E:(10+NA) M: (9+NA)
059834,000082: 23,3772                        TFFALFA            =        26D                                   #        ALFA  1/M               E:(26-NR) M: (24-NR)
059835,000083: 23,3772                        TFFNP              =        28D                                   #        SEMI LATUS RECTUM  M    E: (-38+2 NR)
059836,000084:                                                                                                  #                                          M: (-36+2 NR)
059837,000085: 23,3772                        TFF/RTMU           =        30D                                   #        1/SQRT(MU)              E: (17)   M: (14)
059838,000086: 23,3772                        NRMAG              =        32D                                   #        PRESENT RADIUS  M       E: (-29+NR)
059839,000087:                                                                                                  #                                          M: (-27+NR)
059840,000088: 23,3772                        TFFX               =        34D                                   
059841,000089: 23,3772                        TFFTEM             =        36D                                   #        TEMPORARY

Page 1374

059843,000091:                                                                                                  #                REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
059844,000092:                                                                                                  #                INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES.  THEY ARE ESTAB-
059845,000093:                                                                                                  #                LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
059846,000094:                                                                                                  #                SUBROUTINES.
059847,000095:                                                                                                  #                -NR                             C(X1) = NORM COUNT OF RMAG
059848,000096:                                                                                                  #                -NA                             C(X2) = NORM COUNT OF SQRT(ABS(ALFA))
059849,000097: 

Page 1375

059851,000099:                                                                                                  #  SUBROUTINE NAME:  TFFCONIC                    DATE:  01.29.67
059852,000100:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
059853,000101:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
059854,000102:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
059855,000103:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD MOON MU.
059856,000104:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
059857,000105: 
059858,000106:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
059859,000107:                                                                                                  #        SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA.  THE PARAMETERS ARE LISTED UNDER OUTPUT.
059860,000108:                                                                                                  #        THE EQUATIONS ARE
059861,000109:                                                                                                  #                -   -  -
059862,000110:                                                                                                  #                H = RN*VN                       ANGULAR MOMENTUM
059863,000111:                                                                                                  #                      - -
059864,000112:                                                                                                  #                LCP = H.H / MU                  SEMI LATUS RECTUM
059865,000113:                                                                                                  #                              -  -
059866,000114:                                                                                                  #                ALFA = 2/RN - VN.VN / MU        RECIPROCAL SEMI MAJ AXIS, SIGNED
059867,000115: 
059868,000116:                                                                                                  #        AND ALFA IS POS FOR ELLIPTIC ORBITS
059869,000117:                                                                                                  #                      0 FOR PARABOLIC ORBITS
059870,000118:                                                                                                  #                    NEG FOR HYPERBOLIC ORBITS.
059871,000119:                                                                                                  #        SUBROUTINE ALSO COMPUTES AND SAVES RMAG.
059872,000120: 
059873,000121:                                                                                                  #  CALLING SEQUENCE:
059874,000122:                                                                                                  #        TFFCONIC EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
059875,000123:                                                                                                  #        1/SQRT(MU).  PROGRAM WILL SAVE IN TFF/RTMU.  THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
059876,000124:                                                                                                  #        ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
059877,000125:                                                                                                  #        VONE AT PROPER SCALE.  THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
059878,000126:                                                                                                  #        TFF ROUTINES.
059879,000127: 
059880,000128:                                                                                                  #        ENTRY POINT TFFCONMU EXPECTS THAT TFF/RTMU IS ALREADY LOADED.
059881,000129: 
059882,000130:                                                                                                  #        TO SPECIFY MU:  DLOAD   CALL            IF MU ALREADY STORED:           CALL
059883,000131:                                                                                                  #                                YOURMU          1/RTMU E:(17) M:(14)                    TFFCONMU
059884,000132:                                                                                                  #                                TFFCONIC
059885,000133:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
059886,000134: 
059887,000135:                                                                                                  #  SUBROUTINES CALLED:  NONE
059888,000136: 
059889,000137:                                                                                                  #  NORMAL EXIT MODES:  RVQ
059890,000138: 
059891,000139:                                                                                                  #  ALARMS:  NONE
059892,000140: 
059893,000141:                                                                                                  #  OUTPUT:       THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
059894,000142:                                                                                                  #                RMAG1           E:(-29) M:(-27)         M  RN, PRESENT RADIUS LENGTH.
059895,000143:                                                                                                  #                NRMAG           E:(-29+NR)              M  RMAG, NORMALIZED
059896,000144:                                                                                                  #                                M:(-27+NR)
059897,000145:                                                                                                  #                X1                                      -NR, NORM COUNT
059898,000146:                                                                                                  #                TFFNP           E:(-38+2NR)             M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.  FOR VGAMCALC
059899,000147:                                                                                                  #                                M:(-36+2NR)
059900,000148:                                                                                                  #                TFF/RTMU        E:(17) M:(14)           1/SQRT(MU)
059901,000149:                                                                                                  #                TFFVSQ          E:(20) M:(18)           1/M  -(V SQ/MU):  PRESENT VELOCITY, NORMLIZED.  FOR VGAMCALC
059902,000150:                                                                                                  #                TFFALFA         E:(26-NR)               1/M  ALFA, WEIGHTED BY NR
059903,000151:                                                                                                  #                                M:(24-NR)
059904,000152:                                                                                                  #                TFFRTALF        E:(10+NA)               SQRT(ALFA), NORMALIZED
059905,000153:                                                                                                  #                                M:(9+NA)

Page 1376

059907,000155:                                                                                                  #                X2                                      -NA, NORM COUNT
059908,000156:                                                                                                  #                TFF1/ALF        E:(-22-2NA)             SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
059909,000157:                                                                                                  #                                M:(-20-2NA)
059910,000158:                                                                                                  #                PUSHLOC AT PDL+0
059911,000159: 
059912,000160:                                                                                                  #        THE FOLLOWING IS STORED IN GENERAL ERASABLE
059913,000161:                                                                                                  #                VONE'           E:(10) M:(9)            V/RT(MU), NORMALIZED VELOCITY
059914,000162: 
059915,000163:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
059916,000164:                                                                                                  #                RONE            E:(-29) M:(-27)         M  STATE VECTOR         LEFT BY CALLER
059917,000165:                                                                                                  #                VONE            E:(-7) M:(-5)           M/CS  STATE VECTOR      LEFT BY CALLER
059918,000166:                                                                                                  #                TFF/RTMU        E:(17) M:(14)           1/RT(CS SQ/M CUBE)      IF ENTER VIA TFFCONMU.
059919,000167: 
059920,000168:                                                                                                  #  DEBRIS:       QPRET,  PDL+0 ... PDL+3
059921,000169: 
059922,000170: 33,3776                                           BANK     33                                    
059923,000171: 27,2000                                           SETLOC   TOF-FF                                
059924,000172: 27,2000                                           BANK                                           
059925,000173: 
059926,000174: 27,2757                                           COUNT*   $$/TFF                                
059927,000175: 
059928,000176: 27,2757           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)    E:(17) M:(14)
059929,000177: 
059930,000178: 27,2760           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
059931,000179: 27,2761           02327                                    RONE                                  #  SAVED RN.  M  E:(-29) M:(-27)
059932,000180: 27,2762           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
059933,000181: 27,2763           00045                                    36D                                   #  MAGNITUDE
059934,000182: 27,2764           00015                           STORE    RMAG1                                 #  M  E:(-29) M:(-27)
059935,000183: 
059936,000184: 27,2765           77701                           NORM                                           
059937,000185: 27,2766           00047                                    X1                                    #  -NR
059938,000186: 27,2767           24041                           STOVL    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
059939,000187: 27,2770           02335                                    VONE                                  #  SAVED VN.  M/CS  E:(-7) M:(-5)
059940,000188: 27,2771           77761                           VXSC                                           
059941,000189: 27,2772           00037                                    TFF/RTMU                              #  E:(17) M:(14)
059942,000190: 27,2773           02372                           STORE    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
059943,000191: 
059944,000192: 27,2774           47361                           VXSC     VXV                                   
059945,000193: 27,2775           00041                                    NRMAG                                 #  E:(-29+NR) M:(-27+NR)
059946,000194:                                                                                                  #  UR/2 FROM PDL
059947,000195: 27,2776           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR) M:(-18+NR)
059948,000196: 27,2777           14035                           STODL    TFFNP                                 #  LC P  M  E:(-38+2NR) M:(-36+2NR)
059949,000197:                                                                                                  #  SAVE ALSO FOR VGAMCALC
059950,000198: 27,3000           15325                                    TFF1/4                                
059951,000199: 27,3001           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M  E:(26-NR) M:(24-NR)
059952,000200: 27,3002           00041                                    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
059953,000201: 27,3003           02372                                    VONE'                                 #  SAVED VN.  E:(10) M:(9)
059954,000202: 27,3004           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
059955,000203: 27,3005           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)  E:(20) M:(18)
059956,000204:                                                                                                  #  SAVE FOR VGAMCALC
059957,000205: 27,3006           43257                           SR*      DAD                                   

Page 1377

059959,000207: 27,3007           20573                                    0          -6,1                       #  GET -VSQ/MU  E:(26-NR) M:(24-NR)
059960,000208: 27,3010           77626                           STADR                                          
059961,000209:                                                                                                  #  2/RMAG  FROM PDL+2
059962,000210: 27,3011           77744                           STORE    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
059963,000211: 27,3012           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA  E:(20) M:(18)
059964,000212: 27,3013           20173                                    0          -6,1                       
059965,000213: 27,3014           75446                           ABS      SQRT                                  #  E:(10) M:(9)
059966,000214: 27,3015           77701                           NORM                                           
059967,000215: 27,3016           00050                                    X2                                    #  X2 = -NA
059968,000216: 27,3017           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA) M:(9+NA)
059969,000217: 27,3020           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
059970,000218:                                                                                                  #  ALFA FROM PDL+2  E:(20) M:(18)
059971,000219: 27,3021           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
059972,000220: 27,3022           57024                                    +2                                    
059973,000221: 27,3023           15325                                    TFF1/4                                
059974,000222: 27,3024           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
059975,000223: 27,3025           77616        DUMPCNIC           RVQ                                            
059976,000224:                                                                                                  #                        39 W

Page 1378

059978,000226:                                                                                                  #  SUBROUTINE NAME:  TFFRP/RA                    DATE: 01.17.67
059979,000227:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
059980,000228:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
059981,000229:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
059982,000230:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
059983,000231:                                                                                                  #                                                                        ALSO IMPROVE ACCURACY OF RAPO.
059984,000232: 
059985,000233:                                                                                                  #  FUNCTIONAL DESCRIPTION:  USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
059986,000234:                                                                                                  #        APOGEE RADIUS FOR A GENERAL CONIC.
059987,000235:                                                                                                  #        PROGRAM GIVES PERIGEE RADIUS AS         APOGEE RADIUS IS GIVEN BY
059988,000236:                                                                                                  #                RP = P/(1+E)                            RA = (1+E) / ALFA
059989,000237:                                                                                                  #        WHERE    2
059990,000238:                                                                                                  #                E  = 1 - P ALFA
059991,000239:                                                                                                  #        IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
059992,000240:                                                                                                  #                1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
059993,000241:                                                                                                  #                2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
059994,000242:                                                                                                  #                3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
059995,000243: 
059996,000244:                                                                                                  #        THIS SUBROUTINE REQUIRES THE SIGNED RECIPROCAL SEMI MAJ AXIS, ALFA, AND SEMI LATUS RECTUM AS DATA.
059997,000245: 
059998,000246:                                                                                                  #  CALLING SEQUENCE:     CALL
059999,000247:                                                                                                  #                                TFFRP/RA
060000,000248:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
060001,000249:                                                                                                  #        C(MPAC) UNSPECIFIED
060002,000250: 
060003,000251:                                                                                                  #  SUBROUTINES CALLED:   NONE
060004,000252: 
060005,000253:                                                                                                  #  NORMAL EXIT MODE:     RVQ
060006,000254:                                                                                                  #        IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
060007,000255:                                                                                                  #        OTHERWISE, RAPO = POSMAX.
060008,000256: 
060009,000257:                                                                                                  #  ALARMS:       NONE
060010,000258: 
060011,000259:                                                                                                  #  OUTPUT:       STORED IN PUSH LIST AREA.  SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO TFF/CONIC.
060012,000260:                                                                                                  #        RPER    E:(-29) M:(-27)         M       PERIGEE RADIUS          DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
060013,000261:                                                                                                  #        RAPO    E:(-29) M:(-27)         M       APOGEE RADIUS           WILL BE DESTROYED BY CALCTFF/CALCTPER
060014,000262:                                                                                                  #        PUSHLOC AT PDL+0
060015,000263: 
060016,000264:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
060017,000265:                                                                                                  #        TFFALFA E:(26-NR)               M       1/SEMI MAJ AXIS LEFT BY TFFCONIC
060018,000266:                                                                                                  #                M:(24-NR)
060019,000267:                                                                                                  #        TFFNP   E:(-38+2NR)             M       LC P, SEMI LATUS RECTUM LEFT BY TFFCONIC
060020,000268:                                                                                                  #                M:(-36+2NR)
060021,000269:                                                                                                  #        X1                              -NR, NORM COUNT OF RMAG         LEFT BY TFFCONIC
060022,000270:                                                                                                  #        X2                              -NA, NORM COUNT OF ALFA         LEFT BY TFFCONIC
060023,000271: 
060024,000272:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+1
060025,000273: 

Page 1379

060027,000275: 27,3026                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29) M:(-27)
060028,000276: 27,3026                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29) M:(-27)
060029,000277: 
060030,000278: 27,3026           41345        TFFRP/RA           DLOAD    DMP                                   
060031,000279: 27,3027           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
060032,000280: 27,3030           00035                                    TFFNP                                 #  LC P  M E:(-38+2NR) M:(-36+2NR)
060033,000281: 27,3031           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
060034,000282: 27,3032           20571                                    0          -8D,1                      #  ALFA P (-4)
060035,000283: 27,3033           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
060036,000284:                                                                                                  #  (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
060037,000285: 27,3034           17366                                    DP2(-4)                               
060038,000286: 27,3035           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA) (-4)
060039,000287: 27,3036           15325                                    TFF1/4                                
060040,000288: 27,3037           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
060041,000289: 27,3040           00035                                    TFFNP                                 #  LCP  M  E:(-38+2NR) M:(-36+2NR)
060042,000290: 27,3041           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
060043,000291: 27,3042           20601                                    0,1                                   #  X1=-NR
060044,000292: 27,3043           20572                                    0          -7,1                       #  (EFFECTIVE SL)
060045,000293: 27,3044           14017                           STODL    RPER                                  #  PERIGEE RADIUS  M  E:(-29) M:(-27)
060046,000294:                                                                                                  #  (1+E)  (-2)  FROM PDL+0
060047,000295: 27,3045           41005                           DMP      BOVB                                  
060048,000296: 27,3046           00027                                    TFF1/ALF                              #  E:(-22-2NA) M:(-20-2NA)
060049,000297: 27,3047           57352                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
060050,000298: 27,3050           53654                           BZE      SL*                                   
060051,000299: 27,3051           57060                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
060052,000300: 27,3052           57603                                    0          -5,2                       #  -5+NA
060053,000301: 27,3053           40057                           SL*      BOV                                   
060054,000302: 27,3054           57576                                    0,2                                   
060055,000303: 27,3055           57060                                    MAXRA                                 #  SET POSMAX IF OVFL.
060056,000304: 27,3056           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
060057,000305: 27,3057           57062                                    +3                                    
060058,000306: 27,3060           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID.  SET RAPO =
060059,000307: 27,3061           17372                                    NEARONE                               #  POSMAX AS A TAG.
060060,000308: 27,3062           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M  E:(-29) M:(-27)
060061,000309: 27,3063           77616        DUMPRPRA           RVQ                                            
060062,000310:                                                                                                  #                        30 W

Page 1380

060064,000312:                                                                                                  #  SUBROUTINE NAME:  CALCTPER / CALCTFF          DATE:  01.29.67
060065,000313:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
060066,000314:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
060067,000315:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 67
060068,000316:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 14 APR 67
060069,000317:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 8 JUL 67          NEAR EARTH MUE AND NEG TFF (GONEPAST)
060070,000318:                                                                                                  #  MOD NO:  4    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD VARIABLE MU.
060071,000319:                                                                                                  #  MOD NO:  5    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
060072,000320: 
060073,000321:                                                                                                  #  FUNCTIONAL DESCRIPTION:  PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION RN AND
060074,000322:                                                                                                  #        VELOCITY VN TO A RADIUS LENGTH SPECIFIED BY RTERM, SUPPLIED BY THE USER.  THE POSITION VECTOR
060075,000323:                                                                                                  #        RN MAY BE ON EITHER SIDE OF THE CONIC, BUT RTERM IS CONSIDERED ON THE INBOUND SIDE.
060076,000324:                                                                                                  #        THE EQUATIONS ARE
060077,000325: 
060078,000326:                                                                                                  #                Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)  (INBOUND SIDE)) LEQ +- LCE/SQRT(ALFA)
060079,000327:                                                                                                  #                     -  -
060080,000328:                                                                                                  #                Q1 = RN.VN / SQRT(MU)                                   LEQ +- LCE/SQRT(ALFA)
060081,000329: 
060082,000330:                                                                                                  #                Z = NUM / DEN                                           LEQ +- 1/SQRT(ALFA)
060083,000331: 
060084,000332:                                                                                                  #        WHERE, IF INBOUND
060085,000333:                                                                                                  #                NUM = RTERM -RN                                         LEQ +- 2 LCE/ALFA
060086,000334:                                                                                                  #                DEN = Q2+Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
060087,000335: 
060088,000336:                                                                                                  #        AND, IF OUTBOUND
060089,000337:                                                                                                  #                NUM = Q2-Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
060090,000338:                                                                                                  #                DEN = 2 - ALFA (RTERM + RN).                            LEQ +- 2 LCE
060091,000339: 
060092,000340:                                                                                                  #        IF      ALFA ZZ < 1.0           (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
060093,000341:                                                                                                  #        THEN    X = ALFA Z Z
060094,000342:                                                                                                  #        AND     TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
060095,000343:                                                                                                  #                EXCEPT  IF ALFA PNZ, AND IF TFF NEG,
060096,000344:                                                                                                  #                THEN    TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
060097,000345:                                                                                                  #        OR      IF ALFA ZZ GEQ 1.0      (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
060098,000346:                                                                                                  #        THEN    X = 1/ALFA Z Z
060099,000347:                                                                                                  #        AND     TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
060100,000348:                                                                                                  #        WHERE   T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
060101,000349:                                                                                                  #                             2      3             2
060102,000350:                                                                                                  #                1/3 - X/5 + X /7 - X /9 ...     (X  < 1.0)
060103,000351: 
060104,000352:                                                                                                  #  CALLING SEQUENCE:     TIME TO RTERM                   TIME TO PERIGEE
060105,000353:                                                                                                  #                        CALL                            CALL
060106,000354:                                                                                                  #                                CALCTFF                         CALCTPER
060107,000355:                                                                                                  #                        C(MPAC) = TERMNL RAD M          C(MPAC) = PERIGEE RAD M
060108,000356:                                                                                                  #        FOR EITHER, E:(-29) M:(-27)
060109,000357:                                                                                                  #        FOR EITHER, PUSHLOC = PDL+0, ARBITRARY IF LEQ 8D.

Page 1381

060111,000359: 
060112,000360:                                                                                                  #  SUBROUTINES CALLED:   T(X), VIA RTB
060113,000361: 
060114,000362:                                                                                                  #  NORMAL EXIT MODE:     RVQ
060115,000363:                                                                                                  #        HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS IN MPAC.  USER MUST STORE.
060116,000364:                                                                                                  #                A. TFF = FLIGHT TIME.  NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
060117,000365:                                                                                                  #                B. (THIS OPTION IS NO LONGER USED.)
060118,000366:                                                                                                  #                C. TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
060119,000367:                                                                                                  #                   THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
060120,000368: 
060121,000369:                                                                                                  #  OUTPUT:       C(MPAC)         (-28) CS        TIME OF FLIGHT, OR TIME TO PERIGEE
060122,000370:                                                                                                  #                TFFX            (0)             X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
060123,000371:                                                                                                  #                NRTERM          E:(-29+NR) M    RTERM, WEIGHTED BY NR                   LEFT FOR ENTRY DISPLAY TFF ROUTINES
060124,000372:                                                                                                  #                                M:(-27+NR)
060125,000373:                                                                                                  #                TFFTEM          E:(-59+2NR)     LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
060126,000374:                                                                                                  #                                M:(-55+2NR)     LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
060127,000375:                                                                                                  #                NOTE:   TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
060128,000376:                                                                                                  #                RMAG1           E:(-29) M:(-27) PDL 12 NOT TOUCHED.
060129,000377:                                                                                                  #                TFFQ1           E:(-16) M:(-15) PDL 14D
060130,000378:                                                                                                  #                TFFDELQ         E:(-16) M:(-15) PDL 10D
060131,000379:                                                                                                  #                PUSHLOC AT PDL+0
060132,000380: 
060133,000381:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
060134,000382:                                                                                                  #                RONE            E:(-29) M:(-27) M  STATE VECTOR                         LEFT BY USER
060135,000383:                                                                                                  #                VONE'           E:(+10) M:(+9)  VN/SQRT(MU)                             LEFT BY TFF/CONIC
060136,000384:                                                                                                  #                RMAG1           E:(-29) M:(-27) PRESENT RADIUS, M                       LEFT BY TFFCONIC
060137,000385:                                                                                                  #                C(MPAC)         E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH, M        LEFT BY USER
060138,000386: 
060139,000387:                                                                                                  #                THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
060140,000388:                                                                                                  #                TFF/RTMU        E:(17) M:(14)   1/SQRT(MU)                              LEFT BY TFFCONIC.
060141,000389:                                                                                                  #                NRMAG           E:(-29+NR)      M  RMAG, NORMALIZED                     LEFT BY TFFCONIC
060142,000390:                                                                                                  #                                M:(-27+NR)
060143,000391:                                                                                                  #                X1                              -NR, NORM COUNT                         LEFT BY TFFCONIC
060144,000392:                                                                                                  #                TFFNP           E:(-38+2NR)     M  LCP, SEMI LATUS RECTUM, WEIGHT NR    LEFT BY TFFCONIC
060145,000393:                                                                                                  #                                M:(-36+2NR)
060146,000394:                                                                                                  #                TFFALFA         E:(26-NR)       1/M  ALFA, WEIGHT NR                    LEFT BY TFFCONIC
060147,000395:                                                                                                  #                                M:(24-NR)
060148,000396:                                                                                                  #                TFFRTALF        E:(10+NA)       SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
060149,000397:                                                                                                  #                                M:(9+NA)
060150,000398:                                                                                                  #                X2                              -NA, NORM COUNT                         LEFT BY TFFCONIC
060151,000399:                                                                                                  #                TFF1/ALF        E:(-22-2NA)     SIGNED SEMIMAJ AXIS, WEIGHTED BY NA     LEFT BY TFFCONIC
060152,000400:                                                                                                  #                                M:(-20-2NA)
060153,000401: 
060154,000402:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+3
060155,000403:                                                                                                  #                RTERM           E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH
060156,000404:                                                                                                  #                RAPO            E:(-29) M:(-27) PDL 16D (=NRTERM)
060157,000405:                                                                                                  #                RPER            E:(-29) M:(-27) PDL 14D (=TFFQ1)
060158,000406: 

Page 1382

060160,000408: 27,3064           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER IN MPAC
060161,000409: 27,3065           03436                                    TFFSW                                 
060162,000410: 27,3066           57071                                    +3                                    
060163,000411: 27,3067           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
060164,000412: 27,3070           03676                                    TFFSW                                 
060165,000413: 27,3071           00023                 +3        STORE    RTERM                                 #  E:(-29) M:(-27)
060166,000414: 27,3072           77657                           SL*                                            
060167,000415: 27,3073           20201                                    0,1                                   #  X1=-NR
060168,000416: 27,3074           00021                           STORE    NRTERM                                #  RTERM  E:(-29+NR) M:(-27+NR)
060169,000417: 27,3075           44205                           DMP      BDSU                                  
060170,000418: 27,3076           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
060171,000419: 27,3077           15325                                    TFF1/4                                
060172,000420: 27,3100           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
060173,000421: 27,3101           00021                                    NRTERM                                #  E:(-29+NR) M:(-27+NR)
060174,000422: 27,3102           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
060175,000423:                                                                                                  #  E:(-32+NR) M:(-30+NR)
060176,000424: 27,3103           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
060177,000425: 27,3104           20573                                    0          -6,1                       #  X1 = -NR
060178,000426: 27,3105           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
060179,000427:                                                                                                  #  RTERM(2-ALFA RTERM) FROM PDL +2
060180,000428:                                                                                                  #  E:(-32+NR) M:(-30+NR)
060181,000429: 27,3106           77657                           SR*                                            #  LEAVE  E:(-32) M:(-30)
060182,000430: 27,3107           20601                                    0,1                                   #  X1 = -NR
060183,000431: 27,3110           71214                           BOFF     DLOAD                                 #  CHECK TFF /TPER SWITCH
060184,000432: 27,3111           03756                                    TFFSW                                 
060185,000433: 27,3112           57114                                    +2                                    #  IF TFF, CONTINUE
060186,000434: 27,3113           15335                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
060187,000435: 27,3114           75440                 +2        BMN      SQRT                                  #  E:(-16) M:(-15)
060188,000436: 27,3115           57247                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
060189,000437:                                                                                                  #  RESET PDL, SET TFF=POSMAX, AND EXIT.
060190,000438: 
060191,000439: 27,3116           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
060192,000440: 27,3117           57352                                    TCDANZIG                              #  ANY PORT IN A STORM.
060193,000441: 27,3120           24045                           STOVL    TFFTEM                                #  Q2  E:(-16) M:(-15)
060194,000442: 27,3121           02372                                    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
060195,000443: 27,3122           52441                           DOT      SL3                                   
060196,000444: 27,3123           02327                                    RONE                                  #  SAVED RN.  E:(-29) M:(-27)
060197,000445: 27,3124           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
060198,000446:                                                                                                  #  E:(-16) M:(-15)
060199,000447: 27,3125           44240                           BMN      BDSU                                  
060200,000448: 27,3126           57147                                    INBOUND                               #  USE ALTERNATE Z
060201,000449: 27,3127           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
060202,000450: 
060203,000451:                                                                                                  #  OUTBOUND Z CALC CONTINUES HERE
060204,000452: 
060205,000453: 27,3130           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E:(-16) M:(-15)
060206,000454: 27,3131           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
060207,000455: 27,3132           44205                           DMP      BDSU                                  

Page 1383

060209,000457: 27,3133           00041                                    NRMAG                                 #  RMAG  E:(-29+NR) M:(-27+NR)
060210,000458:                                                                                                  #  (2-RTERM ALFA)  (-3) FROM PDL+0
060211,000459: 27,3134           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E:(-3) OR (-16)
060212,000460:                                                                                                  #                M:(-3) OR (-15)
060213,000461: 27,3135           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
060214,000462: 27,3136           17360                                    LIM(-22)                              #  =1.0-B(-22)
060215,000463: 27,3137           57160                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
060216,000464: 27,3140           65345                           DLOAD    PDDL                                  #  SET DEN=0 OTHERWISE
060217,000465: 27,3141           15335                                    TFFZEROS                              
060218,000466:                                                                                                  #  XCH ZERO WITH PDL+0
060219,000467: 27,3142           57545                           DLOAD    DCOMP                                 
060220,000468: 27,3143           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
060221,000469: 27,3144           71240                           BMN      DLOAD                                 #  FOR TPER:  Z INDET AT DELE/2=0 AND 90.
060222,000470: 27,3145           57254                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
060223,000471: 
060224,000472:                                                                                                  #  Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
060225,000473: 27,3146           77616        DUMPTFF1           RVQ                                            #  RETURN TFF =0
060226,000474: 
060227,000475:                                                                                                  #  INBOUND Z CALC CONTINUES HERE
060228,000476: 
060229,000477: 27,3147           77745        INBOUND            DLOAD                                          #  RESET PDL+0
060230,000478: 27,3150           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
060231,000479: 27,3151           00023                                    RTERM                                 #  E:(-29) M:(-27)
060232,000480: 27,3152           00015                                    RMAG1                                 #  E:(-29) M:(-27)
060233,000481: 27,3153           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E:(-29) M:(-27)
060234,000482: 27,3154           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
060235,000483: 27,3155           52015                           DAD      GOTO                                  
060236,000484: 27,3156           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
060237,000485: 27,3157           57134                                    SAVEDEN                               #  DEN = Q2+Q1  E:(-16) M:(-15)
060238,000486: 
060239,000487: 27,3160           65215        TFFXTEST           DAD      PDDL                                  #  (ABS(DEN) TO PDL+2))  E:(-3) OR (-16)
060240,000488:                                                                                                  #                        M:(-3) OR (-15)
060241,000489: 27,3161           17362                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
060242,000490: 27,3162           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
060243,000491: 27,3163           53605                           DMP      SR*                                   
060244,000492: 27,3164           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
060245,000493: 27,3165           57201                                    0          -3,2                       #  X2=-NA
060246,000494: 27,3166           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)       E:(-3) OR (-16)
060247,000495:                                                                                                  #                                M:(-3) OR (-15)
060248,000496:                                                                                                  #  ABS(DEN) FROM PDL+2   E:(-3) OR (-16)
060249,000497:                                                                                                  #                        M:(-3) OR (-15)
060250,000498: 27,3167           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
060251,000499: 27,3170           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
060252,000500: 27,3171           57252                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
060253,000501: 
060254,000502:                                                                                                  #  OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
060255,000503: 
060256,000504: 27,3172           45471                           DDV      STADR                                 
060257,000505:                                                                                                  #  DEN FROM PDL+0        E:(-3) OR (-16)
060258,000506:                                                                                                  #                        M:(-3) OR (-15)
060259,000507: 27,3173           77732                           STORE    TFFTEM                                #  Z SAVE FOR SIGN OF SDELF.

Page 1384

060261,000509:                                                                                                  #  E:(-13) M:(-12)
060262,000510: 27,3174           63406                           PUSH     DSQ                                   #  Z TO PDL+0
060263,000511: 27,3175           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E:(-26) M:(-24)
060264,000512: 27,3176           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
060265,000513: 27,3177           75261                           SL       SIGN                                  
060266,000514: 27,3200           20206                                    5                                     
060267,000515: 27,3201           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
060268,000516: 27,3202           14045                           STODL    TFFTEM                                #  P ZSQ  E:(-59+2NR) M:(-55+2NR)
060269,000517:                                                                                                  #  (ARG IS USED IN TFF/TRIG)
060270,000518:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
060271,000519: 27,3203           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
060272,000520: 27,3204           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
060273,000521: 27,3205           77657                           SL*                                            
060274,000522: 27,3206           20201                                    0,1                                   #  X1=-NR
060275,000523: 27,3207           00043                           STORE    TFFX                                  #  X
060276,000524: 27,3210           41234                           RTB      DMP                                   
060277,000525: 27,3211           57334                                    T(X)                                  #  POLY
060278,000526:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
060279,000527: 27,3212           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E:(-29) M:(-27)
060280,000528: 27,3213           00023                                    RTERM                                 #  RTERM  E:(-29) M:(-27)
060281,000529: 27,3214           41215                           DAD      DMP                                   
060282,000530: 27,3215           00015                                    RMAG1                                 #  E:(-29) M:(-27)
060283,000531:                                                                                                  #  Z FROM PDL+0  E:(-13) M:(-12)
060284,000532: 27,3216           51042                           SR3      BPL                                   #  TFF SQRT(MU)  E:(-45) M:(-42)
060285,000533: 27,3217           57240                                    ENDTFF                                #  (NO PUSH UP)
060286,000534: 27,3220           75206                           PUSH     SIGN                                  #  TFF SQRT(MU) TO PDL+0
060287,000535: 27,3221           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
060288,000536: 27,3222           71244                           BPL      DLOAD                                 #  GONE PAST ?
060289,000537: 27,3223           57244                                    NEGTFF                                #  YES. TFF < 0.
060290,000538: 27,3224           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
060291,000539: 27,3225           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
060292,000540: 27,3226           57244                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
060293,000541: 
060294,000542:                                                                                                  #  CORRECT FOR ORBITAL PERIOD.
060295,000543: 
060296,000544: 27,3227           77676                           DCOMP                                          #  YES.  CORRECT FOR ORB PERIOD.
060297,000545: 27,3230           56205                           DMP      DDV                                   
060298,000546: 27,3231           17356                                    PI/16                                 #  2 PI (-5)
060299,000547: 27,3232           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
060300,000548: 27,3233           53657                           SL*      SL*                                   
060301,000549: 27,3234           57602                                    0          -4,2                       #  X2=-NA
060302,000550: 27,3235           57602                                    0          -4,2                       
060303,000551: 27,3236           43257                           SL*      DAD                                   
060304,000552: 27,3237           57576                                    0,2                                   
060305,000553:                                                                                                  #  TFF SQRT(MU) FROM PDL+0       E:(-45) M:(-42)
060306,000554: 27,3240           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC          E:(-45) M:(-42)
060307,000555: 27,3241           00037                                    TFF/RTMU                              #  E:(17) M:(14)
060308,000556: 27,3242           57250                                    MAXTFF                                #  SET POSMAX IF OVFL.
060309,000557: 
060310,000558: 27,3243           77616        DUMPTFF2           RVQ                                            #  RETURN TFF (-28) CS IN MPAC.
060311,000559: 

Page 1385

060313,000561: 27,3244           77745        NEGTFF             DLOAD                                          
060314,000562:                                                                                                  #  TFF SQRT(MU) FROM PDL+0, NEGATIVE.
060315,000563: 27,3245           77650                           GOTO                                           
060316,000564: 27,3246           57240                                    ENDTFF                                
060317,000565: 
060318,000566: 27,3247           77745        MAXTFF1            DLOAD                                          #  RESET PDL
060319,000567: 27,3250           43545        MAXTFF             DLOAD    RVQ                                   
060320,000568: 27,3251           17372                                    NEARONE                               
060321,000569: 
060322,000570:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
060323,000571: 
060324,000572:                                                                                                  #  NUM FROM TFFX.        E:(-16) OR (-29)
060325,000573:                                                                                                  #                        M:(-15) OR (-27)
060326,000574: 27,3252           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
060327,000575: 27,3253           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
060328,000576:                                                                                                  #  DEN FROM PDL+0  E:(-3)/( 16)  M:(-3)/(-15)
060329,000577:                                                                                                  #  N/D TO PDL+0  E:(11) M:(10)
060330,000578: 27,3254           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
060331,000579: 27,3255           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
060332,000580: 27,3256           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
060333,000581: 27,3257           14013                           STODL    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
060334,000582:                                                                                                  #  D/N FROM PDL+0
060335,000583: 27,3260           77626                           STADR                                          
060336,000584: 27,3261           77732                           STORE    TFFTEM                                #  D/N  E:(11) M:(10)
060337,000585: 27,3262           53605                           DMP      SL*                                   
060338,000586: 27,3263           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
060339,000587: 27,3264           57576                                    0,2                                   #  1/ALFA Z  E:(-11-NA) M:(-10-NA)
060340,000588: 27,3265           41206                           PUSH     DMP                                   #  TO PDL+0
060341,000589: 27,3266           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
060342,000590: 27,3267           41057                           SL*      BOVB                                  
060343,000591: 27,3270           57576                                    0,2                                   #  X2= -NA
060344,000592: 27,3271           45712                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
060345,000593: 27,3272           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
060346,000594: 27,3273           41234                           RTB      DMP                                   
060347,000595: 27,3274           57334                                    T(X)                                  #  POLY
060348,000596: 27,3275           00043                                    TFFX                                  
060349,000597: 27,3276           45242                           SR3      DSU                                   
060350,000598: 27,3277           17364                                    DP2(-3)                               
060351,000599: 27,3300           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA   E:(-15-NA)
060352,000600:                                                                                                  #                        M:(-14-NA)
060353,000601:                                                                                                  #  1/ALFA Z FROM PDL+0   E:(-11-NA)
060354,000602:                                                                                                  #                        M:(-10-NA)
060355,000603: 27,3301           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
060356,000604: 27,3302           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
060357,000605: 27,3303           00015                                    RMAG1                                 #  E:(-29) M:(-27)
060358,000606: 27,3304           43312                           SL2      DAD                                   
060359,000607: 27,3305           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
060360,000608: 27,3306           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z) =SGN OF SDELF  E:(-16) M:(-15
060361,000609: 27,3307           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
060362,000610: 27,3310           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1386

060364,000612: 27,3311           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
060365,000613: 27,3312           57575                                    1,2                                   #  X2=-NA
060366,000614: 27,3313           53765                           SIGN     SL*                                   
060367,000615: 27,3314           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
060368,000616: 27,3315           57576                                    0,2                                   
060369,000617: 27,3316           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR) M:(-55+2NR)
060370,000618:                                                                                                  #  (ARG FOR USE IN TFF/TRIG)
060371,000619: 27,3317           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
060372,000620: 27,3320           41366                           SQRT     DMP                                   
060373,000621: 27,3321           17356                                    PI/16                                 #  PI (-4)
060374,000622: 27,3322           77615                           DAD                                            
060375,000623:                                                                                                  #  2(XT(X)-1)/Z ALFA FROM PDL    E:(-15-NA)
060376,000624:                                                                                                  #                                M:(-14-NA)
060377,000625: 27,3323           45257                           SL*      DSU                                   
060378,000626: 27,3324           57577                                    0          -1,2                       
060379,000627: 27,3325           00013                                    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
060380,000628: 27,3326           53605                           DMP      SL*                                   
060381,000629: 27,3327           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
060382,000630: 27,3330           57601                                    0          -3,2                       
060383,000631: 27,3331           52057                           SL*      GOTO                                  
060384,000632: 27,3332           57602                                    0          -4,2                       
060385,000633: 27,3333           57240                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
060386,000634: 

Page 1387

060388,000636:                                                                                                  #  PROGRAM NAME:  T(X)                           DATE:  01.17.67
060389,000637:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
060390,000638:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
060391,000639: 
060392,000640:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES CALCTFF AND
060393,000641:                                                                                                  #        CALCTPER TO APPROXIMATE THE SERIES
060394,000642:                                                                                                  #                           2     3
060395,000643:                                                                                                  #                1/3 -X/5 +X /7 -X /9 ...
060396,000644: 
060397,000645:                                                                                                  #        WHERE   X = ALFA Z Z            IF ALFA Z Z LEQ 1
060398,000646:                                                                                                  #                X = 1/(ALFA Z Z)        IF ALFA Z Z G 1
060399,000647: 
060400,000648:                                                                                                  #        ALSO    X IS NEG FOR HYPERBOLIC ORBITS
060401,000649:                                                                                                  #                X = 0 FOR PARABOLIC ORBITS
060402,000650:                                                                                                  #                X IS POSITIVE FOR ELLIPTIC ORBITS
060403,000651: 
060404,000652:                                                                                                  #        FOR FLIGHT 278, THE POLYNOMIAL T(X) IS FITTED OVER THE RANGE (0,+1) AND HAS A MAXIMUM
060405,000653:                                                                                                  #        DEVIATION FROM THE SERIES OF 2 E-5       (T(X) IS A CHEBYCHEV TYPE FIT AND WAS OBTAINED USING
060406,000654:                                                                                                  #        MAC PROGRAM AUTCURFIT294RRB AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE (-.08,+1).)
060407,000655: 
060408,000656:                                                                                                  #  CALLING SEQUENCE:     RTB
060409,000657:                                                                                                  #                                T(X)
060410,000658:                                                                                                  #        C(MPAC) = X
060411,000659: 
060412,000660:                                                                                                  #  SUBROUTINES CALLED:  NONE
060413,000661: 
060414,000662:                                                                                                  #  NORMAL EXIT MODE:  TC DANZIG
060415,000663: 
060416,000664:                                                                                                  #  ALARMS:  NONE
060417,000665: 
060418,000666:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
060419,000667: 
060420,000668:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
060421,000669:                                                                                                  #        C(MPAC) = X
060422,000670: 
060423,000671:                                                                                                  #  DEBRIS:  NONE
060424,000672: 
060425,000673: 27,3334           07171        T(X)               TC       POLY                                  
060426,000674: 27,3335           00004                           DEC      4          B-14                       #  N-1
060427,000675: 27,3336           12525 12525                     2DEC     3.333333333 E-1                        
060428,000676: 27,3340           71463 57703                     2DEC*    -1.999819135 E-1*                       
060429,000677: 27,3342           04423 17645                     2DEC*    1.418148467 E-1*                       
060430,000678: 27,3344           74604 43667                     2DEC*    -1.01310997 E-1*                       
060431,000679: 27,3346           01626 37256                     2DEC*    5.609004986 E-2*                       
060432,000680: 27,3350           77404 52071                     2DEC*    -1.536156925 E-2*                       
060433,000681: 
060434,000682: 27,3352           06030        ENDT(X)            TC       DANZIG                                
060435,000683: 
060436,000684: 27,3353  27,3352               TCDANZIG           =        ENDT(X)                               
060437,000685: 

Page 1388

060439,000687:                                                                                                  #  TFF CONSTANTS
060440,000688: 
060441,000689: 32,3770                                           BANK     32                                    
060442,000690: 
060443,000691: 27,2000                                           SETLOC   TOF-FF1                               
060444,000692: 27,2000                                           BANK                                           
060445,000693: 
060446,000694:                                                                                                  #                                                NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
060447,000695:                                                                                                  # MUE            =       3.990815471 E10         M CUBE/CS SQ
060448,000696:                                                                                                  # RTMUE          =       1.997702549 E5 B-18*    MODIFIED EARTH MU
060449,000697: 
060450,000698: 27,3353           24775 30424  1/RTMU             2DEC*    .5005750271 E-5        B17*            #  MODIFIED EARTH MU
060451,000699: 
060452,000700:                                                                                                  #                                                NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
060453,000701:                                                                                                  # MUM            =       4.902778 E8             M CUBE/CS SQ
060454,000702:                                                                                                  # RTMUM          2DEC*   2.21422176 E4 B-18*
060455,000703: 27,3355           06220 37553  PI/16              2DEC     3.141592653 B-4                        
060456,000704: 27,3357           37777 37700  LIM(-22)           2OCT     3777737700                            #  1.0 -B(-22)
060457,000705: 27,3361           00000 00100  DP(-22)            2OCT     0000000100                            #  B(-22)
060458,000706: 27,3363           04000 00000  DP2(-3)            2DEC     1          B-3                        
060459,000707: 27,3365           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
060460,000708: 
060461,000709:                                                                                                  #  RPAD1         2DEC    6373338 B-29            M (-29) = 20909901.57 FT
060462,000710: 27,3367  22,3151               RPAD1              =        RPAD                                  
060463,000711: 
060464,000712: 27,3367           00305 11205  R300K              2DEC     6464778    B-29                       #  (-29) M
060465,000713: 27,3371           37777 37777  NEARONE            2DEC     .999999999                            
060466,000714: 27,3373  26,3334               TFFZEROS           EQUALS   HI6ZEROS                              
060467,000715: 27,3373  26,3324               TFF1/4             EQUALS   HIDP1/4                               

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