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 Luminary 131 (Apollo 13) 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 001 OF AGC PROGRAM LMY99 BY NASA 2021112-061
	16:27 JULY 14,1969
Note that the date is the date of the printout, not the date of the program revision.

054277,000002:                                                                                                  ## Copyright:   Public domain.
054278,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
054279,000004:                                                                                                  ## Purpose:     Part of the source code for Luminary 1A build 099.
054280,000005:                                                                                                  ##              It is part of the source code for the Lunar Module's (LM)
054281,000006:                                                                                                  ##              Apollo Guidance Computer (AGC), for Apollo 11.
054282,000007:                                                                                                  ## Assembler:   yaYUL
054283,000008:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
054284,000009:                                                                                                  ## Website:     www.ibiblio.org/apollo.
054285,000010:                                                                                                  ## Pages:       1268-1283
054286,000011:                                                                                                  ## Mod history: 2009-05-26 RSB  Adapted from the corresponding 
054287,000012:                                                                                                  ##                              Luminary131 file, using page 
054288,000013:                                                                                                  ##                              images from Luminary 1A.
054289,000014:                                                                                                  ##              2011-01-06 JL   Fixed pseudo-label indentation.
054290,000015:                                                                                                  ##              2016-12-17 RSB  Proofed text comments with octopus/ProoferComments
054291,000016:                                                                                                  ##                              and corrected the errors found.
054292,000017:                                                                                                  ##              2017-03-14 RSB  Comment-text fixes noted in proofing Luminary 116.
054293,000018:                                                                                                  ##              2017-03-16 RSB  Comment-text fixes identified in 5-way
054294,000019:                                                                                                  ##                              side-by-side diff of Luminary 69/99/116/131/210.
054295,000020: 
054296,000021:                                                                                                  ## This source code has been transcribed or otherwise adapted from
054297,000022:                                                                                                  ## digitized images of a hardcopy from the MIT Museum.  The digitization
054298,000023:                                                                                                  ## was performed by Paul Fjeld, and arranged for by Deborah Douglas of
054299,000024:                                                                                                  ## the Museum.  Many thanks to both.  The images (with suitable reduction
054300,000025:                                                                                                  ## in storage size and consequent reduction in image quality as well) are
054301,000026:                                                                                                  ## available online at www.ibiblio.org/apollo.  If for some reason you
054302,000027:                                                                                                  ## find that the images are illegible, contact me at info@sandroid.org
054303,000028:                                                                                                  ## about getting access to the (much) higher-quality images which Paul
054304,000029:                                                                                                  ## actually created.
054305,000030:                                                                                                  ##
054306,000031:                                                                                                  ## Notations on the hardcopy document read, in part:
054307,000032:                                                                                                  ##
054308,000033:                                                                                                  ##      Assemble revision 001 of AGC program LMY99 by NASA 2021112-61
054309,000034:                                                                                                  ##      16:27 JULY 14, 1969 
054310,000035: 

Page 1268

054312,000037:                                                                                                  #  THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES.  THE TFF ROUTINES NEVER
054313,000038:                                                                                                  #  KNOW WHICH ORIGIN APPLIES.  IT IS THE USER WHO KNOWS, AND WHO SUPPLIES RONE, VONE AND 1/SQRT(MU) AT THE
054314,000039:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
054315,000040: 
054316,000041:                                                                                                  #        EARTH ORIGIN    POSITION        -29     METERS
054317,000042:                                                                                                  #                        VELOCITY        -7      METERS/CENTISECOND
054318,000043:                                                                                                  #                        1/SQRT(MU)      +17     SQRT(CS SQ/METERS CUBED)
054319,000044: 
054320,000045:                                                                                                  #        MOON ORIGIN     POSITION        -27     METERS
054321,000046:                                                                                                  #                        VELOCITY        -5      METERS/CENTISECONDS
054322,000047:                                                                                                  #                        1/SQRT(MU)      +14     SQRT(CS SQ/METERS CUBED)
054323,000048: 
054324,000049:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE.  IN ALL CASES,
054325,000050:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28).  PROGRAM TFF/CONIC WILL GENERATE VONE/RTMU AND
054326,000051:                                                                                                  #  LEAVE IT IN VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
054327,000052: 
054328,000053:                                                                                                  #  THE USER MUST STORE THE STATE VECTOR IN RONE, VONE  AND MU IN THE FORM 1/SQRT(MU) IN TFF/RTMU
054329,000054:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING TFF/CONIC.  SINCE RONE, VONE ARE IN THE EXTENDED VERB STORAGE AREA,
054330,000055:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
054331,000056: 
054332,000057:                                                                                                  #  PROGRAMS CALC/TFF AND CALC/TPER ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
054333,000058:                                                                                                  #  RADIUS.  THIS RESTRICTION CAN BE REMOVED BY A 15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
054334,000059: 
054335,000060:                                                                                                  #  THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
054336,000061: 
054337,000062:                                                                                                  #                                        BELOW   E:  IS USED FOR EARTH ORIGIN SCALE
054338,000063:                                                                                                  #                                                M:  IS USED FOR MOON  ORIGIN SCALE
054339,000064: 
054340,000065:                                                                                                  # TFFSW          =       119D    BIT1    0 = CALCTFF             1 = CALCTPER
054341,000066: 10,2213                        TFFDELQ            =        10D                                   #        Q2-Q1                   E: (-16)  M: (-15)
054342,000067: 10,2213                        RMAG1              =        12D                                   #        ABVAL(RN)  M            E: (-29)  M: (-27)
054343,000068:                                                                                                  # RPER           =       14D             PERIGEE RADIUS  M       E: (-29)  M: (-27)
054344,000069: 10,2213                        TFFQ1              =        14D                                   #        R.V / SQRT(MUE)         E: (-16)  M: (-15)
054345,000070:                                                                                                  # SDELF/2                                SIN(THETA) /2
054346,000071: 10,2213                        CDELF/2            =        14D                                   #        COS(THETA) /2
054347,000072:                                                                                                  # RAPO           =       16D             APOGEE RADIUS  M        E: (-29)  M: (-27)
054348,000073: 10,2213                        NRTERM             =        16D                                   #        TERMINAL RADIUS  M      E: (-29+NR)
054349,000074:                                                                                                  #                                          M: (-27+NR)
054350,000075: 10,2213                        RTERM              =        18D                                   #        TERMINAL RADIUS  M      E: (-29)  M: (-27)
054351,000076: 10,2213                        TFFVSQ             =        20D                                   #        -(V SQUARED/MU)  1/M    E: (20)   M: (18)
054352,000077: 10,2213                        TFF1/ALF           =        22D                                   #        SEMI MAJ AXIS  M        E: (-22-2 NA)
054353,000078:                                                                                                  #                                          M: (-20-2 NA)
054354,000079: 10,2213                        TFFRTALF           =        24D                                   #        SQRT(ALFA)              E:(10+NA) M: (9+NA)
054355,000080: 10,2213                        TFFALFA            =        26D                                   #        ALFA  1/M               E:(26-NR) M: (24-NR)
054356,000081: 10,2213                        TFFNP              =        28D                                   #        SEMI LATUS RECTUM  M    E: (-38+2 NR)
054357,000082:                                                                                                  #                                          M: (-36+2 NR)
054358,000083: 10,2213                        TFF/RTMU           =        30D                                   #        1/SQRT(MU)              E: (17)   M: (14)
054359,000084: 10,2213                        NRMAG              =        32D                                   #        PRESENT RADIUS  M       E: (-29+NR)
054360,000085:                                                                                                  #                                          M: (-27+NR)
054361,000086: 10,2213                        TFFX               =        34D                                   
054362,000087: 10,2213                        TFFTEM             =        36D                                   #        TEMPORARY

Page 1269

054364,000089:                                                                                                  #                REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
054365,000090:                                                                                                  #                INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES.  THEY ARE ESTAB-
054366,000091:                                                                                                  #                LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
054367,000092:                                                                                                  #                SUBROUTINES.
054368,000093:                                                                                                  #                -NR                             C(X1) = NORM COUNT OF RMAG
054369,000094:                                                                                                  #                -NA                             C(X2) = NORM COUNT OF SQRT(ABS(ALFA))
054370,000095: 

Page 1270

054372,000097:                                                                                                  #  SUBROUTINE NAME:  TFFCONIC                                            DATE:  01.29.67
054373,000098:                                                                                                  #  MOD NO:  0                                                            LOG SECTION:  TIME OF FREE FALL
054374,000099:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
054375,000100:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
054376,000101:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD MOON MU.
054377,000102:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
054378,000103: 
054379,000104:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
054380,000105:                                                                                                  #        SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA.  THE PARAMETERS ARE LISTED UNDER OUTPUT.
054381,000106:                                                                                                  #        THE EQUATIONS ARE
054382,000107:                                                                                                  #                -   -  -
054383,000108:                                                                                                  #                H = RN*VN                       ANGULAR MOMENTUM
054384,000109:                                                                                                  #                      - -
054385,000110:                                                                                                  #                LCP = H.H / MU                  SEMI LATUS RECTUM
054386,000111:                                                                                                  #                              -  - 
054387,000112:                                                                                                  #                ALFA = 2/RN - VN.VN / MU        RECIPROCAL SEMI MAJ AXIS, SIGNED
054388,000113: 
054389,000114:                                                                                                  #        AND ALFA IS POS FOR ELLIPTIC ORBITS
054390,000115:                                                                                                  #                      0 FOR PARABOLIC ORBITS
054391,000116:                                                                                                  #                    NEG FOR HYPERBOLIC ORBITS.
054392,000117:                                                                                                  #        SUBROUTINE ALSO COMPUTES AND SAVES RMAG.
054393,000118: 
054394,000119:                                                                                                  #  CALLING SEQUENCE:
054395,000120:                                                                                                  #        TFFCONIC EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
054396,000121:                                                                                                  #        1/SQRT(MU).  PROGRAM WILL SAVE IN TFF/RTMU.  THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
054397,000122:                                                                                                  #        ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
054398,000123:                                                                                                  #        VONE AT PROPER SCALE.  THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
054399,000124:                                                                                                  #        TFF ROUTINES.
054400,000125: 
054401,000126:                                                                                                  #        ENTRY POINT TFFCONMU EXPECTS THAT TFF/RTMU IS ALREADY LOADED.
054402,000127: 
054403,000128:                                                                                                  #        TO SPECIFY MU:  DLOAD   CALL                            IF MU ALREADY STORED:   CALL
054404,000129:                                                                                                  #                                YOURMU  1/RTMU E:(17) M:(14)                                    TFFCONMU
054405,000130:                                                                                                  #                                TFFCONIC
054406,000131:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
054407,000132: 
054408,000133:                                                                                                  #  SUBROUTINES CALLED:  NONE
054409,000134: 
054410,000135:                                                                                                  #  NORMAL EXIT MODES:  RVQ
054411,000136: 
054412,000137:                                                                                                  #  ALARMS:  NONE
054413,000138: 
054414,000139:                                                                                                  #  OUTPUT:       THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
054415,000140:                                                                                                  #                RMAG1           E:(-29) M:(-27) M  RN, PRESENT RADIUS LENGTH.
054416,000141:                                                                                                  #                NRMAG           E:(-29+NR)      M  RMAG, NORMALIZED
054417,000142:                                                                                                  #                                M:(-27+NR)
054418,000143:                                                                                                  #                X1                              -NR, NORM COUNT
054419,000144:                                                                                                  #                TFFNP           E:(-38+2NR)     M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.      FOR VGAMCALC
054420,000145:                                                                                                  #                                M:(-36+2NR)
054421,000146:                                                                                                  #                TFF/RTMU        E:(17) M:(14)   1/SQRT(MU)
054422,000147:                                                                                                  #                TFFVSQ          E:(20) M:(18)   1/M  -(V SQ/MU):  PRESENT VELOCITY,NORMLIZED.   FOR VGAMCALC
054423,000148:                                                                                                  #                TFFALFA         E:(26-NR)       1/M  ALFA, WEIGHTED BY NR
054424,000149:                                                                                                  #                                M:(24-NR)
054425,000150:                                                                                                  #                TFFRTALF        E:(10+NA)       SQRT(ALFA), NORMALIZED
054426,000151:                                                                                                  #                                M:(9+NA)

Page 1271

054428,000153:                                                                                                  #                X2                              -NA, NORMCOUNT
054429,000154:                                                                                                  #                TFF1/ALF        E:(-22-2NA)     SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
054430,000155:                                                                                                  #                                M:(-20-2NA)
054431,000156:                                                                                                  #                PUSHLOC AT PDL+0
054432,000157: 
054433,000158:                                                                                                  #        THE FOLLOWING IS STORED IN GENERAL ERASABLE
054434,000159:                                                                                                  #                VONE'           E:(10) M:(9)    V/RT(MU), NORMALIZED VELOCITY
054435,000160: 
054436,000161:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
054437,000162:                                                                                                  #                RONE            E:(-29) M:(-27) M  STATE VECTOR         LEFT BY CALLER
054438,000163:                                                                                                  #                VONE            E:(-7) M:(-5)   M/CS  STATE VECTOR      LEFT BY CALLER
054439,000164:                                                                                                  #                TFF/RTMU        E:(17) M:(14)   1/RT(CS SQ/M CUBE)      IF ENTER VIA TFFCONMU.
054440,000165: 
054441,000166:                                                                                                  #  DEBRIS:       QPRET,          PDL+0 ... PDL+3
054442,000167: 
054443,000168: 33,3777                                           BANK     33                                    
054444,000169: 27,2000                                           SETLOC   TOF-FF                                
054445,000170: 27,2000                                           BANK                                           
054446,000171: 
054447,000172: 27,3360                                           COUNT*   $$/TFF                                
054448,000173: 
054449,000174: 27,3360           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)    E:(17) M:(14)
054450,000175: 
054451,000176: 27,3361           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
054452,000177: 27,3362           02207                                    RONE                                  #  SAVED RN.  M  E:(-29) M:(-27)
054453,000178: 27,3363           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
054454,000179: 27,3364           00045                                    36D                                   #  MAGNITUDE
054455,000180: 27,3365           00015                           STORE    RMAG1                                 #  M  E:(-29) M:(-27)
054456,000181: 
054457,000182: 27,3366           77701                           NORM                                           
054458,000183: 27,3367           00047                                    X1                                    #  -NR
054459,000184: 27,3370           24041                           STOVL    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
054460,000185: 27,3371           02215                                    VONE                                  #  SAVED VN.  M/CS  E:(-7) M:(-5)
054461,000186: 27,3372           77761                           VXSC                                           
054462,000187: 27,3373           00037                                    TFF/RTMU                              #  E:(17) M:(14)
054463,000188: 27,3374           02170                           STORE    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
054464,000189: 
054465,000190: 27,3375           47361                           VXSC     VXV                                   
054466,000191: 27,3376           00041                                    NRMAG                                 #  E:(-29+NR) M:(-27+NR)
054467,000192:                                                                                                  #  UR/2 FROM PDL
054468,000193: 27,3377           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR) M:(-18+NR)
054469,000194: 27,3400           14035                           STODL    TFFNP                                 #  LC P  M  E:(-38+2NR) M:(-36+2NR)
054470,000195:                                                                                                  #  SAVE ALSO FOR VGAMCALC
054471,000196: 27,3401           06512                                    TFF1/4                                
054472,000197: 27,3402           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M  E:(26-NR) M:(24-NR)
054473,000198: 27,3403           00041                                    NRMAG                                 #  RMAG  M  E:(-29+NR) M:(-27+NR)
054474,000199: 27,3404           02170                                    VONE'                                 #  SAVED VN.  E:(10) M:(9)
054475,000200: 27,3405           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
054476,000201: 27,3406           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)  E:(20) M:(18)
054477,000202:                                                                                                  #  SAVE FOR VGAMCALC
054478,000203: 27,3407           43257                           SR*      DAD                                   

Page 1272

054480,000205: 27,3410           20573                                    0          -6,1                       #  GET -VSQ/MU  E:(26-NR) M:(24-NR)
054481,000206: 27,3411           77626                           STADR                                          
054482,000207:                                                                                                  #  2/RMAG  FROM PDL+2
054483,000208: 27,3412           77744                           STORE    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
054484,000209: 27,3413           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA  E:(20) M:(18)
054485,000210: 27,3414           20173                                    0          -6,1                       
054486,000211: 27,3415           75446                           ABS      SQRT                                  #  E:(10) M:(9)
054487,000212: 27,3416           77701                           NORM                                           
054488,000213: 27,3417           00050                                    X2                                    #  X2 = -NA
054489,000214: 27,3420           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA) M:(9+NA)
054490,000215: 27,3421           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
054491,000216:                                                                                                  #  ALFA FROM PDL+2  E:(20) M:(18)
054492,000217: 27,3422           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
054493,000218: 27,3423           57425                                    +2                                    
054494,000219: 27,3424           06512                                    TFF1/4                                
054495,000220: 27,3425           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054496,000221: 27,3426           77616        DUMPCNIC           RVQ                                            
054497,000222: 
054498,000223:                                                                                                  #                                                              39 W

Page 1273

054500,000225:                                                                                                  #  SUBROUTINE NAME:  TFFRP/RA                                            DATE: 01.17.67
054501,000226:                                                                                                  #  MOD NO:  0                                                            LOG SECTION:  TIME OF FREE FALL
054502,000227:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
054503,000228:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 11 APR 67
054504,000229:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
054505,000230:                                                                                                  #                                                                        ALSO IMPROVE ACCURACY OF RAPO.
054506,000231: 
054507,000232:                                                                                                  #  FUNCTIONAL DESCRIPTION:  USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
054508,000233:                                                                                                  #        APOGEE RADIUS FOR A GENERAL CONIC.
054509,000234:                                                                                                  #        PROGRAM GIVES PERIGEE RADIUS AS         APOGEE RADIUS IS GIVEN BY
054510,000235:                                                                                                  #                RP = P/(1+E)                            RA = (1+E) / ALFA
054511,000236:                                                                                                  #        WHERE    2
054512,000237:                                                                                                  #                E  = 1 - P ALFA
054513,000238:                                                                                                  #        IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
054514,000239:                                                                                                  #                1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
054515,000240:                                                                                                  #                2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
054516,000241:                                                                                                  #                3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
054517,000242: 
054518,000243:                                                                                                  #        THIS SUBROUTINE REQUIRES THE SIGNED RECIPROCAL SEMI MAJ AXIS, ALFA, AND SEMI LATUS RECTUM AS DATA.
054519,000244: 
054520,000245:                                                                                                  #  CALLING SEQUENCE:     CALL
054521,000246:                                                                                                  #                                TFFRP/RA
054522,000247:                                                                                                  #        PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
054523,000248:                                                                                                  #        C(MPAC) UNSPECIFIED
054524,000249: 
054525,000250:                                                                                                  #  SUBROUTINES CALLED:   NONE
054526,000251: 
054527,000252:                                                                                                  #  NORMAL EXIT MODE:     RVQ
054528,000253:                                                                                                  #        IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
054529,000254:                                                                                                  #        OTHERWISE, RAPO = POSMAX.
054530,000255: 
054531,000256:                                                                                                  #  ALARMS:       NONE
054532,000257: 
054533,000258:                                                                                                  #  OUTPUT:       STORED IN PUSH LIST AREA.  SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO TFF/CONIC.
054534,000259:                                                                                                  #        RPER    E:(-29) M:(-27)         M       PERIGEE RADIUS          DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
054535,000260:                                                                                                  #        RAPO    E:(-29) M:(-27)         M       APOGEE RADIUS           WILL BE DESTROYED BY CALCTFF/CALCTPER
054536,000261:                                                                                                  #        PUSHLOC AT PDL+0
054537,000262: 
054538,000263:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
054539,000264:                                                                                                  #        TFFALFA E:(26-NR)               M       1/SEMI MAJ AXIS         LEFT BY TFFCONIC
054540,000265:                                                                                                  #                M:(24-NR)
054541,000266:                                                                                                  #        TFFNP   E:(-38+2NR)             M       LC P, SEMI LATUS RECTUM LEFT BY TFFCONIC
054542,000267:                                                                                                  #                M:(-36+2NR)
054543,000268:                                                                                                  #        X1                              -NR, NORM COUNT OF RMAG         LEFT BY TFFCONIC
054544,000269:                                                                                                  #        X2                              -NA, NORM COUNT OF ALFA         LEFT BY TFFCONIC
054545,000270: 
054546,000271:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+1
054547,000272: 

Page 1274

054549,000274: 27,3427                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29) M:(-27)
054550,000275: 27,3427                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29) M:(-27)
054551,000276: 
054552,000277: 27,3427           41345        TFFRP/RA           DLOAD    DMP                                   
054553,000278: 27,3430           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR) M:(24-NR)
054554,000279: 27,3431           00035                                    TFFNP                                 #  LC P  M E:(-38+2NR) M:(-36+2NR)
054555,000280: 27,3432           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
054556,000281: 27,3433           20571                                    0          -8D,1                      #  ALFA P (-4)
054557,000282: 27,3434           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
054558,000283:                                                                                                  #  (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
054559,000284: 27,3435           17765                                    DP2(-4)                               
054560,000285: 27,3436           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA) (-4)
054561,000286: 27,3437           06512                                    TFF1/4                                
054562,000287: 27,3440           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
054563,000288: 27,3441           00035                                    TFFNP                                 #  LCP  M  E:(-38+2NR) M:(-36+2NR)
054564,000289: 27,3442           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
054565,000290: 27,3443           20601                                    0,1                                   #  X1=-NR
054566,000291: 27,3444           20572                                    0          -7,1                       #  (EFFECTIVE SL)
054567,000292: 27,3445           14017                           STODL    RPER                                  #  PERIGEE RADIUS  M  E:(-29) M:(-27)
054568,000293:                                                                                                  #  (1+E)  (-2)  FROM PDL+0
054569,000294: 27,3446           41005                           DMP      BOVB                                  
054570,000295: 27,3447           00027                                    TFF1/ALF                              #  E:(-22-2NA) M:(-20-2NA)
054571,000296: 27,3450           57753                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
054572,000297: 27,3451           53654                           BZE      SL*                                   
054573,000298: 27,3452           57461                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
054574,000299: 27,3453           57603                                    0          -5,2                       #  -5+NA
054575,000300: 27,3454           40057                           SL*      BOV                                   
054576,000301: 27,3455           57576                                    0,2                                   
054577,000302: 27,3456           57461                                    MAXRA                                 #  SET POSMAX IF OVFL.
054578,000303: 27,3457           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
054579,000304: 27,3460           57463                                    +3                                    
054580,000305: 27,3461           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID.  SET RAPO =
054581,000306: 27,3462           17771                                    NEARONE                               #  POSMAX AS A TAG.
054582,000307: 27,3463           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M  E:(-29) M:(-27)
054583,000308: 27,3464           77616        DUMPRPRA           RVQ                                            
054584,000309: 
054585,000310:                                                                                                  #                                                                30 W

Page 1275

054587,000312:                                                                                                  #  SUBROUTINE NAME:  CALCTPER / CALCTFF                                  DATE:  01.29.67
054588,000313:                                                                                                  #  MOD NO:  0                                                            LOG SECTION:  TIME OF FREE FALL
054589,000314:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
054590,000315:                                                                                                  #  MOD NO:  1    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 67
054591,000316:                                                                                                  #  MOD NO:  2    MOD BY:  RR BAIRNSFATHER        DATE: 14 APR 67
054592,000317:                                                                                                  #  MOD NO:  3    MOD BY:  RR BAIRNSFATHER        DATE: 8 JUL 67          NEAR EARTH MUE AND NEG TFF (GONEPAST)
054593,000318:                                                                                                  #  MOD NO:  4    MOD BY:  RR BAIRNSFATHER        DATE: 21 NOV 67         ADD VARIABLE MU.
054594,000319:                                                                                                  #  MOD NO:  5    MOD BY:  RR BAIRNSFATHER        DATE: 21 MAR 68         ACCEPT DIFFERENT EARTH/MOON SCALES
054595,000320: 
054596,000321:                                                                                                  #  FUNCTIONAL DESCRIPTION:  PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION RN AND
054597,000322:                                                                                                  #        VELOCITY VN TO A RADIUS LENGTH SPECIFIED BY RTERM, SUPPLIED BY THE USER.  THE POSITION VECTOR
054598,000323:                                                                                                  #        RN MAY BE ON EITHER SIDE OF THE CONIC, BUT RTERM IS CONSIDERED ON THE INBOUND SIDE.
054599,000324:                                                                                                  #        THE EQUATIONS ARE
054600,000325: 
054601,000326:                                                                                                  #                Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)  (INBOUND SIDE)) LEQ +- LCE/SQRT(ALFA)
054602,000327:                                                                                                  #                     -  -
054603,000328:                                                                                                  #                Q1 = RN.VN / SQRT(MU)                                   LEQ +- LCE/SQRT(ALFA)
054604,000329: 
054605,000330:                                                                                                  #                Z = NUM / DEN                                           LEQ +- 1/SQRT(ALFA)
054606,000331: 
054607,000332:                                                                                                  #        WHERE, IF INBOUND
054608,000333:                                                                                                  #                NUM = RTERM -RN                                         LEQ +- 2 LCE/ALFA
054609,000334:                                                                                                  #                DEN = Q2+Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
054610,000335: 
054611,000336:                                                                                                  #        AND, IF OUTBOUND
054612,000337:                                                                                                  #                NUM = Q2-Q1                                             LEQ +- 2 LCE/SQRT(ALFA)
054613,000338:                                                                                                  #                DEN = 2 - ALFA (RTERM + RN).                            LEQ +- 2 LCE
054614,000339: 
054615,000340:                                                                                                  #        IF      ALFA ZZ < 1.0           (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
054616,000341:                                                                                                  #        THEN    X = ALFA Z Z
054617,000342:                                                                                                  #        AND     TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
054618,000343:                                                                                                  #                EXCEPT  IF ALFA PNZ, AND IF TFF NEG,
054619,000344:                                                                                                  #                THEN    TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
054620,000345:                                                                                                  #        OR      IF ALFA ZZ GEQ 1.0      (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
054621,000346:                                                                                                  #        THEN    X = 1/ALFA Z Z
054622,000347:                                                                                                  #        AND     TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
054623,000348:                                                                                                  #        WHERE   T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
054624,000349:                                                                                                  #                             2      3             2
054625,000350:                                                                                                  #                1/3 - X/5 + X /7 - X /9 ...     (X  < 1.0)
054626,000351: 
054627,000352:                                                                                                  #  CALLING SEQUENCE:     TIME TO RTERM                   TIME TO PERIGEE
054628,000353:                                                                                                  #                        CALL                            CALL
054629,000354:                                                                                                  #                                CALCTFF                         CALCTPER
054630,000355:                                                                                                  #                        C(MPAC) = TERMNL RAD M          C(MPAC) = PERIGEE RAD M
054631,000356:                                                                                                  #        FOR EITHER, E:(-29) M:(-27)
054632,000357:                                                                                                  #        FOR EITHER, PUSHLOC = PDL+0, ARBITRARY IF LEQ 8D.

Page 1276

054634,000359: 
054635,000360:                                                                                                  #  SUBROUTINES CALLED:   T(X), VIA RTB
054636,000361: 
054637,000362:                                                                                                  #  NORMAL EXIT MODE:     RVQ
054638,000363:                                                                                                  #        HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS IN MPAC.  USER MUST STORE.
054639,000364:                                                                                                  #                A. TFF = FLIGHT TIME.  NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
054640,000365:                                                                                                  #                B. (THIS OPTION IS NO LONGER USED.)
054641,000366:                                                                                                  #                C. TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
054642,000367:                                                                                                  #                   THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
054643,000368: 
054644,000369:                                                                                                  #  OUTPUT:       C(MPAC)         (-28) CS        TIME OF FLIGHT, OR TIME TO PERIGEE
054645,000370:                                                                                                  #                TFFX            (0)             X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
054646,000371:                                                                                                  #                NRTERM          E:(-29+NR) M    RTERM, WEIGHTED BY NR                   LEFT FOR ENTRY DISPLAY TFF ROUTINES
054647,000372:                                                                                                  #                                M:(-27+NR)
054648,000373:                                                                                                  #                TFFTEM          E:(-59+2NR)     LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
054649,000374:                                                                                                  #                                M:(-55+2NR)     LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
054650,000375:                                                                                                  #                NOTE:   TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
054651,000376:                                                                                                  #                RMAG1           E:(-29) M:(-27) PDL 12 NOT TOUCHED.
054652,000377:                                                                                                  #                TFFQ1           E:(-16) M:(-15) PDL 14D
054653,000378:                                                                                                  #                TFFDELQ         E:(-16) M:(-15) PDL 10D
054654,000379:                                                                                                  #                PUSHLOC AT PDL+0
054655,000380: 
054656,000381:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
054657,000382:                                                                                                  #                RONE            E:(-29) M:(-27) M  STATE VECTOR                         LEFT BY USER
054658,000383:                                                                                                  #                VONE'           E:(+10) M:(+9)  VN/SQRT(MU)                             LEFT BY TFF/CONIC
054659,000384:                                                                                                  #                RMAG1           E:(-29) M:(-27) PRESENT RADIUS, M                       LEFT BY TFFCONIC
054660,000385:                                                                                                  #                C(MPAC)         E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH, M        LEFT BY USER
054661,000386: 
054662,000387:                                                                                                  #                THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
054663,000388:                                                                                                  #                TFF/RTMU        E:(17) M:(14)   1/SQRT(MU)                              LEFT BY TFFCONIC.
054664,000389:                                                                                                  #                NRMAG           E:(-29+NR)      M  RMAG, NORMALIZED                     LEFT BY TFFCONIC
054665,000390:                                                                                                  #                                M:(-27+NR)
054666,000391:                                                                                                  #                X1                              -NR, NORM COUNT                         LEFT BY TFFCONIC
054667,000392:                                                                                                  #                TFFNP           E:(-38+2NR)     M  LCP, SEMI LATUS RECTUM, WEIGHT NR    LEFT BY TFFCONIC
054668,000393:                                                                                                  #                                M:(-36+2NR)
054669,000394:                                                                                                  #                TFFALFA         E:(26-NR)       1/M  ALFA, WEIGHT NR                    LEFT BY TFFCONIC
054670,000395:                                                                                                  #                                M:(24-NR)
054671,000396:                                                                                                  #                TFFRTALF        E:(10+NA)       SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
054672,000397:                                                                                                  #                                M:(9+NA)
054673,000398:                                                                                                  #                X2                              -NA, NORMCOUNT                          LEFT BY TFFCONIC
054674,000399:                                                                                                  #                TFF1/ALF        E:(-22-2NA)     SIGNED SEMIMAJ AXIS, WEIGHTED BY NA     LEFT BY TFFCONIC
054675,000400:                                                                                                  #                                M:(-20-2NA)
054676,000401: 
054677,000402:                                                                                                  #  DEBRIS:       QPRET, PDL+0 ... PDL+3
054678,000403:                                                                                                  #                RTERM           E:(-29) M:(-27) RTERM, TERMINAL RADIUS LENGTH
054679,000404:                                                                                                  #                RAPO            E:(-29) M:(-27) PDL 16D (=NRTERM)
054680,000405:                                                                                                  #                RPER            E:(-29) M:(-27) PDL 14D (=TFFQ1)
054681,000406: 

Page 1277

054683,000408: 27,3465           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER IN MPAC
054684,000409: 27,3466           03436                                    TFFSW                                 
054685,000410: 27,3467           57472                                    +3                                    
054686,000411: 27,3470           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
054687,000412: 27,3471           03676                                    TFFSW                                 
054688,000413: 27,3472           00023                 +3        STORE    RTERM                                 #  E:(-29) M:(-27)
054689,000414: 27,3473           77657                           SL*                                            
054690,000415: 27,3474           20201                                    0,1                                   #  X1=-NR
054691,000416: 27,3475           00021                           STORE    NRTERM                                #  RTERM  E:(-29+NR) M:(-27+NR)
054692,000417: 27,3476           44205                           DMP      BDSU                                  
054693,000418: 27,3477           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
054694,000419: 27,3500           06512                                    TFF1/4                                
054695,000420: 27,3501           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
054696,000421: 27,3502           00021                                    NRTERM                                #  E:(-29+NR) M:(-27+NR)
054697,000422: 27,3503           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
054698,000423:                                                                                                  #  E:(-32+NR) M:(-30+NR)
054699,000424: 27,3504           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
054700,000425: 27,3505           20573                                    0          -6,1                       #  X1 = -NR
054701,000426: 27,3506           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
054702,000427:                                                                                                  #  RTERM(2-ALFA RTERM) FROM PDL +2
054703,000428:                                                                                                  #  E:(-32+NR) M:(-30+NR)
054704,000429: 27,3507           77657                           SR*                                            #  LEAVE  E:(-32) M:(-30)
054705,000430: 27,3510           20601                                    0,1                                   #  X1 = -NR
054706,000431: 27,3511           71214                           BOFF     DLOAD                                 #  CHECK TFF /TPER SWITCH
054707,000432: 27,3512           03756                                    TFFSW                                 
054708,000433: 27,3513           57515                                    +2                                    #  IF TFF, CONTINUE
054709,000434: 27,3514           06522                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
054710,000435: 27,3515           75440                 +2        BMN      SQRT                                  #  E:(-16) M:(-15)
054711,000436: 
054712,000437: 27,3516           57650                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
054713,000438:                                                                                                  #  RESET PDL, SET TFF=POSMAX, AND EXIT.
054714,000439: 
054715,000440: 27,3517           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
054716,000441: 27,3520           57753                                    TCDANZIG                              #  ANY PORT IN A STORM.
054717,000442: 27,3521           24045                           STOVL    TFFTEM                                #  Q2  E:(-16) M:(-15)
054718,000443: 27,3522           02170                                    VONE'                                 #  VN/SQRT(MU)  E:(10) M:(9)
054719,000444: 27,3523           52441                           DOT      SL3                                   
054720,000445: 27,3524           02207                                    RONE                                  #  SAVED RN.  E:(-29) M:(-27)
054721,000446: 27,3525           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
054722,000447:                                                                                                  #  E:(-16) M:(-15)
054723,000448: 27,3526           44240                           BMN      BDSU                                  
054724,000449: 27,3527           57550                                    INBOUND                               #  USE ALTERNATE Z
054725,000450: 27,3530           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
054726,000451: 
054727,000452:                                                                                                  #  OUTBOUND Z CALC CONTINUES HERE
054728,000453: 
054729,000454: 27,3531           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E:(-16) M:(-15)
054730,000455: 27,3532           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
054731,000456: 27,3533           44205                           DMP      BDSU                                  

Page 1278

054733,000458: 27,3534           00041                                    NRMAG                                 #  RMAG  E:(-29+NR) M:(-27+NR)
054734,000459:                                                                                                  #  (2-RTERM ALFA)  (-3) FROM PDL+0
054735,000460: 27,3535           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E:(-3) OR (-16)
054736,000461:                                                                                                  #                M:(-3) OR (-15)
054737,000462: 27,3536           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
054738,000463: 27,3537           17757                                    LIM(-22)                              #  =1.0-B(-22)
054739,000464: 27,3540           57561                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
054740,000465: 27,3541           65345                           DLOAD    PDDL                                  #  SET DEN=0 OTHERWISE
054741,000466: 27,3542           06522                                    TFFZEROS                              
054742,000467:                                                                                                  #  XCH ZERO WITH PDL+0
054743,000468: 27,3543           57545                           DLOAD    DCOMP                                 
054744,000469: 27,3544           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
054745,000470: 27,3545           71240                           BMN      DLOAD                                 #  FOR TPER:  Z INDET AT DELE/2=0 AND 90.
054746,000471: 27,3546           57655                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
054747,000472: 
054748,000473:                                                                                                  #  Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
054749,000474: 27,3547           77616        DUMPTFF1           RVQ                                            #  RETURN TFF =0
054750,000475: 
054751,000476:                                                                                                  #  INBOUND Z CALC CONTINUES HERE
054752,000477: 
054753,000478: 27,3550           77745        INBOUND            DLOAD                                          #  RESET PDL+0
054754,000479: 27,3551           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
054755,000480: 27,3552           00023                                    RTERM                                 #  E:(-29) M:(-27)
054756,000481: 27,3553           00015                                    RMAG1                                 #  E:(-29) M:(-27)
054757,000482: 27,3554           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E:(-29) M:(-27)
054758,000483: 27,3555           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
054759,000484: 27,3556           52015                           DAD      GOTO                                  
054760,000485: 27,3557           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
054761,000486: 27,3560           57535                                    SAVEDEN                               #  DEN = Q2+Q1  E:(-16) M:(-15)
054762,000487: 
054763,000488: 27,3561           65215        TFFXTEST           DAD      PDDL                                  #  (ABS(DEN) TO PDL+2))  E:(-3) OR (-16)
054764,000489:                                                                                                  #                        M:(-3) OR (-15)
054765,000490: 27,3562           17761                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
054766,000491: 27,3563           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
054767,000492: 27,3564           53605                           DMP      SR*                                   
054768,000493: 27,3565           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
054769,000494: 27,3566           57201                                    0          -3,2                       #  X2=-NA
054770,000495: 27,3567           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)       E:(-3) OR (-16)
054771,000496:                                                                                                  #                                M:(-3) OR (-15)
054772,000497:                                                                                                  #  ABS(DEN) FROM PDL+2   E:(-3) OR (-16)
054773,000498:                                                                                                  #                        M:(-3) OR (-15)
054774,000499: 27,3570           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
054775,000500: 27,3571           00043                                    TFFX                                  #  NUM  E:(-16) OR (-29)  M:(-15) OR (-27)
054776,000501: 27,3572           57653                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
054777,000502: 
054778,000503:                                                                                                  #  OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
054779,000504: 
054780,000505: 27,3573           45471                           DDV      STADR                                 
054781,000506:                                                                                                  #  DEN FROM PDL+0        E:(-3) OR (-16)
054782,000507:                                                                                                  #                        M:(-3) OR (-15)
054783,000508: 27,3574           77732                           STORE    TFFTEM                                #  Z SAVE FOR SIGN OF SDELF.

Page 1279

054785,000510:                                                                                                  #  E:(-13) M:(-12)
054786,000511: 27,3575           63406                           PUSH     DSQ                                   #  Z TO PDL+0
054787,000512: 27,3576           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E:(-26) M:(-24)
054788,000513: 27,3577           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
054789,000514: 27,3600           75261                           SL       SIGN                                  
054790,000515: 27,3601           20206                                    5                                     
054791,000516: 27,3602           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
054792,000517: 27,3603           14045                           STODL    TFFTEM                                #  P ZSQ  E:(-59+2NR) M:(-55+2NR)
054793,000518:                                                                                                  #  (ARG IS USED IN TFF/TRIG)
054794,000519:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
054795,000520: 27,3604           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
054796,000521: 27,3605           00033                                    TFFALFA                               #  ALFA  E:(26-NR) M:(24-NR)
054797,000522: 27,3606           77657                           SL*                                            
054798,000523: 27,3607           20201                                    0,1                                   #  X1=-NR
054799,000524: 27,3610           00043                           STORE    TFFX                                  #  X
054800,000525: 27,3611           41234                           RTB      DMP                                   
054801,000526: 27,3612           57735                                    T(X)                                  #  POLY
054802,000527:                                                                                                  #  ZSQ FROM PDL+2  E:(-26) M:(-24)
054803,000528: 27,3613           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E:(-29) M:(-27)
054804,000529: 27,3614           00023                                    RTERM                                 #  RTERM  E:(-29) M:(-27)
054805,000530: 27,3615           41215                           DAD      DMP                                   
054806,000531: 27,3616           00015                                    RMAG1                                 #  E:(-29) M:(-27)
054807,000532:                                                                                                  #  Z FROM PDL+0  E:(-13) M:(-12)
054808,000533: 27,3617           51042                           SR3      BPL                                   #  TFF SQRT(MU)  E:(-45) M:(-42)
054809,000534: 27,3620           57641                                    ENDTFF                                #  (NO PUSH UP)
054810,000535: 27,3621           75206                           PUSH     SIGN                                  #  TFF SQRT(MU) TO PDL+0
054811,000536: 27,3622           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
054812,000537: 27,3623           71244                           BPL      DLOAD                                 #  GONE PAST ?
054813,000538: 27,3624           57645                                    NEGTFF                                #  YES. TFF < 0.
054814,000539: 27,3625           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054815,000540: 27,3626           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
054816,000541: 27,3627           57645                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
054817,000542: 
054818,000543:                                                                                                  #  CORRECT FOR ORBITAL PERIOD.
054819,000544: 
054820,000545: 27,3630           77676                           DCOMP                                          #  YES.  CORRECT FOR ORB PERIOD.
054821,000546: 27,3631           56205                           DMP      DDV                                   
054822,000547: 27,3632           17755                                    PI/16                                 #  2 PI (-5)
054823,000548: 27,3633           00031                                    TFFRTALF                              #  SQRT(ALFA)  E:(10+NA) M:(9+NA)
054824,000549: 27,3634           53657                           SL*      SL*                                   
054825,000550: 27,3635           57602                                    0          -4,2                       #  X2=-NA
054826,000551: 27,3636           57602                                    0          -4,2                       
054827,000552: 27,3637           43257                           SL*      DAD                                   
054828,000553: 27,3640           57576                                    0,2                                   
054829,000554:                                                                                                  #  TFF SQRT(MU) FROM PDL+0       E:(-45) M:(-42)
054830,000555: 27,3641           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC          E:(-45) M:(-42)
054831,000556: 27,3642           00037                                    TFF/RTMU                              #  E:(17) M:(14)
054832,000557: 27,3643           57651                                    MAXTFF                                #  SET POSMAX IF OVFL.
054833,000558: 
054834,000559: 27,3644           77616        DUMPTFF2           RVQ                                            #  RETURN TFF (-28) CS IN MPAC.
054835,000560: 

Page 1280

054837,000562: 27,3645           77745        NEGTFF             DLOAD                                          
054838,000563:                                                                                                  #  TFF SQRT(MU) FROM PDL+0, NEGATIVE.
054839,000564: 27,3646           77650                           GOTO                                           
054840,000565: 27,3647           57641                                    ENDTFF                                
054841,000566: 
054842,000567: 27,3650           77745        MAXTFF1            DLOAD                                          #  RESET PDL
054843,000568: 27,3651           43545        MAXTFF             DLOAD    RVQ                                   
054844,000569: 27,3652           17771                                    NEARONE                               
054845,000570: 
054846,000571:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
054847,000572: 
054848,000573:                                                                                                  #  NUM FROM TFFX.        E:(-16) OR (-29)
054849,000574:                                                                                                  #                        M:(-15) OR (-27)
054850,000575: 27,3653           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
054851,000576: 27,3654           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
054852,000577:                                                                                                  #  DEN FROM PDL+0  E:(-3)/( 16) M:(-3)/(-15)
054853,000578:                                                                                                  #  N/D TO PDL+0  E:(11) M:(10)
054854,000579: 27,3655           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
054855,000580: 27,3656           00045                                    TFFTEM                                #  Q2  E:(-16) M:(-15)
054856,000581: 27,3657           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
054857,000582: 27,3660           14013                           STODL    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
054858,000583:                                                                                                  #  D/N FROM PDL+0
054859,000584: 27,3661           77626                           STADR                                          
054860,000585: 27,3662           77732                           STORE    TFFTEM                                #  D/N  E:(11) M:(10)
054861,000586: 27,3663           53605                           DMP      SL*                                   
054862,000587: 27,3664           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054863,000588: 27,3665           57576                                    0,2                                   #  1/ALFA Z  E:(-11-NA) M:(-10-NA)
054864,000589: 27,3666           41206                           PUSH     DMP                                   #  TO PDL+0
054865,000590: 27,3667           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
054866,000591: 27,3670           41057                           SL*      BOVB                                  
054867,000592: 27,3671           57576                                    0,2                                   #  X2= -NA
054868,000593: 27,3672           21712                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
054869,000594: 27,3673           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
054870,000595: 27,3674           41234                           RTB      DMP                                   
054871,000596: 27,3675           57735                                    T(X)                                  #  POLY
054872,000597: 27,3676           00043                                    TFFX                                  
054873,000598: 27,3677           45242                           SR3      DSU                                   
054874,000599: 27,3700           17763                                    DP2(-3)                               
054875,000600: 27,3701           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA   E:(-15-NA)
054876,000601:                                                                                                  #                        M:(-14-NA)
054877,000602:                                                                                                  #  1/ALFA Z FROM PDL+0   E:(-11-NA)
054878,000603:                                                                                                  #                        M:(-10-NA)
054879,000604: 27,3702           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
054880,000605: 27,3703           00045                                    TFFTEM                                #  1/Z  E:(11) M:(10)
054881,000606: 27,3704           00015                                    RMAG1                                 #  E:(-29) M:(-27)
054882,000607: 27,3705           43312                           SL2      DAD                                   
054883,000608: 27,3706           00017                                    TFFQ1                                 #  Q1  E:(-16) M:(-15)
054884,000609: 27,3707           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z) =SGN OF SDELF  E:(-16) M:(-15
054885,000610: 27,3710           00035                                    TFFNP                                 #  LC P  E:(-38+2NR) M:(-36+2NR)
054886,000611: 27,3711           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1281

054888,000613: 27,3712           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054889,000614: 27,3713           57575                                    1,2                                   #  X2=-NA
054890,000615: 27,3714           53765                           SIGN     SL*                                   
054891,000616: 27,3715           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
054892,000617: 27,3716           57576                                    0,2                                   
054893,000618: 27,3717           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR) M:(-55+2NR)
054894,000619:                                                                                                  #  (ARG FOR USE IN TFF/TRIG)
054895,000620: 27,3720           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054896,000621: 27,3721           41366                           SQRT     DMP                                   
054897,000622: 27,3722           17755                                    PI/16                                 #  PI (-4)
054898,000623: 27,3723           77615                           DAD                                            
054899,000624:                                                                                                  #  2(XT(X)-1)/Z ALFA FROM PDL    E:(-15-NA)
054900,000625:                                                                                                  #                                M:(-14-NA)
054901,000626: 27,3724           45257                           SL*      DSU                                   
054902,000627: 27,3725           57577                                    0          -1,2                       
054903,000628: 27,3726           00013                                    TFFDELQ                               #  Q2-Q1  E:(-16) M:(-15)
054904,000629: 27,3727           53605                           DMP      SL*                                   
054905,000630: 27,3730           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA) M:(-20-2NA)
054906,000631: 27,3731           57601                                    0          -3,2                       
054907,000632: 27,3732           52057                           SL*      GOTO                                  
054908,000633: 27,3733           57602                                    0          -4,2                       
054909,000634: 27,3734           57641                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
054910,000635: 

Page 1282

054912,000637:                                                                                                  #  PROGRAM NAME:  T(X)                           DATE:  01.17.67
054913,000638:                                                                                                  #  MOD NO:  0                                    LOG SECTION:  TIME OF FREE FALL
054914,000639:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
054915,000640: 
054916,000641:                                                                                                  #  FUNCTIONAL DESCRIPTION:  THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES CALCTFF AND
054917,000642:                                                                                                  #        CALCTPER TO APPROXIMATE THE SERIES
054918,000643:                                                                                                  #                           2     3
054919,000644:                                                                                                  #                1/3 -X/5 +X /7 -X /9 ...
054920,000645: 
054921,000646:                                                                                                  #        WHERE   X = ALFA Z Z            IF ALFA Z Z LEQ 1
054922,000647:                                                                                                  #                X = 1/(ALFA Z Z)        IF ALFA Z Z G 1
054923,000648: 
054924,000649:                                                                                                  #        ALSO    X IS NEG FOR HYPERBOLIC ORBITS
054925,000650:                                                                                                  #                X = 0 FOR PARABOLIC ORBITS
054926,000651:                                                                                                  #                X IS POSITIVE FOR ELLIPTIC ORBITS
054927,000652: 
054928,000653:                                                                                                  #        FOR FLIGHT 278, THE POLYNOMIAL T(X) IS FITTED OVER THE RANGE (0,+1) AND HAS A MAXIMUM
054929,000654:                                                                                                  #        DEVIATION FROM THE SERIES OF 2 E-5   (T(X) IS A CHEBYCHEV TYPE FIT AND WAS OBTAINED USING
054930,000655:                                                                                                  #        MAC PROGRAM AUTCURFIT294RRB AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE (-.08,+1).)
054931,000656: 
054932,000657:                                                                                                  #  CALLING SEQUENCE:     RTB
054933,000658:                                                                                                  #                                T(X)
054934,000659:                                                                                                  #        C(MPAC) = X
054935,000660: 
054936,000661:                                                                                                  #  SUBROUTINES CALLED:  NONE
054937,000662: 
054938,000663:                                                                                                  #  NORMAL EXIT MODE:  TC   DANZIG
054939,000664: 
054940,000665:                                                                                                  #  ALARMS:  NONE
054941,000666: 
054942,000667:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
054943,000668: 
054944,000669:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
054945,000670:                                                                                                  #        C(MPAC) = X
054946,000671: 
054947,000672:                                                                                                  #  DEBRIS:  NONE
054948,000673: 
054949,000674: 27,3735           07222        T(X)               TC       POLY                                  
054950,000675: 27,3736           00004                           DEC      4          B-14                       #  N-1
054951,000676: 27,3737           12525 12525                     2DEC     3.333333333 E-1                        
054952,000677: 
054953,000678: 27,3741           71463 57703                     2DEC*    -1.999819135 E-1*                       
054954,000679: 
054955,000680: 27,3743           04423 17645                     2DEC*    1.418148467 E-1*                       
054956,000681: 
054957,000682: 27,3745           74604 43667                     2DEC*    -1.01310997 E-1*                       
054958,000683: 
054959,000684: 27,3747           01626 37256                     2DEC*    5.609004986 E-2*                       
054960,000685: 
054961,000686: 27,3751           77404 52071                     2DEC*    -1.536156925 E-2*                       
054962,000687: 
054963,000688: 27,3753           06061        ENDT(X)            TC       DANZIG                                
054964,000689: 
054965,000690: 27,3754  27,3753               TCDANZIG           =        ENDT(X)                               
054966,000691: 

Page 1283

054968,000693:                                                                                                  #  TFF CONSTANTS
054969,000694: 
054970,000695: 32,3773                                           BANK     32                                    
054971,000696: 
054972,000697: 27,2000                                           SETLOC   TOF-FF1                               
054973,000698: 27,2000                                           BANK                                           
054974,000699: 
054975,000700:                                                                                                  #                                                NOTE _  NOTE _  ADJUSTED MUE FOR NEAR EARTH TRAJ.
054976,000701:                                                                                                  # MUE            =       3.990815471 E10         M CUBE/CS SQ
054977,000702:                                                                                                  # RTMUE          =       1.997702549 E5 B-18*    MODIFIED EARTH MU
054978,000703: 
054979,000704:                                                                                                  #                                                NOTE _  NOTE _  ADJUSTED MUE FOR NEAR EARTH TRAJ.
054980,000705:                                                                                                  # MUM            =       4.902778 E8             M CUBE/CS SQ
054981,000706:                                                                                                  # RTMUM          2DEC*   2.21422176 E4 B-18*
054982,000707: 
054983,000708: 27,3754           06220 37553  PI/16              2DEC     3.141592653 B-4                        
054984,000709: 
054985,000710: 27,3756           37777 37700  LIM(-22)           2OCT     3777737700                            #  1.0 -B(-22)
054986,000711: 
054987,000712: 27,3760           00000 00100  DP(-22)            2OCT     0000000100                            #  B(-22)
054988,000713: 
054989,000714: 27,3762           04000 00000  DP2(-3)            2DEC     1          B-3                        
054990,000715: 
054991,000716: 27,3764           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
054992,000717: 
054993,000718:                                                                                                  #  RPAD1         2DEC    6373338 B-29            M (-29) = 20909901.57 FT
054994,000719: 
054995,000720: 27,3766  23,2314               RPAD1              =        RPAD                                  
054996,000721: 
054997,000722: 27,3766           00305 11205  R300K              2DEC     6464778    B-29                       #  (-29) M
054998,000723: 
054999,000724: 27,3770           37777 37777  NEARONE            2DEC     .999999999                            
055000,000725: 
055001,000726: 27,3772  23,2521               TFFZEROS           EQUALS   HI6ZEROS                              
055002,000727: 27,3772  23,2511               TFF1/4             EQUALS   HIDP1/4                               
055003,000728: 

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