Source Code

These source-code files were transcribed from a printout in Don Eyles's personal collection, scanned by archive.org, and financially sponsored by Linden Sims. A team of volunteers performed the transcription and proof-reading. The scanned page images are available at the Virtual AGC Project website, as well as higher-quality (but much larger) images at the Virtual AGC Project's collection in the Internet Archive. Report any problems by creating "issues" at the Virtual AGC Project's GitHub Repository.

Notations on the program listing read, in part:

	GAP:  ASSEMBLE REVISION 56 OF AGC PROGRAM ZERLINA BY ZOROASTER
	9:12 OCT. 21,1970
Note that the date is the date of the printout, not the date of the program revision.

054953,000002:                                                                                                  ## Copyright:   Public domain.
054954,000003:                                                                                                  ## Filename:    TIME_OF_FREE_FALL.agc
054955,000004:                                                                                                  ## Purpose:     A log section of Zerlina 56, the final revision of
054956,000005:                                                                                                  ##              Don Eyles's offline development program for the variable 
054957,000006:                                                                                                  ##              guidance period servicer. It also includes a new P66 with LPD 
054958,000007:                                                                                                  ##              (Landing Point Designator) capability, based on an idea of John 
054959,000008:                                                                                                  ##              Young's. Neither of these advanced features were actually flown,
054960,000009:                                                                                                  ##              but Zerlina was also the birthplace of other big improvements to
054961,000010:                                                                                                  ##              Luminary including the terrain model and new (Luminary 1E)
054962,000011:                                                                                                  ##              analog display programs. Zerlina was branched off of Luminary 145,
054963,000012:                                                                                                  ##              and revision 56 includes all changes up to and including Luminary
054964,000013:                                                                                                  ##              183. It is therefore quite close to the Apollo 14 program,
054965,000014:                                                                                                  ##              Luminary 178, where not modified with new features.
054966,000015:                                                                                                  ## Reference:   pp. 1257-1272
054967,000016:                                                                                                  ## Assembler:   yaYUL
054968,000017:                                                                                                  ## Contact:     Ron Burkey <info@sandroid.org>.
054969,000018:                                                                                                  ## Website:     www.ibiblio.org/apollo/index.html
054970,000019:                                                                                                  ## Mod history: 2017-07-28 MAS  Created from Luminary 210.
054971,000020:                                                                                                  ##              2017-08-29 RSB  Transcribed.
054972,000021: 

Page 1257

054974,000023:                                                                                                  #           THE TFF SUBROUTINES MAY BE USED IN EITHER EARTH OR MOON CENTERED COORDINATES. THE TFF ROUTINES NEVER
054975,000024:                                                                                                  #  KNOW WHICH ORIGIN APPLIES. IT IS THE USER WHO KNOWS, AND WHO SUPPLIES  RONE, VONE AND 1/SQRT(MU)  AT THE
054976,000025:                                                                                                  #  APPROPRIATE SCALE LEVEL FOR THE PROPER PRIMARY BODY.
054977,000026: 
054978,000027:                                                                                                  #           EARTH ORIGIN           POSITION      -29       METERS
054979,000028:                                                                                                  #                                  VELOCITY      -7        METERS/CENTISECOND
054980,000029:                                                                                                  #                                  1/SQRT(MU)    +17       SQRT(CS SQ/METERS CUBED)
054981,000030: 
054982,000031:                                                                                                  #           MOON ORIGIN            POSITION      -27       METERS
054983,000032:                                                                                                  #                                  VELOCITY      -5        METERS/CENTISECONDS
054984,000033:                                                                                                  #                                  1/SQRT(MU)    +14       SQRT(CS SQ/METERS CUBED)
054985,000034: 
054986,000035:                                                                                                  #  ALL DATA PROVIDED TO AND RECEIVED FROM ANY TFF SUBROUTINE WILL BE AT ONE OF THE LEVELS ABOVE. IN ALL CASES,
054987,000036:                                                                                                  #  THE FREE FALL TIME IS RETURNED IN CENTISECONDS AT (-28). PROGRAM  TFF/CONIC  WILL GENERATE VONE/RTMU  AND
054988,000037:                                                                                                  #  LEAVE IT IN  VONE' AT (+10) IF EARTH ORIGIN AND (+9) IF MOON ORIGIN.
054989,000038:                                                                                                  #           THE USER MUST STORE THE STATE VECTOR IN  RONE, VONE  AND MU IN  THE FORM 1/SQRT(MU) IN  TFF/RTMU
054990,000039:                                                                                                  #  AT THE PROPER SCALE BEFORE CALLING  TFF/CONIC. SINCE  RONE, VONE  ARE IN THE EXTENDED VERB STORAGE AREA,
054991,000040:                                                                                                  #  THE USER MUST ALSO LOCK OUT THE EXTENDED VERBS, AND RELEASE THEM WHEN FINISHED.
054992,000041:                                                                                                  #           PROGRAMS     CALC/TFF  AND  CALC/TPER  ASSUME THAT THE TERMINAL RADIUS IS LESS THAN THE PRESENT
054993,000042:                                                                                                  #  RADIUS. THIS RESTRICTION CAN BE REMOVED BY A  15 W CODING CHANGE, BUT AT PRESENT IT IS NOT DEEMED NECESSARY.
054994,000043: 
054995,000044:                                                                                                  #           THE FOLLOWING ERASABLE QUANTITIES ARE USED BY THE TFF ROUTINES, AND ARE LOCATED IN THE PUSH LIST.
054996,000045: 
054997,000046:                                                                                                  #  BELOW      E:   IS USED FOR EARTH ORIGIN SCALE
054998,000047:                                                                                                  #             M:   IS USED FOR MOON  ORIGIN SCALE
054999,000048: 
055000,000049:                                                                                                  # TFFSW          =       119D       BIT1      0 = CALCTFF        1 = CALCTPER
055001,000050: 10,2213                        TFFDELQ            =        10D                                   #             Q2-Q1              E: (-16)  M: (-15)
055002,000051: 10,2213                        RMAG1              =        12D                                   #             ABVAL(RN)  M       E: (-29)  M: (-27)
055003,000052:                                                                                                  # RPER           =       14D                  PERIGEE RADIUS M   E: (-29)  M: (-27)
055004,000053: 10,2213                        TFFQ1              =        14D                                   #             R.V / SQRT(MUE)    E: (-16)  M: (-15)
055005,000054:                                                                                                  # SDELF/2                                     SIN(THETA) /2
055006,000055: 10,2213                        CDELF/2            =        14D                                   #             COS(THETA) /2
055007,000056:                                                                                                  # RAPO           =       16D                  APOGEE RADIUS  M   E: (-29)  M: (-27)
055008,000057: 10,2213                        NRTERM             =        16D                                   #             TERMINAL RADIUS M  E: (-29+NR)
055009,000058:                                                                                                  #                                M: (-27+NR)
055010,000059: 10,2213                        RTERM              =        18D                                   #             TERMINAL RADIUS M  E: (-29)  M: (-27)
055011,000060: 10,2213                        TFFVSQ             =        20D                                   #             -(V SQUARED/MU)  1/M  E: (20)  M: (18)
055012,000061: 10,2213                        TFF1/ALF           =        22D                                   #             SEMI MAJ AXIS  M  E: (-22-2 NA)
055013,000062:                                                                                                  #                               M: (-20-2 NA)
055014,000063: 10,2213                        TFFRTALF           =        24D                                   #             SQRT(ALFA)  E: (10+NA)  M: (9+NA)
055015,000064: 10,2213                        TFFALFA            =        26D                                   #             ALFA  1/M   E: (26-NR)  M: (24-NR)
055016,000065: 10,2213                        TFFNP              =        28D                                   #             SEMI LATUS RECTUM  M  E: (-38+2 NR)
055017,000066:                                                                                                  #                                   M: (-36+2 NR)
055018,000067: 10,2213                        TFF/RTMU           =        30D                                   #             1/SQRT(MU)         E: (17)   M: (14)
055019,000068: 10,2213                        NRMAG              =        32D                                   #             PRESENT RADIUS  M  E: (-29+NR)
055020,000069:                                                                                                  #                                M: (-27+NR)
055021,000070: 10,2213                        TFFX               =        34D                                   
055022,000071: 10,2213                        TFFTEM             =        36D                                   #             TEMPORARY
055023,000072: 

Page 1258

055025,000074:                                                                                                  #                                           REGISTERS S1, S2 ARE UNTOUCHED BY ANY TFF SUBROUTINE
055026,000075:                                                                                                  #                                           INDEX REGISTERS X1, X2 ARE USED BY ALL TFF SUBROUTINES. THEY ARE ESTAB-
055027,000076:                                                                                                  #                                           LISHED IN TFF/CONIC AND MUST BE PRESERVED BETWEEN CALLS TO SUBSEQUENT
055028,000077:                                                                                                  #                                           SUBROUTINES.
055029,000078:                                                                                                  #                                           -NR                             C(X1) = NORM COUNT OF RMAG
055030,000079:                                                                                                  #                                           -NA                             C(X2)= NORM COUNT OF SQRT(ABS(ALFA))
055031,000080: 

Page 1259

055033,000082: 
055034,000083: 
055035,000084:                                                                                                  #  SUBROUTINE NAME:     TFFCONIC                                           DATE:    01.29.67
055036,000085:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
055037,000086:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
055038,000087:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  11 APR 67
055039,000088:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  21 NOV 67     ADD MOON MU.
055040,000089:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
055041,000090:                                                                                                  #  FUNCTIONAL DESCRIPTION:      THIS SUBROUTINE IS CALLED TO COMPUTE THOSE CONIC PARAMETERS REQUIRED BY THE TFF
055042,000091:                                                                                                  #           SUBROUTINES AND TO ESTABLISH THEM IN THE PUSH LIST AREA. THE PARAMETERS ARE LISTED UNDER OUTPUT.
055043,000092:                                                                                                  #           THE EQUATIONS ARE
055044,000093:                                                                                                  #                  -   -  -
055045,000094:                                                                                                  #                  H = RN*VN                                               ANGULAR MOMENTUM
055046,000095:                                                                                                  #                        - -
055047,000096:                                                                                                  #                  LCP = H.H / MU                                          SEMI LATUS RECTUM
055048,000097:                                                                                                  #                                -  -
055049,000098:                                                                                                  #                  ALFA = 2/RN - VN.VN / MU                                RECIPROCAL SEMI MAJ AXIS, SIGNED
055050,000099: 
055051,000100:                                                                                                  #           AND ALFA IS POS FOR ELLIPTIC  ORBITS
055052,000101:                                                                                                  #                        0  FOR PARABOLIC ORBITS
055053,000102:                                                                                                  #                       NEG FOR HYPERBOLIC ORBITS.
055054,000103:                                                                                                  #           SUBROUTINE ALSO COMPUTES AND SAVES  RMAG.
055055,000104:                                                                                                  #  CALLING SEQUENCE:
055056,000105:                                                                                                  #           TFFCONIC  EXPECTS CALLER TO ENTER WITH CORRECT GRAVITATIONAL CONSTANT IN MPAC, IN THE FORM
055057,000106:                                                                                                  #           1/SQRT(MU). PROGRAM WILL SAVE IN  TFF/RTMU  . THE SCALE IS DETERMINED BY WHETHER EARTH OR MOON
055058,000107:                                                                                                  #           ORIGIN IS USED.  THE CALLER MUST LOCK OUT THE EXTENDED VERBS BEFORE PROVIDING STATE VECTOR IN RONE,
055059,000108:                                                                                                  #           VONE  AT PROPER SCALE. THE EXTENDED VERBS MUST BE RESTORED WHEN THE CALLER IS FINISHED USING THE
055060,000109:                                                                                                  #           TFF ROUTINES.
055061,000110:                                                                                                  #           ENTRY POINT  TFFCONMU  EXPECTS THAT  TFF/RTMU  IS ALREADY LOADED.
055062,000111:                                                                                                  #           TO SPECIFY MU:      DLOAD  CALL                IF MU ALREADY STORED:    CALL
055063,000112:                                                                                                  #                                      YOURMU       1/RTMU   E: (17)  M: (14)              TFFCONMU
055064,000113:                                                                                                  #                                      TFFCONIC
055065,000114:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 18D
055066,000115: 
055067,000116:                                                                                                  #  SUBROUTINES CALLED:  NONE
055068,000117:                                                                                                  #  NORMAL EXIT MODES:   RVQ
055069,000118:                                                                                                  #  ALARMS:  NONE
055070,000119:                                                                                                  #  OUTPUT:  THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
055071,000120:                                                                                                  #           RMAG1  E:(-29) M:(-27) M  RN, PRESENT RADIUS LENGTH.
055072,000121:                                                                                                  #           NRMAG  E: (-29+NR)     M  RMAG, NORMALIZED
055073,000122:                                                                                                  #                  M: (-27+NR)
055074,000123:                                                                                                  #           X1                     -NR, NORM COUNT
055075,000124:                                                                                                  #           TFFNP  E: (-38+2NR)    M  LCP, SEMI LATUS RECTUM, WEIGHTED BY NR.       FOR VGAMCALC
055076,000125:                                                                                                  #                  M: (-36+2NR)
055077,000126:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)       1/SQRT(MU)
055078,000127:                                                                                                  #           TFFVSQ E:(20)  M:(18)  1/M   -(V SQ/MU): PRESENT VELOCITY,NORMLIZED.    FOR VGAMCALC
055079,000128:                                                                                                  #           TFFALFA  E: (26-NR)    1/M   ALFA, WEIGHTED BY NR
055080,000129:                                                                                                  #                    M: (24-NR)
055081,000130:                                                                                                  #           TFFRTALF  E: (10+NA)   SQRT(ALFA), NORMALIZED
055082,000131:                                                                                                  #                     M: (9+NA)

Page 1260

055084,000133:                                                                                                  #           X2                     -NA, NORM COUNT
055085,000134:                                                                                                  #           TFF1/ALF  E: (-22-2NA) SIGNED SEMI MAJ AXIS, WEIGHTED BY NA
055086,000135:                                                                                                  #                     M: (-20-2NA)
055087,000136:                                                                                                  #           PUSHLOC AT PDL+0
055088,000137:                                                                                                  #           THE FOLLOWING  IS STORED IN GENERAL ERASABLE
055089,000138:                                                                                                  #           VONE'  E:(10)  M:(9)   V/RT(MU), NORMALIZED VELOCITY
055090,000139:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
055091,000140:                                                                                                  #           RONE   E:(-29)  M:(-27)  M      STATE VECTOR                   LEFT BY CALLER
055092,000141:                                                                                                  #           VONE   E:(-7)   M:(-5)   M/CS   STATE VECTOR                   LEFT BY CALLER
055093,000142:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)      1/RT(CS SQ/M CUBE)               IF ENTER VIA  TFFCONMU.
055094,000143:                                                                                                  #  DEBRIS:  QPRET,    PDL+0 ... PDL+3
055095,000144: 
055096,000145: 
055097,000146: 33,3766                                           BANK     33                                    
055098,000147: 27,2000                                           SETLOC   TOF-FF                                
055099,000148: 27,2000                                           BANK                                           
055100,000149: 
055101,000150: 27,3342                                           COUNT*   $$/TFF                                
055102,000151: 
055103,000152: 27,3342           00037        TFFCONIC           STORE    TFF/RTMU                              #  1/SQRT(MU)       E: (17)   M: (14)
055104,000153: 
055105,000154: 27,3343           53575        TFFCONMU           VLOAD    UNIT                                  #  COME HERE WITH TFFRTMU LOADED.
055106,000155: 27,3344           02200                                    RONE                                  #  SAVED RN.  M     E: (-29)  M: (-27)
055107,000156: 27,3345           77725                           PDDL                                           #  UR/2 TO PDL+0, +5
055108,000157: 27,3346           00045                                    36D                                   #  MAGNITUDE
055109,000158: 27,3347           00015                           STORE    RMAG1                                 #  M    E: (-29)   M: (-27)
055110,000159: 
055111,000160: 27,3350           77701                           NORM                                           
055112,000161: 27,3351           00047                                    X1                                    #  -NR
055113,000162: 27,3352           24041                           STOVL    NRMAG                                 #  RMAG  M   E: (-29+NR)  M: (-27+NR)
055114,000163: 27,3353           02206                                    VONE                                  #  SAVED VN.  M/CS   E: (-7)   M: (-5)
055115,000164: 27,3354           77761                           VXSC                                           
055116,000165: 27,3355           00037                                    TFF/RTMU                              #  E: (17)   M: (14)
055117,000166: 27,3356           02161                           STORE    VONE'                                 #  VN/SQRT(MU)   E: (10)   M: (9)
055118,000167: 
055119,000168: 27,3357           47361                           VXSC     VXV                                   
055120,000169: 27,3360           00041                                    NRMAG                                 #  E: (-29+NR)  M: (-27+NR)
055121,000170:                                                                                                  #  UR/2 FROM PDL
055122,000171: 27,3361           47572                           VSL1     VSQ                                   #  BEFORE:  E:(-19+NR)  M:(-18+NR)
055123,000172: 27,3362           14035                           STODL    TFFNP                                 #  LC P  M   E:(-38+2NR)  M:(-36+2NR)
055124,000173:                                                                                                  #  SAVE ALSO FOR VGAMCALC
055125,000174: 27,3363           06510                                    TFF1/4                                
055126,000175: 27,3364           63271                           DDV      PDVL                                  #  (2/RMAG)  1/M   E:(26-NR)   M:(24-NR)
055127,000176: 27,3365           00041                                    NRMAG                                 #  RMAG  M   E:(-29+NR)  M:(-27+NR)
055128,000177: 27,3366           02161                                    VONE'                                 #  SAVED VN.   E: (10)   M: (9)
055129,000178: 27,3367           57436                           VSQ      DCOMP                                 #  KEEP MPAC+2 HONEST FOR SQRT.
055130,000179: 27,3370           00025                           STORE    TFFVSQ                                #  -(V SQ/MU)   E:(20)   M:(18)
055131,000180:                                                                                                  #  SAVE FOR VGAMCALC
055132,000181: 27,3371           43257                           SR*      DAD                                   

Page 1261

055134,000183: 27,3372           20573                                    0          -6,1                       #  GET -VSQ/MU   E:(26-NR)   M:(24-NR)
055135,000184: 27,3373           77626                           STADR                                          
055136,000185:                                                                                                  #  2/RMAG   FROM PDL+2
055137,000186: 27,3374           77744                           STORE    TFFALFA                               #  ALFA  1/M   E:(26-NR)   M:(24-NR)
055138,000187: 27,3375           41457                           SL*      PUSH                                  #  TEMP SAVE ALFA    E:(20)   M:(18)
055139,000188: 27,3376           20173                                    0          -6,1                       
055140,000189: 27,3377           75446                           ABS      SQRT                                  #  E:(10)   M:(9)
055141,000190: 27,3400           77701                           NORM                                           
055142,000191: 27,3401           00050                                    X2                                    #  X2 = -NA
055143,000192: 27,3402           00031                           STORE    TFFRTALF                              #  SQRT( ABS(ALFA) )  E:(10+NA)   M:(9+NA)
055144,000193: 27,3403           75316                           DSQ      SIGN                                  #  NOT SO ACCURATE, BUT OK
055145,000194:                                                                                                  #  ALFA FROM PDL+2   E:(20)   M:(18)
055146,000195: 27,3404           55254                           BZE      BDDV                                  #  SET 1/ALFA =0, TO SHOW SMALL ALFA
055147,000196: 27,3405           57407                                    +2                                    
055148,000197: 27,3406           06510                                    TFF1/4                                
055149,000198: 27,3407           00027                 +2        STORE    TFF1/ALF                              #  1/ALFA   E:(-22-2 NA)   M:(-20-2 NA)
055150,000199: 27,3410           77616        DUMPCNIC           RVQ                                            
055151,000200: 
055152,000201:                                                                                                  #                          39 W
055153,000202: 

Page 1262

055155,000204:                                                                                                  #  SUBROUTINE NAME:     TFFRP/RA                                           DATE:  01.17.67
055156,000205:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
055157,000206:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
055158,000207:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  11 APR 67
055159,000208:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
055160,000209:                                                                                                  #                                                                          ALSO IMPROVE ACCURACY OF RAPO.
055161,000210:                                                                                                  #  FUNCTIONAL DESCRIPTION:         USED BY CALCTPER AND TFF DISPLAYS TO CALCULATE PERIGEE RADIUS AND ALSO
055162,000211:                                                                                                  #           APOGEE RADIUS FOR A GENERAL CONIC.
055163,000212:                                                                                                  #           PROGRAM GIVES PERIGEE RADIUS AS               APOGEE RADIUS IS GIVEN BY
055164,000213:                                                                                                  #                  RP = P /(1+E)                                 RA = (1+E) / ALFA
055165,000214:                                                                                                  #           WHERE   2
055166,000215:                                                                                                  #                  E  = 1 - P ALFA
055167,000216:                                                                                                  #           IF RA IS NEGATIVE OR SHOWS DIVIDE OVERFLOW, THEN RA = POSMAX BECAUSE
055168,000217:                                                                                                  #                  1. APOGEE RADIUS IS NOT MEANINGFUL FOR HYPERBOLA
055169,000218:                                                                                                  #                  2. APOGEE RADIUS IS NOT DEFINED FOR PARABOLA
055170,000219:                                                                                                  #                  3. APOGEE RADIUS EXCEEDS THE SCALING FOR ELLIPSE.
055171,000220:                                                                                                  #           THIS SUBROUTINE REQUIRES THE SIGNED  RECIPROCAL SEMI MAJ AXIS,  ALFA,  AND SEMI LATUS RECTUM AS DATA.
055172,000221:                                                                                                  #  CALLING SEQUENCE:  CALL
055173,000222:                                                                                                  #                            TFFRP/RA
055174,000223:                                                                                                  #           PUSHLOC = PDL+0, ARBITRARY IF LEQ 10D
055175,000224:                                                                                                  #           C(MPAC) UNSPECIFIED
055176,000225: 
055177,000226:                                                                                                  #  SUBROUTINES CALLED:  NONE
055178,000227:                                                                                                  #  NORMAL EXIT MODE:    RVQ
055179,000228:                                                                                                  #           IF ELLIPSE, WITHIN NORMAL SCALING, RAPO IS CORRECT.
055180,000229:                                                                                                  #           OTHERWISE, RAPO = POSMAX.
055181,000230:                                                                                                  #  ALARMS:  NONE
055182,000231:                                                                                                  #  OUTPUT:  STORED IN PUSH LIST AREA. SCALE OF OUTPUT AGREES WITH DATA SUPPLIED TO  TFF/CONIC.
055183,000232:                                                                                                  #           RPER   E:(-29)  M:(-27)  M     PERIGEE RADIUS                  DESTROYED BY CALCTFF/CALCTPER, TFFTRIG.
055184,000233:                                                                                                  #           RAPO   E:(-29)  M:(-27)  M     APOGEE  RADIUS                  WILL BE DESTROYED BY CALCTFF/CALCTPER
055185,000234:                                                                                                  #           PUSHLOC AT PDL+0
055186,000235:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
055187,000236:                                                                                                  #           TFFALFA E:(26-NR)      M   1/SEMI MAJ AXIS                     LEFT BY TFFCONIC
055188,000237:                                                                                                  #                   M:(24-NR)
055189,000238:                                                                                                  #           TFFNP  E: (-38+2NR)    M  LC P, SEMI LATUS RECTUM              LEFT BY TFFCONIC
055190,000239:                                                                                                  #                  M: (-36+2NR)
055191,000240:                                                                                                  #           X1                     -NR, NORM COUNT OF RMAG                 LEFT BY TFFCONIC
055192,000241:                                                                                                  #           X2                     -NA, NORM COUNT OF ALFA                 LEFT BY TFFCONIC
055193,000242:                                                                                                  #  DEBRIS:  QPRET,    PDL+0 ... PDL+1
055194,000243: 

Page 1263

055196,000245: 27,3411                        RAPO               =        16D                                   #  APOGEE RADIUS  M  E:(-29)  M:(-27)
055197,000246: 27,3411                        RPER               =        14D                                   #  PERIGEE RADIUS  M  E:(-29)  M:(-27)
055198,000247: 
055199,000248: 27,3411           41345        TFFRP/RA           DLOAD    DMP                                   
055200,000249: 27,3412           00033                                    TFFALFA                               #  ALFA  1/M  E:(26-NR)   M:(24-NR)
055201,000250: 27,3413           00035                                    TFFNP                                 #  LC P  M   E:(-38+2NR)   M:(-36+2NR)
055202,000251: 27,3414           57457                           SR*      DCOMP                                 #  ALFA P (-12+NR)
055203,000252: 27,3415           20571                                    0          -8D,1                      #  ALFA P  (-4)
055204,000253: 27,3416           51415                           DAD      ABS                                   #  (DCOMP GIVES VALID TP RESULT FOR SQRT)
055205,000254:                                                                                                  #  (ABS PROTECTS SQRT IF E IS VERY NEAR 0)
055206,000255: 27,3417           17747                                    DP2(-4)                               
055207,000256: 27,3420           43366                           SQRT     DAD                                   #  E SQ = (1- P ALFA)   (-4)
055208,000257: 27,3421           06510                                    TFF1/4                                
055209,000258: 27,3422           55206                           PUSH     BDDV                                  #  (1+E)  (-2)  TO PDL+0
055210,000259: 27,3423           00035                                    TFFNP                                 #  LCP  M E:(-38+2NR)   M:(-36+2NR)
055211,000260: 27,3424           53657                           SR*      SR*                                   #  (DOES SR THEN SL TO AVOID OVFL)
055212,000261: 27,3425           20601                                    0,1                                   #  X1=-NR
055213,000262: 27,3426           20572                                    0          -7,1                       #  (EFFECTIVE SL)
055214,000263: 27,3427           14017                           STODL    RPER                                  #  PERIGEE RADIUS  M   E:(-29)   M:(-27)
055215,000264:                                                                                                  #  (1+E)  (-2)   FROM PDL+0
055216,000265: 27,3430           41005                           DMP      BOVB                                  
055217,000266: 27,3431           00027                                    TFF1/ALF                              #  E:(-22-2NA)  M:(-20-2NA)
055218,000267: 27,3432           57735                                    TCDANZIG                              #  CLEAR OVFIND, IF ON.
055219,000268: 27,3433           53654                           BZE      SL*                                   
055220,000269: 27,3434           57443                                    MAXRA                                 #  SET POSMAX, IF ALFA=0
055221,000270: 27,3435           57603                                    0          -5,2                       #  -5+NA
055222,000271: 27,3436           40057                           SL*      BOV                                   
055223,000272: 27,3437           57576                                    0,2                                   
055224,000273: 27,3440           57443                                    MAXRA                                 #  SET POSMAX IF OVFL.
055225,000274: 27,3441           77644                           BPL                                            #  CONTINUE WITH VALID RAPO.
055226,000275: 27,3442           57445                                    +3                                    
055227,000276: 27,3443           77745        MAXRA              DLOAD                                          #  RAPO CALC IS NOT VALID. SET RAPO =
055228,000277: 27,3444           17753                                    NEARONE                               #  POSMAX AS A TAG.
055229,000278: 27,3445           00021                 +3        STORE    RAPO                                  #  APOGEE RADIUS  M   E:(-29)   M:(-27)
055230,000279: 27,3446           77616        DUMPRPRA           RVQ                                            
055231,000280: 
055232,000281:                                                                                                  #                          30 W
055233,000282: 

Page 1264

055235,000284:                                                                                                  #  SUBROUTINE NAME:     CALCTPER  /  CALCTFF                               DATE:    01.29.67
055236,000285:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
055237,000286:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
055238,000287:                                                                                                  #  MOD NO:  1           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 67
055239,000288:                                                                                                  #  MOD NO:  2           MOD BY:  RR BAIRNSFATHER      DATE:  14 APR 67
055240,000289:                                                                                                  #  MOD NO:  3           MOD BY:  RR BAIRNSFATHER      DATE:  8JUL 67       NEAR EARTH MUE AND NEG TFF (GONEPAST)
055241,000290:                                                                                                  #  MOD NO:  4           MOD BY:  RR BAIRNSFATHER      DATE:  21 NOV 67     ADD VARIABLE MU.
055242,000291:                                                                                                  #  MOD NO:  5           MOD BY:  RR BAIRNSFATHER      DATE:  21 MAR 68     ACCEPT DIFFERENT EARTH/MOON SCALES
055243,000292:                                                                                                  #  FUNCTIONAL DESCRIPTION:      PROGRAM CALCULATES THE FREE-FALL TIME OF FLIGHT FROM PRESENT POSITION  RN  AND
055244,000293:                                                                                                  #           VELOCITY  VN  TO A RADIUS LENGTH SPECIFIED BY  RTERM  , SUPPLIED BY THE USER. THE POSITION VECTOR
055245,000294:                                                                                                  #           RN  MAY BE ON EITHER SIDE OF THE CONIC, BUT  RTERM  IS CONSIDERED ON THE INBOUND SIDE.
055246,000295:                                                                                                  #           THE EQUATIONS ARE
055247,000296: 
055248,000297:                                                                                                  #                  Q2 = -SQRT(RTERM (2-RTERM ALFA) - LCP)    (INBOUND SIDE))        LEQ +- LCE/SQRT(ALFA)
055249,000298:                                                                                                  #                       -  -
055250,000299:                                                                                                  #                  Q1 = RN.VN / SQRT(MU)                                            LEQ +- LCE/SQRT(ALFA)
055251,000300: 
055252,000301:                                                                                                  #                  Z = NUM / DEN                                                    LEQ +- 1/SQRT(ALFA)
055253,000302: 
055254,000303:                                                                                                  #           WHERE, IF INBOUND
055255,000304:                                                                                                  #                  NUM = RTERM - RN                                                 LEQ +- 2 LCE/ALFA
055256,000305:                                                                                                  #                  DEN = Q2+Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
055257,000306: 
055258,000307:                                                                                                  #           AND, IF OUTBOUND
055259,000308:                                                                                                  #                  NUM = Q2-Q1                                                      LEQ +- 2 LCE/SQRT(ALFA)
055260,000309:                                                                                                  #                  DEN = 2 - ALFA (RTERM + RN) .                                    LEQ +- 2 LCE
055261,000310: 
055262,000311:                                                                                                  #           IF     ALFA ZZ  <  1.0               (FOR ALL CONICS EXCEPT ELLIPSES HAVING ABS(DEL ECC ANOM) G 90 DEG)
055263,000312: 
055264,000313:                                                                                                  #           THEN   X = ALFA Z Z
055265,000314:                                                                                                  #           AND    TFF = (RTERM +RN -2 ZZ T(X) ) Z/SQRT(MU)
055266,000315: 
055267,000316:                                                                                                  #                  EXCEPT IF ALFA PNZ, AND IF TFF NEG,
055268,000317:                                                                                                  #                  THEN   TFF = 2 PI /(ALFA SQRT(ALFA)) + TFF
055269,000318: 
055270,000319:                                                                                                  #           OR IF  ALFA ZZ  GEQ  1.0             (FOR ELLIPSES HAVING ABS(DEL ECC ANOM) GEQ 90 DEG)
055271,000320: 
055272,000321:                                                                                                  #           THEN   X = 1/ALFA Z Z
055273,000322:                                                                                                  #           AND    TFF = (PI/SQRT(ALFA) -Q2 +Q1 +2(X T(X) -1) /ALFA Z) /ALFA SQRT(MU)
055274,000323: 
055275,000324:                                                                                                  #           WHERE  T(X) IS A POLYNOMIAL APPROXIMATION TO THE SERIES
055276,000325:                                                                                                  #                             2     3                        2
055277,000326:                                                                                                  #                  1/3 -X/5 +X /7 -X /9 ...                (X   <  1.0)
055278,000327: 
055279,000328:                                                                                                  #  CALLING SEQUENCE:  TIME TO RTERM                           TIME TO PERIGEE
055280,000329:                                                                                                  #                     CALL                                    CALL
055281,000330:                                                                                                  #                            CALCTFF                                 CALCTPER
055282,000331:                                                                                                  #                     C(MPAC) = TERMNL RAD  M                 C(MPAC) = PERIGEE RAD  M
055283,000332:                                                                                                  #           FOR EITHER,   E: (-29)    M: (-27)
055284,000333:                                                                                                  #           FOR EITHER, PUSHLOC = PDL+0, ARBITRARY IF LEQ 8D.
055285,000334: 

Page 1265

055287,000336:                                                                                                  #  SUBROUTINES CALLED:  T(X),  VIA RTB
055288,000337:                                                                                                  #  NORMAL EXIT MODE:  RVQ
055289,000338:                                                                                                  #           HOWEVER, PROGRAM EXITS WITH ONE OF THE FOLLOWING VALUES FOR TFF (-28) CS  IN MPAC. USER MUST STORE.
055290,000339:                                                                                                  #                  A.  TFF= FLIGHT TIME. NORMAL CASE FOR POSITIVE FLIGHT TIME LESS THAN ONE ORBITAL PERIOD.
055291,000340:                                                                                                  #                  B.  (THIS OPTION IS NO LONGER USED.)
055292,000341:                                                                                                  #                  C.  TFF = POSMAX.  THIS INDICATES THAT THE CONIC FROM THE PRESENT POSITION WILL NOT RETURN TO
055293,000342:                                                                                                  #                      THE SPECIFIED ALTITUDE.  ALSO INDICATES OUTBOUND PARABOLA OR HYPERBOLA.
055294,000343:                                                                                                  #  OUTPUT:  C(MPAC)  (-28)  CS     TIME OF FLIGHT, OR TIME TO PERIGEE
055295,000344:                                                                                                  #           TFFX    (0)            X,                                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
055296,000345:                                                                                                  #           NRTERM  E: (-29+NR)    M  RTERM, WEIGHTED BY NR                LEFT FOR ENTRY DISPLAY TFF ROUTINES
055297,000346:                                                                                                  #                   M: (-27+NR)
055298,000347:                                                                                                  #           TFFTEM  E: (-59+2NR)   LCP Z Z SGN(SDELF)                      LEFT FOR ENTRY DISPLAY TFF ROUTINES
055299,000348:                                                                                                  #                   M: (-55+2NR)   LCP /ALFA SGN(SDELF)                    LEFT FOR ENTRY DISPLAY TFF ROUTINES
055300,000349:                                                                                                  #           NOTE:  TFFTEM = PDL 36D AND WILL BE DESTROYED BY .:UNIT:.
055301,000350:                                                                                                  #           RMAG1  E:(-29)  M:(-27)  PDL 12 NOT TOUCHED.
055302,000351:                                                                                                  #           TFFQ1  E:(-16)  M:(-15)  PDL 14D
055303,000352:                                                                                                  #           TFFDELQ E:(-16) M:(-15)  PDL 10D
055304,000353:                                                                                                  #           PUSHLOC AT PDL+0
055305,000354:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
055306,000355:                                                                                                  #           RONE   E:(-29)  M:(-27)  M   STATE VECTOR                      LEFT BY USER
055307,000356:                                                                                                  #           VONE'  E:(+10)  M:(+9)   VN/SQRT(MU)                           LEFT BY TFF/CONIC
055308,000357:                                                                                                  #           RMAG1  E:(-29)  M:(-27)  PRESENT RADIUS,  M                    LEFT BY TFFCONIC
055309,000358:                                                                                                  #           C(MPAC)E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH, M      LEFT BY USER
055310,000359: 
055311,000360:                                                                                                  #           THE FOLLOWING ARE STORED IN THE PUSH LIST AREA.
055312,000361:                                                                                                  #           TFF/RTMU  E:(17)  M:(14)  1/SQRT(MU)                           LEFT BY TFFCONIC.
055313,000362:                                                                                                  #           NRMAG  E: (-29+NR)  M  RMAG, NORMALIZED                        LEFT BY TFFCONIC
055314,000363:                                                                                                  #                  M: (-27+NR)
055315,000364:                                                                                                  #           X1                     -NR, NORM COUNT                         LEFT BY TFFCONIC
055316,000365:                                                                                                  #           TFFNP  E: (-38+2NR)  M   LCP, SEMI LATUS RECTUM, WEIGHT  NR    LEFT BY TFFCONIC
055317,000366:                                                                                                  #                  M: (-36+2NR)
055318,000367:                                                                                                  #           TFFALFA  E: (26-NR)    1/M  ALFA, WEIGHT  NR                   LEFT BY TFFCONIC
055319,000368:                                                                                                  #                    M: (24-NR)
055320,000369:                                                                                                  #           TFFRTALF  E:(10+NA)    SQRT(ALFA), NORMALIZED                  LEFT BY TFFCONIC
055321,000370:                                                                                                  #                     M:(9+NA)
055322,000371:                                                                                                  #           X2                     -NA, NORM COUNT                         LEFT BY TFFCONIC
055323,000372:                                                                                                  #           TFF1/ALF  E: (-22-2NA)  SIGNED SEMIMAJ AXIS, WEIGHTED BY NA    LEFT BY TFFCONIC
055324,000373:                                                                                                  #                     M: (-20-2NA)
055325,000374:                                                                                                  #  DEBRIS:  QPRET,   PDL+0 ... PDL+3
055326,000375:                                                                                                  #           RTERM  E:(-29)  M:(-27)  RTERM, TERMINAL RADIUS LENGTH
055327,000376:                                                                                                  #           RAPO   E:(-29)  M:(-27)  PDL 16D  (=NRTERM)
055328,000377:                                                                                                  #           RPER   E:(-29)  M:(-27)  PDL 14D   (=TFFQ1)
055329,000378: 

Page 1266

055331,000380: 27,3447           77614        CALCTPER           SETGO                                          #  ENTER WITH RPER  IN MPAC
055332,000381: 27,3450           03436                                    TFFSW                                 
055333,000382: 27,3451           57454                                    +3                                    
055334,000383: 27,3452           77614        CALCTFF            CLEAR                                          #  ENTER WITH RTERM IN MPAC
055335,000384: 27,3453           03676                                    TFFSW                                 
055336,000385: 27,3454           00023                 +3        STORE    RTERM                                 #  E: (-29)  M: (-27)
055337,000386: 27,3455           77657                           SL*                                            
055338,000387: 27,3456           20201                                    0,1                                   #  X1=-NR
055339,000388: 27,3457           00021                           STORE    NRTERM                                #  RTERM  E: (-29+NR)  M: (-27+NR)
055340,000389: 27,3460           44205                           DMP      BDSU                                  
055341,000390: 27,3461           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
055342,000391: 27,3462           06510                                    TFF1/4                                
055343,000392: 27,3463           41206                           PUSH     DMP                                   #  (2-ALFA RTERM)  (-3)  TO PDL+0
055344,000393: 27,3464           00021                                    NRTERM                                #  E: (-29+NR)  M: (-27+NR)
055345,000394: 27,3465           53725                           PDDL     SR*                                   #  RTERM(2-ALFA RTERM) TO PDL+2
055346,000395:                                                                                                  #  E: (-32+NR)   M: (-30+NR)
055347,000396: 27,3466           00035                                    TFFNP                                 #  LC P  E:(-38+2NR)  M:(-36+2NR)
055348,000397: 27,3467           20573                                    0          -6,1                       #  X1 = -NR
055349,000398: 27,3470           43276                           DCOMP    DAD                                   #  DUE TO SHIFTS, KEEP PRECISION FOR SQRT
055350,000399:                                                                                                  #  RTERM(2-ALFA RTERM) FROM PDL+2
055351,000400:                                                                                                  #  E: (-32+NR)  M: (-30+NR)
055352,000401: 27,3471           77657                           SR*                                            #  LEAVE  E: (-32)  M: (-30)
055353,000402: 27,3472           20601                                    0,1                                   #  X1 = -NR
055354,000403: 27,3473           71214                           BOFF     DLOAD                                 #  CHECK TFF / TPER SWITCH
055355,000404: 27,3474           03756                                    TFFSW                                 
055356,000405: 27,3475           57477                                    +2                                    #  IF TFF, CONTINUE
055357,000406: 27,3476           06520                                    TFFZEROS                              #  IF TPER, SET Q2 = 0
055358,000407: 27,3477           75440                 +2        BMN      SQRT                                  #  E: (-16)  M: (-15)
055359,000408: 
055360,000409: 27,3500           57632                                    MAXTFF1                               #  NO FREE FALL CONIC TO RTERM FROM HERE
055361,000410:                                                                                                  #  RESET PDL, SET TFF=POSMAX, AND EXIT.
055362,000411: 
055363,000412: 27,3501           41076                           DCOMP    BOVB                                  #  RT IS ON INBOUND SIDE.  ASSURE OVFIND=0
055364,000413: 27,3502           57735                                    TCDANZIG                              #  ANY PORT IN A STORM.
055365,000414: 27,3503           24045                           STOVL    TFFTEM                                #  Q2   E: (-16)  M: (-15)
055366,000415: 27,3504           02161                                    VONE'                                 #  VN/SQRT(MU) E: (10)  M: (9)
055367,000416: 27,3505           52441                           DOT      SL3                                   
055368,000417: 27,3506           02200                                    RONE                                  #  SAVED RN.  E: (-29)  M: (-27)
055369,000418: 27,3507           00017                           STORE    TFFQ1                                 #  Q1, SAVE FOR GONEPAST TEST.
055370,000419:                                                                                                  #  E: (-16)  M: (-15)
055371,000420: 27,3510           44240                           BMN      BDSU                                  
055372,000421: 27,3511           57532                                    INBOUND                               #  USE ALTERNATE Z
055373,000422: 27,3512           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
055374,000423: 
055375,000424:                                                                                                  #                                          OUTBOUND Z CALC CONTINUES HERE
055376,000425: 
055377,000426: 27,3513           14043                           STODL    TFFX                                  #  NUM=Q2-Q1  E: (-16)  M: (-15)
055378,000427: 27,3514           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
055379,000428: 27,3515           44205                           DMP      BDSU                                  

Page 1267

055381,000430: 27,3516           00041                                    NRMAG                                 #  RMAG  E: (-29+NR)  M: (-27+NR)
055382,000431:                                                                                                  #  (2-RTERM ALFA)  (-3) FROM PDL+0
055383,000432: 27,3517           51406        SAVEDEN            PUSH     ABS                                   #  DEN TO PDL+0  E: (-3) OR (-16)
055384,000433:                                                                                                  #                M: (-3) OR (-15)
055385,000434: 27,3520           40015                           DAD      BOV                                   #  INDETERMINANCY TEST
055386,000435: 27,3521           17741                                    LIM(-22)                              #  =1.0-B(-22)
055387,000436: 27,3522           57543                                    TFFXTEST                              #  GO IF DEN >/= B(-22)
055388,000437: 27,3523           65345                           DLOAD    PDDL                                  #  SET DEN=0  OTHERWISE
055389,000438: 27,3524           06520                                    TFFZEROS                              
055390,000439:                                                                                                  #  XCH ZERO WITH PDL+0
055391,000440: 27,3525           57545                           DLOAD    DCOMP                                 
055392,000441: 27,3526           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
055393,000442: 27,3527           71240                           BMN      DLOAD                                 #  FOR TPER: Z INDET AT DELE/2=0 AND 90.
055394,000443: 27,3530           57637                                    TFFEL1                                #  ASSUME 90, AND LEAVE 0 IN PDL: 1/Z=D/N
055395,000444: 
055396,000445:                                                                                                  #  Z INDET. AT PERIGEE FOR PARAB OR HYPERB.
055397,000446: 27,3531           77616        DUMPTFF1           RVQ                                            #  RETURN  TFF =0
055398,000447: 
055399,000448:                                                                                                  #                                          INBOUND Z CALC CONTINUES HERE
055400,000449: 27,3532           77745        INBOUND            DLOAD                                          #  RESET PDL+0
055401,000450: 27,3533           45345                           DLOAD    DSU                                   #  ALTERNATE Z CALC
055402,000451: 27,3534           00023                                    RTERM                                 #  E: (-29)  M: (-27)
055403,000452: 27,3535           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
055404,000453: 27,3536           14043                           STODL    TFFX                                  #  NUM=RTERM-RN  E: (-29)  M: (-27)
055405,000454: 27,3537           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
055406,000455: 27,3540           52015                           DAD      GOTO                                  
055407,000456: 27,3541           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
055408,000457: 27,3542           57517                                    SAVEDEN                               #  DEN = Q2+Q1   E: (-16)  M: (-15)
055409,000458: 
055410,000459: 27,3543           65215        TFFXTEST           DAD      PDDL                                  #   (ABS(DEN) TO PDL+2))  E: (-3) OR (-16)
055411,000460:                                                                                                  #                         M: (-3) OR (-15)
055412,000461: 27,3544           17743                                    DP(-22)                               #  RESTORE ABS(DEN) TO MPAC
055413,000462: 27,3545           00043                                    TFFX                                  #  NUM E:(-16) OR (-29)  M:(-15) OR (-27)
055414,000463: 27,3546           53605                           DMP      SR*                                   
055415,000464: 27,3547           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
055416,000465: 27,3550           57201                                    0          -3,2                       #  X2=-NA
055417,000466: 27,3551           77671                           DDV                                            #  C(MPAC) =NUM SQRT(ALFA)  E:(-3) OR (-16)
055418,000467:                                                                                                  #                           M:(-3) OR (-15)
055419,000468:                                                                                                  #  ABS(DEN) FROM PDL+2  E:(-3) OR (-16)
055420,000469:                                                                                                  #                       M:(-3) OR (-15)
055421,000470: 27,3552           40145                           DLOAD    BOV                                   #  (THE DLOAD IS SHARED WITH TFFELL)
055422,000471: 27,3553           00043                                    TFFX                                  #  NUM  E: (-16) OR (-29)  M:(-15) OR (-27)
055423,000472: 27,3554           57635                                    TFFELL                                #  USE EQN FOR DELE GEQ 90, LEQ -90
055424,000473: 
055425,000474:                                                                                                  #                                          OTHERWISE, CONTINUE FOR GENERAL CONIC FOR TFF EQN
055426,000475: 
055427,000476: 27,3555           45471                           DDV      STADR                                 
055428,000477:                                                                                                  #  DEN FROM PDL+0   E: (-3) OR (-16)
055429,000478:                                                                                                  #                   M: (-3) OR (-15)
055430,000479: 27,3556           77732                           STORE    TFFTEM                                #  Z  SAVE FOR SIGN OF SDELF.

Page 1268

055432,000481:                                                                                                  #  E: (-13)  M: (-12)
055433,000482: 27,3557           63406                           PUSH     DSQ                                   #  Z TO PDL+0
055434,000483: 27,3560           41206                           PUSH     DMP                                   #  Z SQ TO PDL+2  E: (-26)  M: (-24)
055435,000484: 27,3561           00035                                    TFFNP                                 #  LC P  E: (-38+2NR)  M: (-36+2NR)
055436,000485: 27,3562           75261                           SL       SIGN                                  
055437,000486: 27,3563           20206                                    5                                     
055438,000487: 27,3564           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF (ENTRY DISPLAY)
055439,000488: 27,3565           14045                           STODL    TFFTEM                                #  P ZSQ  E: (-59+2NR)  M: (-55+2NR)
055440,000489:                                                                                                  #  (ARG IS USED IN TFF/TRIG)
055441,000490:                                                                                                  #  ZSQ FROM PDL+2   E: (-26)  M: (-24)
055442,000491: 27,3566           41206                           PUSH     DMP                                   #  RESTORE PUSH LOC
055443,000492: 27,3567           00033                                    TFFALFA                               #  ALFA  E: (26-NR)  M: (24-NR)
055444,000493: 27,3570           77657                           SL*                                            
055445,000494: 27,3571           20201                                    0,1                                   #  X1=-NR
055446,000495: 27,3572           00043                           STORE    TFFX                                  #  X
055447,000496: 27,3573           41234                           RTB      DMP                                   
055448,000497: 27,3574           57717                                    T(X)                                  #   POLY
055449,000498:                                                                                                  #  ZSQ FROM PDL+2  E: (-26)  M: (-24)
055450,000499: 27,3575           44302                           SR2      BDSU                                  #  2 ZSQ T(X)  E: (-29)  M: (-27)
055451,000500: 27,3576           00023                                    RTERM                                 #  RTERM  E: (-29)  M: (-27)
055452,000501: 27,3577           41215                           DAD      DMP                                   
055453,000502: 27,3600           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
055454,000503:                                                                                                  #  Z FROM PDL+0  E: (-13)  M: (-12)
055455,000504: 27,3601           51042                           SR3      BPL                                   #  TFF SQRT(MU)   E: (-45)  M: (-42)
055456,000505: 27,3602           57623                                    ENDTFF                                #  (NO PUSH UP)
055457,000506: 27,3603           75206                           PUSH     SIGN                                  #  TFF SQRT(MU)  TO PDL+0
055458,000507: 27,3604           00017                                    TFFQ1                                 #  Q1 FOR GONEPAST TEST
055459,000508: 27,3605           71244                           BPL      DLOAD                                 #  GONE PAST ?
055460,000509: 27,3606           57627                                    NEGTFF                                #  YES. TFF < 0 .
055461,000510: 27,3607           00027                                    TFF1/ALF                              #  1/ALFA  E: (-22-2NA)  M: (-20-2NA)
055462,000511: 27,3610           51076                           DCOMP    BPL                                   #  ALFA > 0 ?
055463,000512: 27,3611           57627                                    NEGTFF                                #  NO. TFF IS NEGATIVE.
055464,000513: 
055465,000514:                                                                                                  #                                          CORRECT FOR ORBITAL PERIOD.
055466,000515: 
055467,000516: 27,3612           77676                           DCOMP                                          #  YES. CORRECT FOR ORB PERIOD.
055468,000517: 27,3613           56205                           DMP      DDV                                   
055469,000518: 27,3614           17737                                    PI/16                                 #  2 PI (-5)
055470,000519: 27,3615           00031                                    TFFRTALF                              #  SQRT(ALFA)  E: (10+NA)  M: (9+NA)
055471,000520: 27,3616           53657                           SL*      SL*                                   
055472,000521: 27,3617           57602                                    0          -4,2                       #  X2=-NA
055473,000522: 27,3620           57602                                    0          -4,2                       
055474,000523: 27,3621           43257                           SL*      DAD                                   
055475,000524: 27,3622           57576                                    0,2                                   
055476,000525:                                                                                                  #  TFF SQRT(MU) FROM PDL+0  E:(-45) M:(-42)
055477,000526: 27,3623           40005        ENDTFF             DMP      BOV                                   #  TFF SQRT(MU) IN MPAC     E:(-45) M:(-42)
055478,000527: 27,3624           00037                                    TFF/RTMU                              #  E: (17)  M: (14)
055479,000528: 27,3625           57633                                    MAXTFF                                #  SET POSMAX IF OVFL.
055480,000529: 
055481,000530: 27,3626           77616        DUMPTFF2           RVQ                                            #  RETURN  TFF   (-28) CS IN MPAC.
055482,000531: 

Page 1269

055484,000533: 27,3627           77745        NEGTFF             DLOAD                                          
055485,000534:                                                                                                  #  TFF SQRT(MU)  FROM PDL+0, NEGATIVE.
055486,000535: 27,3630           77650                           GOTO                                           
055487,000536: 27,3631           57623                                    ENDTFF                                
055488,000537: 
055489,000538: 27,3632           77745        MAXTFF1            DLOAD                                          #  RESET PDL
055490,000539: 27,3633           43545        MAXTFF             DLOAD    RVQ                                   
055491,000540: 27,3634           17753                                    NEARONE                               
055492,000541: 
055493,000542:                                                                                                  #  TIME OF FLIGHT ELLIPSE WHEN DEL (ECCENTRIC ANOM) GEQ 90 AND LEQ -90.
055494,000543: 
055495,000544:                                                                                                  #  NUM FROM TFFX.  E: (-16) OR (-29)
055496,000545:                                                                                                  #                  M: (-15) OR (-27)
055497,000546: 27,3635           77712        TFFELL             SL2                                            #  NUM  E:(-14) OR (-27)  M:(-13) OR (-25)
055498,000547: 27,3636           41465                           BDDV     PUSH                                  #  TEMP SAVE D/N IN PDL+0
055499,000548:                                                                                                  #  DEN FROM PDL+0 E:(-3)/( 16) M:(-3)/(-15)
055500,000549:                                                                                                  #  N/D TO PDL+0  E: (11)  M: (10)
055501,000550: 27,3637           45345        TFFEL1             DLOAD    DSU                                   #  (ENTER WITH D/N=0 IN PDL+0)
055502,000551: 27,3640           00045                                    TFFTEM                                #  Q2  E: (-16)  M: (-15)
055503,000552: 27,3641           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
055504,000553: 27,3642           14013                           STODL    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
055505,000554:                                                                                                  #  D/N FROM PDL+0
055506,000555: 27,3643           77626                           STADR                                          
055507,000556: 27,3644           77732                           STORE    TFFTEM                                #  D/N  E: (11)  M: (10)
055508,000557: 27,3645           53605                           DMP      SL*                                   
055509,000558: 27,3646           00027                                    TFF1/ALF                              #  1/ALFA E: (-22-2NA)  M: (-20-2NA)
055510,000559: 27,3647           57576                                    0,2                                   #  1/ALFA Z  E: (-11-NA)  M: (-10-NA)
055511,000560: 27,3650           41206                           PUSH     DMP                                   #  TO PDL+0
055512,000561: 27,3651           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
055513,000562: 27,3652           41057                           SL*      BOVB                                  
055514,000563: 27,3653           57576                                    0,2                                   #  X2= -NA
055515,000564: 27,3654           21674                                    SIGNMPAC                              #  IN CASE X= 1.0, CONTINUE
055516,000565: 27,3655           00043                           STORE    TFFX                                  #  X=1/ALFA ZSQ
055517,000566: 27,3656           41234                           RTB      DMP                                   
055518,000567: 27,3657           57717                                    T(X)                                  #  POLY
055519,000568: 27,3660           00043                                    TFFX                                  
055520,000569: 27,3661           45242                           SR3      DSU                                   
055521,000570: 27,3662           17745                                    DP2(-3)                               
055522,000571: 27,3663           41405                           DMP      PUSH                                  #  2(X T(X)-1) /Z ALFA  E: (-15-NA)
055523,000572:                                                                                                  #                       M: (-14-NA)
055524,000573:                                                                                                  #  1/ALFA Z FROM PDL+0  E: (-11-NA)
055525,000574:                                                                                                  #                       M: (-10-NA)
055526,000575: 27,3664           41345                           DLOAD    DMP                                   #  GET SIGN FOR SDELF
055527,000576: 27,3665           00045                                    TFFTEM                                #  1/Z  E: (11)  M: (10)
055528,000577: 27,3666           00015                                    RMAG1                                 #  E: (-29)  M: (-27)
055529,000578: 27,3667           43312                           SL2      DAD                                   
055530,000579: 27,3670           00017                                    TFFQ1                                 #  Q1  E: (-16)  M: (-15)
055531,000580: 27,3671           14045                           STODL    TFFTEM                                #  (Q1+R 1/Z)  =SGN OF SDELF E:(-16) M:(-15
055532,000581: 27,3672           00035                                    TFFNP                                 #  LC P E: (-38+2NR) M: (-36+2NR)
055533,000582: 27,3673           53605                           DMP      SL*                                   #  CALC FOR ARG FOR TFF/TRIG.

Page 1270

055535,000584: 27,3674           00027                                    TFF1/ALF                              #  1/ALFA   E:(-22-2NA)  M:(-20-2NA)
055536,000585: 27,3675           57575                                    1,2                                   #  X2=-NA
055537,000586: 27,3676           53765                           SIGN     SL*                                   
055538,000587: 27,3677           00045                                    TFFTEM                                #  AFFIX SIGN FOR SDELF
055539,000588: 27,3700           57576                                    0,2                                   
055540,000589: 27,3701           14045                           STODL    TFFTEM                                #  P/ALFA  E:(-59+2NR)  M:(-55+2NR)
055541,000590:                                                                                                  #  (ARG FOR USE IN TFF/TRIG)
055542,000591: 27,3702           00027                                    TFF1/ALF                              #  1/ALFA E:(-22-2NA)  M:(-20-2NA)
055543,000592: 27,3703           41366                           SQRT     DMP                                   
055544,000593: 27,3704           17737                                    PI/16                                 #  PI (-4)
055545,000594: 27,3705           77615                           DAD                                            
055546,000595:                                                                                                  #  2(XT(X)-1)/Z ALFA FROM PDL E:(-15-NA)
055547,000596:                                                                                                  #                             M:(-14-NA)
055548,000597: 27,3706           45257                           SL*      DSU                                   
055549,000598: 27,3707           57577                                    0          -1,2                       
055550,000599: 27,3710           00013                                    TFFDELQ                               #  Q2-Q1  E: (-16)  M: (-15)
055551,000600: 27,3711           53605                           DMP      SL*                                   
055552,000601: 27,3712           00027                                    TFF1/ALF                              #  1/ALFA  E:(-22-2NA)  M:(-20-2NA)
055553,000602: 27,3713           57601                                    0          -3,2                       
055554,000603: 27,3714           52057                           SL*      GOTO                                  
055555,000604: 27,3715           57602                                    0          -4,2                       
055556,000605: 27,3716           57623                                    ENDTFF                                #  TFF SQRT(MU) IN MPAC E:(-45) M:(-42)
055557,000606: 

Page 1271

055559,000608:                                                                                                  #  PROGRAM NAME:      T(X)                                                 DATE:    01.17.67
055560,000609:                                                                                                  #  MOD NO:  0                                                              LOG SECTION:    TIME OF FREE FALL
055561,000610:                                                                                                  #  MOD BY:  RR BAIRNSFATHER
055562,000611:                                                                                                  #  FUNCTIONAL DESCRIPTION:      THE POLYNOMIAL T(X) IS USED BY TIME OF FLIGHT SUBROUTINES  CALCTFF AND
055563,000612:                                                                                                  #           CALCTPER TO APPROXIMATE THE SERIES
055564,000613:                                                                                                  #                             2     3
055565,000614:                                                                                                  #                  1/3 -X/5 +X /7 -X /9 ...
055566,000615: 
055567,000616:                                                                                                  #           WHERE  X = ALFA Z Z       IF ALFA Z Z  LEQ 1
055568,000617:                                                                                                  #                  X = 1/(ALFA Z Z )  IF ALFA Z Z   G  1
055569,000618: 
055570,000619:                                                                                                  #           ALSO   X IS NEG FOR HYPERBOLIC ORBITS
055571,000620:                                                                                                  #                  X = 0 FOR PARABOLIC ORBITS
055572,000621:                                                                                                  #                  X IS POSITIVE FOR ELLIPTIC ORBITS
055573,000622:                                                                                                  #           FOR FLIGHT 278, THE POLYNOMIAL  T(X) IS FITTED OVER THE RANGE  (0,+1)  AND HAS A MAXIMUM
055574,000623:                                                                                                  #           DEVIATION FROM THE SERIES OF  2 E-5       (T(X) IS A CHEBYCHEV  TYPE FIT AND WAS OBTAINED USING
055575,000624:                                                                                                  #           MAC PROGRAM AUTCURFIT294RRB  AND IS VALID TO THE SAME TOLERANCE OVER THE RANGE  (-.08,+1). )
055576,000625:                                                                                                  #  CALLING SEQUENCE:  RTB
055577,000626:                                                                                                  #                            T(X)
055578,000627:                                                                                                  #           C(MPAC) = X
055579,000628: 
055580,000629:                                                                                                  #  SUBROUTINES CALLED:  NONE
055581,000630:                                                                                                  #  NORMAL EXIT MODE:    TC   DANZIG
055582,000631:                                                                                                  #  ALARMS:  NONE
055583,000632:                                                                                                  #  OUTPUT:  C(MPAC) = T(X)
055584,000633:                                                                                                  #  ERASABLE INITIALIZATION REQUIRED:
055585,000634:                                                                                                  #           C(MPAC)  =  X
055586,000635:                                                                                                  #  DEBRIS:  NONE
055587,000636: 
055588,000637: 27,3717           07234        T(X)               TC       POLY                                  
055589,000638: 27,3720           00004                           DEC      4          B-14                       #  N-1
055590,000639: 27,3721           12525 12525                     2DEC     3.333333333 E-1                        
055591,000640: 
055592,000641: 27,3723           71463 57703                     2DEC*    -1.999819135 E-1*                       
055593,000642: 
055594,000643: 27,3725           04423 17645                     2DEC*    1.418148467 E-1*                       
055595,000644: 
055596,000645: 27,3727           74604 43667                     2DEC*    -1.01310997 E-1*                       
055597,000646: 
055598,000647: 27,3731           01626 37256                     2DEC*    5.609004986 E-2*                       
055599,000648: 
055600,000649: 27,3733           77404 52071                     2DEC*    -1.536156925 E-2*                       
055601,000650: 
055602,000651: 27,3735           06073        ENDT(X)            TC       DANZIG                                
055603,000652: 
055604,000653: 27,3736  27,3735               TCDANZIG           =        ENDT(X)                               
055605,000654: 

Page 1272

055607,000656:                                                                                                  #  TFF CONSTANTS
055608,000657: 
055609,000658: 32,3733                                           BANK     32                                    
055610,000659: 
055611,000660: 27,2000                                           SETLOC   TOF-FF1                               
055612,000661: 27,2000                                           BANK                                           
055613,000662: 
055614,000663:                                                                                                  #                             NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
055615,000664: 
055616,000665:                                                                                                  # MUE            =       3.990 815 471 E10  M CUBE/CS SQ
055617,000666:                                                                                                  # RTMUE          =       1.997702549 E5 B-18*     MODIFIED EARTH MU
055618,000667: 
055619,000668:                                                                                                  #                             NOTE _  NOTE _ ADJUSTED MUE FOR NEAR EARTH TRAJ.
055620,000669: 
055621,000670:                                                                                                  # MUM            =       4.902 778  E8     M CUBE /CS SQ
055622,000671: 
055623,000672:                                                                                                  # RTMUM          2DEC*   2.21422176 E4 B-18*
055624,000673: 27,3736           06220 37553  PI/16              2DEC     3.141592653 B-4                        
055625,000674: 
055626,000675: 27,3740           37777 37700  LIM(-22)           2OCT     3777737700                            #  1.0 -B(-22)
055627,000676: 
055628,000677: 27,3742           00000 00100  DP(-22)            2OCT     0000000100                            #  B(-22)
055629,000678: 
055630,000679: 27,3744           04000 00000  DP2(-3)            2DEC     1          B-3                        
055631,000680: 
055632,000681: 27,3746           02000 00000  DP2(-4)            2DEC     1          B-4                        #  1/16
055633,000682: 
055634,000683:                                                                                                  # RPAD1          2DEC    6373338 B-29      M  (-29)   =20 909 901.57 FT
055635,000684: 
055636,000685: 27,3750  23,2335               RPAD1              =        RPAD                                  
055637,000686: 
055638,000687: 27,3750           00305 11205  R300K              2DEC     6464778    B-29                       #  (-29) M
055639,000688: 
055640,000689: 27,3752           37777 37777  NEARONE            2DEC     .999999999                            
055641,000690: 
055642,000691: 27,3754  23,2517               TFFZEROS           EQUALS   HI6ZEROS                              
055643,000692: 27,3754  23,2507               TFF1/4             EQUALS   HIDP1/4                               
055644,000693: 

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