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Proof LUNAR_AND_SOLAR_EPHEMERIDES_SUBROUTINES #605 (#713)

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Co-authored-by: James Harris <wopian@wopian.me>
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57
Luminary099/LUNAR_AND_SOLAR_EPHEMERIDES_SUBROUTINES.agc
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@ -25,7 +25,7 @@
# 16:27 JULY 14, 1969 # 16:27 JULY 14, 1969
# Page 984 # Page 984
# NAME -- LSPOS -- LOCATE SUN AND MOON DATE -- 25 OCT 67 # NAME - LSPOS - LOCATE SUN AND MOON DATE - 25 OCT 67
# MOD NO.1 # MOD NO.1
# MOD BY NEVILLE ASSEMBLY SUNDANCE # MOD BY NEVILLE ASSEMBLY SUNDANCE
# #
@ -33,8 +33,9 @@
# #
# COMPUTES UNIT POSITION VECTOR OF THE SUN AND MOON IN THE BASIC REFERENCE SYSTEM. THE SUN VECTOR S IS # COMPUTES UNIT POSITION VECTOR OF THE SUN AND MOON IN THE BASIC REFERENCE SYSTEM. THE SUN VECTOR S IS
# LOCATED VIA TWO ANGLES. THE FIRST ANGLE(OBLIQUITY) IS THE ANGLE BETWEEN THE EARTH EQUATOR AND THE ECLIPTIC. THE # LOCATED VIA TWO ANGLES. THE FIRST ANGLE(OBLIQUITY) IS THE ANGLE BETWEEN THE EARTH EQUATOR AND THE ECLIPTIC. THE
# POSITION VECTOR OF THE SUN IS # SECOND ANGLE IS THE LONGITUDE OF THE SUN MEASURED IN THE ECLIPTIC.
# _ # THE POSITION VECTOR OF THE SUN IS
# -
# S=(COS(LOS), COS(OBL)*SIN(LOS), SIN(OBL)*SIN(LOS)), WHERE # S=(COS(LOS), COS(OBL)*SIN(LOS), SIN(OBL)*SIN(LOS)), WHERE
# #
# LOS=LOS +LOS *T-(C *SIN(2PI*T)/365.24 +C *COS(2PI*T)/365.24) # LOS=LOS +LOS *T-(C *SIN(2PI*T)/365.24 +C *COS(2PI*T)/365.24)
@ -43,25 +44,22 @@
# 0 # 0
# LOS (RAD/DAY) IS THE MEAN RATE FOR THE PARTICULAR YEAR. # LOS (RAD/DAY) IS THE MEAN RATE FOR THE PARTICULAR YEAR.
# R # R
# # LOS AND LOS ARE STORED AS LOSO AND LOSR IN RATESP.
# LOS AND LOS ARE STORED AS LOSC AND LOSR IN RATESP.
# 0 R # 0 R
# COS(OBL) AND SIN(OBL) ARE STORED IN THE MATRIX KONMAT. # COS(OBL) AND SIN(OBL) ARE STORED IN THE MATRIX KONMAT.
# # T, TIME MEASURED IN DAYS(24 HOURS), IS STORED IN TIMEP.
# T, TIME MEASURED IN DAYS (24 HOURS) IS STORED IN TIMEP.
#
# C AND C ARE FUDGE FACTORS TO MINIMIZE THE DEVIATION. THEY ARE STORED AS ONE CONSTANT(CMOD), SINCE # C AND C ARE FUDGE FACTORS TO MINIMIZE THE DEVIATION. THEY ARE STORED AS ONE CONSTANT(CMOD), SINCE
# 0 1 2 2 1/2 # 0 1 2 2 1/2
# C *SIN(X)+C *COS(X) CAN BE WRITTEN AS (C +C ) *SIN(X+PHI), WHERE PHI=ARCTAN(C /C ). # C *SIN(X)+C *COS(X) CAN BE WRITTEN AS (C +C ) *SIN(X+PHI), WHERE PHI=ARCTAN(C /C ).
# 0 1 1 0 # 0 1 0 1 1 0
# #
# THE MOON IS LOCATED VIA FOUR ANGLES, THE FIRST IS THE OBLIQUITY. THE SECOND IS THE MEAN LONGITUDE OF THE MOON, # THE MOON IS LOCATED VIA FOUR ANGLES. THE FIRST IS THE OBLIQUITY. THE SECOND IS THE MEAN LONGITUDE OF THE MOON,
# MEASURED IN THE ECLIPTIC FROM THE MEAN EQUINOX TO THE MEAN ASCENDING NODE OF THE LUNAR ORBIT, AND THEN ALONG THE # MEASURED IN THE ECLIPTIC FROM THE MEAN EQUINOX TO THE MEAN ASCENDING NODE OF THE LUNAR ORBIT, AND THEN ALONG THE
# ORBIT. THE THIRD ANGLE IS THE ANGLE BETWEEN THE ECLIPTIC AND THE LUNAR ORBIT. THE FOURTH ANGLE IS THE LONGITUDE # ORBIT. THE THIRD ANGLE IS THE ANGLE BETWEEN THE ECLIPTIC AND THE LUNAR ORBIT. THE FOURTH ANGLE IS THE LONGITUDE
# OF THE NODE OF THE MOON, MEASURED IN THE LUNAR ORBIT. LET THESE ANGLES BE OBL,LOM,IM, AND LON RESPECTIVELY. # OF THE NODE OF THE MOON, MEASURED IN THE LUNAR ORBIT. LET THESE ANGLES BE OBL,LOM,IM, AND LON RESPECTIVELY.
# #
# THE SIMPLIFIED POSITION VECTOR OF THE MOON IS # THE SIMPLIFIED POSITION VECTOR OF THE MOON IS
# _ # -
# M=(COS(LOM), COS(OBL)*SIN(LOM)-SIN(OBL)*SIN(IM)*SIN(LOM-LON), SIN(OBL)*SIN(LOM)+COS(OBL)*SIN(IM)*SIN(LOM-LON)) # M=(COS(LOM), COS(OBL)*SIN(LOM)-SIN(OBL)*SIN(IM)*SIN(LOM-LON), SIN(OBL)*SIN(LOM)+COS(OBL)*SIN(IM)*SIN(LOM-LON))
# #
# WHERE # WHERE
@ -69,60 +67,49 @@
# 0 R 0 1 0 1 # 0 R 0 1 0 1
# LON=LON +LON # LON=LON +LON
# 0 R # 0 R
# A , A , B AND B ARE STORE AS AMOD AND BMOD (SEE DESCRIPTION OF CMOD, ABOVE). COS(OBL), SIN(OBL)*SIN(IM), # A , A , B AND B ARE STORED AS AMOD AND BMOD (SEE DESCRIPTION OF CMOD, ABOVE). COS(OBL), SIN(OBL)*SIN(IM),
# 0 1 0 1 # 0 1 0 1
# SIN(OBL), AND COS(OBL)*SIN(IM) ARE STORED IN KONMAT AS K1, K2, K3, AND K4, RESPECTIVELY. LOM , LOM , LON , LON # SIN(OBL), AND COS(OBL)*SIN(IM) ARE STORED IN KONMAT AS K1, K2, K3 AND K4, RESPECTIVELY. LOM , LOM , LON , LON
# 0 R 0 R # ARE STORED AS LOMO, LOMR, LONO, AND LONR IN RATESP. 0 R 0 R
# ARE STORED AS LOM0, LOMR, LON0, AND LONR IN RATESP.
#
# THE THREE PHIS ARE STORED AS AARG, BARG, AND CARG(SUN). ALL CONSTANTS ARE UPDATED BY YEAR. # THE THREE PHIS ARE STORED AS AARG, BARG, AND CARG(SUN). ALL CONSTANTS ARE UPDATED BY YEAR.
# #
# CALLING SEQUENCE # CALLING SEQUENCE
# Page 985 # Page 985
# CALL LSPOS. RETURN IS VIA CPRET. # CALL LSPOS. RETURN IS VIA QPRET.
#
# ALARMS OR ABORTS # ALARMS OR ABORTS
# NONE # NONE
#
# ERASABLE INITIALIZATION REQUIRED # ERASABLE INITIALIZATION REQUIRED
# TEPHEM -- TIME FROM MIGNIGHT 1 JULY PRECEDING THE LAUNCH TO THE TIME OF THE LAUNCH (WHEN THE AGC CLOCK WENT # TEPHEM - TIME FROM MIGNIGHT 1 JULY PRECEDING THE LAUNCH TO THE TIME OF THE LAUNCH (WHEN THE AGC CLOCK WENT
# TO ZERO). TEPHEM IS TP WITH UNITS OF CENTI-SECONDS. # TO ZERO). TEPHEM IS TP WITH UNITS OF CENTI-SECONDS.
#
# TIME2 AND TIME1 ARE IN MPAC AND MPAC +1 WHEN PROGRAM IS CALLED. # TIME2 AND TIME1 ARE IN MPAC AND MPAC +1 WHEN PROGRAM IS CALLED.
#
# OUTPUT # OUTPUT
# UNIT POSITIONAL VECTOR OF SUN IN VSUN. (SCALED B-1) # UNIT POSITIONAL VECTOR OF SUN IN VSUN. (SCALED B-1)
# UNIT POSITIONAL VECTOR OF MOON IN VMOON. (SCALED B-1) # UNIT POSITIONAL VECTOR OF MOON IN VMOON. (SCALED B-1)
#
# SUBROUTINES USED # SUBROUTINES USED
# NONE # NONE
#
# DEBRIS # DEBRIS
# CURRENT CORE SET,WORK AREA AND FREEFLAG # CURRENT CORE SET,WORK AREA AND FREEFLAG
BANK 04 BANK 04
SETLOC EPHEM SETLOC EPHEM
BANK BANK
EBANK= VSUN EBANK= VSUN
COUNT* $$/EPHEM COUNT* $$/EPHEM
LUNPOS EQUALS LSPOS LUNPOS EQUALS LSPOS
LSPOS SETPD SR LSPOS SETPD SR
0 0
14D # TP 14D # TP
TAD DDV TAD DDV
# HG comments in [...] are hand written comments in original listing ## Comments in [...] are hand-written notations in original listing
TEPHEM # TIME OF LAUNCH [IN CENTISEC B 42] TEPHEM # TIME OF LAUNCH [in centisec B 42]
CSTODAY # 24 HOURS -- 8640000 CENTI-SECS/DAY B-33 CSTODAY # 24 HOURS-8640000 CENTI-SECS/DAY B-33
STORE TIMEP # T IN DAYS [@ B 9 = 512 DAYS] STORE TIMEP # T IN DAYS [@ B 9 = 512 days]
AXT,1 AXT,2 # [GRANULRITY = 0.164 SEC] AXT,1 AXT,2 # [∴ granularity ≈ 0.164 sec]
0 0
0 0
CLEAR CLEAR
FREEFLAG # SWITCH BIT FREEFLAG # SWITCH BIT
POSITA DLOAD POSITA DLOAD
KONMAT +2 # ZEROS KONMAT +2 # ZERO$
STORE GTMP STORE GTMP
POSITB DLOAD DMP* POSITB DLOAD DMP*
TIMEP # T TIMEP # T
@ -145,7 +132,7 @@ POSITD DLOAD DMP*
RATESP,2 # LOMR,LOSR,LONR RATESP,2 # LOMR,LOSR,LONR
SL DAD* SL DAD*
5D 5D
RATESP +6,2 # LOM0,LOS0,LON0 RATESP +6,2 # LOMO,LOSO,LONO
DSU DSU
GTMP GTMP
STORE STMP,2 # LOM,LOS,LON STORE STMP,2 # LOM,LOS,LON
@ -184,7 +171,7 @@ POSITE DLOAD
STORE GTMP STORE GTMP
GOTO GOTO
POSITD POSITD
LUNVEL RVQ LUNVEL RVQ # TO FOOL INTEGRATION
SETLOC EPHEM1 SETLOC EPHEM1
BANK BANK