proof(luminary099): page 1169

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# Page 1169
# PROGRAM DESCRIPTION - TIME-RADIUS SUBROUTINE DATE - 11 OCTOBER 1967
# MOD NO. -1 LOG SECTION - CONIC SUBROUTINES
# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88
# MOD NO. -1 LOG SECTION - CONIC SUBROUTINES
# MOD BY KRAUSE ASSEMBLY - COLOSSUS REVISION 88
#
#
# FUNCTIONAL DESCRIPTION -
#
# THIS SUBROUTINE, GIVEN AN INITIAL STATE VECTOR AND A DESIRED RADIUS TO WHICH THE
# STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION,
# PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A
# CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE
# EXTENDED USING OTHER PRIMARY BODIES BY SIMMPE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES,
# ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY.
#
# STATE IS TO BE UPDATED ALONG A CONIC TRAJECTORY, CALCULATES THE CORRESPONDING TIME-OF-FLIGHT AND, IN ADDITION,
# PROVIDES THE OPTION OF COMPUTING THE NEW UPDATED STATE VECTOR. THE RESULTING TRAJECTORY MAY BE A SECTION OF A
# CIRCLE, ELLIPSE, PARABOLA, OR HYPERBOLA WITH RESPECT TO THE EARTH OR THE MOON. THE USE OF THE SUBROUTINE CAN BE
# EXTENDED USING OTHER PRIMARY BODIES BY SIMPLE ADDITIONS TO THE MUTABLE WITHOUT INTRODUCING ANY CODING CHANGES,
# ACCEPTING THE INHERENT SCALE FACTOR CHANGES IN POSITION AND VELOCITY.
# IF THE DESIRED RADIUS IS BEYOND THE RADIUS OF APOCENTER OF THE CONIC OR BELOW THE RADIUS OF PERICENTER,
# APSESW WILL BE SET AND THE SUBROUTINE WILL RETURN THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY.
# APSESW WILL BE SET AND THE SUBROUTINE WILL RETURN THE APOCENTER OR PERICENTER SOLUTION, RESPECTIVELY.
#
#
# THE RESTRICTIONS ARE -
# 1. THE ANGLE BETWEEN ANY POSITION VECTOR AND ITS VELOCITY VECTOR MUST BE GREATER THAN 1 DEGREE 47.5 MINUTES
# AND LESS THAN 178 DEGREES 12.5 MINUTES.
# AND LESS THAN 178 DEGREES 12.5 MINUTES.
# 2. THE PARAMETERS IN THE PROBLEM MUST NOT EXCEED THEIR SCALING LIMITS SPECIFIED IN THE GSOP. IF THE LIMITS
# ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.
# ARE EXCEEDED, THE RESULTING SOLUTION WILL BE MEANINGLESS.
# 3. AN ACCURACY DEGRADATION OCCURS AS THE SENSITIVITIES OF TIME AND UPDATED STATE VECTOR TO CHANGES IN
# RDESIRED INCREASE. THIS WILL OCCUR NEAR EITHER APSIS OF THE CONIC AND WHEN THE CONIC IS NEARLY CIRCULAR. IN
# PARTICULAR, IF THE CONIC IS AN EXACT CIRCLE, THE PROBLEM IS UNDEFINED AND THE SUBROUTINE WILL ABORT.
# RDESIRED INCREASE. THIS WILL OCCUR NEAR EITHER APSIS OF THE CONIC AND WHEN THE CONIC IS NEARLY CIRCULAR. IN
# PARTICULAR, IF THE CONIC IS AN EXACT CIRCLE, THE PROBLEM IS UNDEFINED AND THE SUBROUTINE WILL ABORT.
#
# THE AGC COMPUTATION TIME IS APPROXIMATELY .363 SECONDS
#
# THE AGC COMPUTATION TIME IS APPROXIMATELY .363 SECONDS.
#
# REFERENCES -
# R-479, MISSION PROGRAMMING DEFINITION MEMO NO. 10, LUNAR LANDING MISSION GSOP-SECTION 5.5, SGA MEMO 67-8.
#
# INPUT - ERASABLE INITIALIZATION REQUIRED.
# * SCALE FACTOR *
# VARIABLE *IN POWERS OF 2 * DESCRIPTION AND REMARKS
# -------- *-------------- * -----------------------
# RVEC * +29 FOR EARTH * DP INITIAL POSITION VECTOR IN METERS
# * +27 FOR MOON *
# VVEC * +7 FOR EARTH * DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND
# * +5 FOR MOON *
# RDESIRED * +29 FOR EARTH * DP TERMINAL RADIAL DISTANCE ON CONIC TRAJECTORY FOR WHICH TRANSFER TIME IS TO BE
# * +27 FOR MOON * COMPUTED
# SGNRDOT * NONE * SP TAG SET TO +.5 OR -.5 ACCORDING TO WHETHER THE RADIAL VELOCITY AT RDESIRED IS TO BE
# * * POSITIVE OR NEGATIVE, RESPECTIVELY. THIS TAG REDUCES THE DOUBLE-VALUED PROBLEM TO A
#
# INPUT - ERASABLE INITIALIZATION REQUIRED
#
# * SCALE FACTOR *
# VARIABLE *IN POWERS OF 2* DESCRIPTION AND REMARKS
# -------- *--------------* -----------------------
# RVEC * +29 FOR EARTH* DP INITIAL POSITION VECTOR IN METERS
# * +27 FOR MOON *
# VVEC * +7 FOR EARTH * DP INITIAL VELOCITY VECTOR IN METERS/CENTISECOND
# * +5 FOR MOON *
# RDESIRED * +29 FOR EARTH* DP TERMINAL RADIAL DISTANCE ON CONIC TRAJECTORY FOR WHICH TRANSFER TIME IS TO BE
# * +27 FOR MOON * COMPUTED.
# SGNRDOT * NONE * SP TAG SET TO +.5 OR -.5 ACCORDING TO WHETHER THE RADIAL VELOCITY AT RDESIRED IS TO BE
# * * POSITIVE OR NEGATIVE, RESPECTIVELY. THIS TAG REDUCES THE DOUBLE-VALUED PROBLEM TO A
# Page 1170
# * * SINGLE-VALUED PROBLEM.
# X1 (38D) * NONE * INDEX REGISTER TO BE SET TO -2D OR -10D ACCORDING TO WHETHER THE EARTH OR MOON,