***** File EPGIOTTO.DOC
GIOTTO EXPERIMENTER SUPPORT DATA.
I. Abstract:
A new experimenter support tape (EXSUP5) was made available to
investigating teams and was provided for this disk by Trevor Morley.
The Giotto Ephemeris on that tape represented the most recent
predicted orbit. The Comet Halley orbit corresponded to the latest
ephemeris estimated in ESOC 17.03.86.
The documentation enclosed is adapted from the documentation
for tape EXSUP5, which updated EXSUP4 with the following amendments:-
a detailed tape layout, a sample listing of part of the position data
file, and a sample of position/velocities. In addition, for EXSUP5,
the subroutine PETRA, used to compute Kepler orbits at the home sites
of experimenters, was contained on the tape and is provided here
as a source listing found in appendix A4.
II. Table of Contents:
1. Introduction.
2. Description of Tape EXSUP5.
3. The Position Data File.
3.1 The Control Record.
3.2 The Position Data Record.
4. The Interface/Auxiliary Software.
4.1 Subroutine GIODAT ( interface routine to the sequential
formatted Position Data File ).
4.2 Subroutine TRAVEL ( generation of experimenter support data ).
4.3 Subroutine PETRA ( compute Kepler Orbits ).
5. Station Coordinates.
5.1 General.
5.2 Table of Station Coordinates.
Appendix:
A1 The Position Data File
A2 Source listing of subroutine GIODAT.
A3 Source listing of subroutine TRAVEL.
A4 Source listing of subroutine PETRA.
1. Introduction.
In this document, the Position Data, the interface routine to this data
and the software for generation of experimenter support data, will
be described.
To ensure a safe 'transport' of the Position Data and to limit
potential conversion problems between different computers it has been
decided to deliver this as a sequential access file containing
formatted data.
In addition to this data file the following interface/auxiliary
software can be found on the tape:-
Software for:-
- Acquisition of Position Data from the sequential file and
determination of the approximate velocities derived from
the position data.
- Generation of Giotto experimenter support data ( signal
travel time, etc. ).
In order to reduce the processing time, the use of a binary direct
access file for the Position Data is recommended.
Software for generation of a direct access file from the
formatted sequential file, and for acquisition of Position Data
from this, is not included in this export package.
Please note that the subroutine PETRA is now enclosed in this
export package. See section 4.3 and Appendix A4.
2. Description of tape EXSUP5
Tape EXSUP5 is not described, since the Position data
file and subroutine listings are included in the Appendices.
3. The Position Data File.
In this section the data layout for the position data and control
data for this will be described.
3.1 The Control Record.
The logical Control Record consists of two physical records
each totaling 80 characters per line as shown below by :-
Variable Format Description
--------------------------------------------------------
IY I5 Year in which the tape was
generated.
MO I5 Ditto for month.
DA D16.10 Ditto for day.
NS I5 Size of Position Record in
characters.
NR I5 Number of logical Position
Records.
---------------------------------------------------------
ET1 D16.10 Earliest Epoch - MJD ( E.T )
ET2 D16.10 Latest Epoch - MJD ( E.T )
SUTC D16.10 MJD ( E.T ) at which UTC jumps.
ETUTC1 D16.10 E.T - UTC before SUTC.
ETUTC2 D16.10 E.T - UTC after SUTC.
-----------------------------------------------------------
Note: SUTC and ETUTC2 are T.B.D at present.
SUTC is preset to mjd 13230 ( after latest epoch on file ).
ETUTC2 is preset to ETUTC1.
3.2 The Position Data Record.
The logical Position Data Record consists of three physical
records each totaling 80 characters.
Each logical Position Record is shown below by -:
Variable Format Description
------------------------------------------------------------------------
ET D16.10 Epoch = MJD ( E.T )
PG(1) D16.10 Component of position vector of the Giotto
probe at ET.
PG(2) D16.10 Component of position vector of the Giotto
probe at ET.
PG(3) D16.10 Component of position vector of the Giotto
probe at ET.
PH(1) D16.10 Component of position vector of the Giotto
for Halley's comet.
------------------------------------------------------------------------
PH(2) D16.10 Component of position vector of the Giotto
for Halley's comet.
PH(3) D16.10 Component of position vector of the Giotto
for Halley's comet.
PE(1) D16.10 Component of position vector of the Giotto
for Earth.
PE(2) D16.10 Component of position vector of the Giotto
for Earth.
PE(3) D16.10 Component of position vector of the Giotto
for Earth.
------------------------------------------------------------------------
PS(1) D16.10 Component of position vector of the Giotto
for Sun.
PS(2) D16.10 Component of position vector of the Giotto
for Sun.
PS(3) D16.10 Component of position vector of the Giotto
for Sun.
------------------------------------------------------------------------
Note: Reference frame: M.E.S of 1950.
Origin = solar system barycenter.
Position units: km
Time units: days
The Position Data File is stored in Appendix A1.
4. Interface/Auxiliary Software.
In this section the auxiliary software found on the tape
will be described.
4.1 Subroutine GIODAT ( interface routine to the sequential
formatted Position Data File).
Input variable:
TUTC : Universal coordinated time since 1950.0 in days.
Output variables:
PVG(1-3) : Position of the Giotto probe at time TUTC ( units: km ).
PVG(4-6) : Approximate velocity of the Giotto probe
at time TUTC ( units: km/s ).
PVH(1-3) :
PVH(4-6) : Ditto for Halley's comet.
PVE(1-3) :
PVE(4-6) : Ditto for Earth.
PVS(1-3) :
PVS(4-6) : Ditto for Sun.
The positions will be acquired from the sequential file using
quadratic interpolation.
For the Position Records on the file a time step size was selected
which will give an accuracy better than 1 sigma-error limit.
The approximate velocities are derived from the position data.
A source listing of subroutine GIODAT can be seen in Appendix A2.
4.2 Subroutine TRAVEL ( generation of Experimenter Support Data ).
Subroutine TRAVEL provides the signal travel time between a
station of Earth and the Giotto S/C as well as position of
station and S/C at the times of signal reception and transmission.
The states of the Giotto S/C, the Earth and the sun are acquired
from the formatted Position Data File on unit 7 ( described in
section 3 ) via subroutine GIODAT (described in section 4.1 ).
The station coordinates are computed without precession. Thus an
accuracy of approx. 1 msec for the travel times computed can be
expected.
Input variables:
TUTC : Signal reception time ( Universal Coordinated Time since
1950.0 in days ).
S(3) : Cartesian Coordinates of station in the body fixed system
at Epoch TUTC ( units: km ).
Output variables:
DTG : Signal travel time ( sec ) Giotto S/C - Station
P(1-3): Position of station at TUTC in Heliocentric EME50 ( units: km ).
G(1-3): Ditto for the Giotto S/C at TUTC-DTG.
See Appendix A3 for a source listing of subroutine TRAVEL.
4.3 Subroutine PETRA ( computing of Kepler Orbits ).
About one day prior to the encounter, position and velocity data
for the relevant bodies as well as misc. data, was sent to
the experimenters.
Subroutine PETRA can be used to compute a Kepler orbit, thus
obtaining position/velocities at the Encounter Epoch.
See Appendix A4 for a source listing.
5. The Station Coordinates.
In this section some general comments on station coordinates
will be given as well as a table of coordinates for stations
relevant to the Giotto mission.
5.1 General.
Section 5.2 contains a table with the coordinates of some
stations that are involved in the Giotto mission.
These coordinates are needed in the computation of the signal
travel times between the Giotto S/C and the station ( see
also subroutine TRAVEL ).
The coordinates are Cartesian position vectors ( X,Y,Z ) in
the Body Fixed System.
The X-Y plane of this system is the equatorial plane of
the Earth with the X-axis going through the Greenwich
Meridian.
5.2 Table of Station Coordinates.
Station name X ( km ) Y ( km ) Z ( km )
Carnarvon -2328 5302 -2666
Tidbinbilla -4461 2682 -3675
Madrid 4847 -370 4117
Goldstone -2350 -4652 3666
**********************************************************************
Note added to explanation:
The orbital data applicable to P/Halley encounter were set up using
exactly the same ESOC orbit files as were used at the time for
providing the data tapes to the experimenters. However, for your
purposes, I have increased the number of steps per day (to 27) and
restricted the interval to 5 - 17 March. So that there is no
misunderstanding concerning our definition of MJD:
14 March 1986 = MJD 13221.
Logically speaking, the data set consists of one header record and
325 data records. The total number of physical records is thus 977,
each 80 bytes long.
Use of the interpolation routine GIODAT will result in small
differences compared with the data on the original ESOC files. I have
tested this over the interval and find the average differences to be
7 km for both the spacecraft and the Earth, 10 km for the comet and
only 3 m for the Sun. Around the time of closest approach, because of
the way the ESOC files were set up, these differences are much smaller
than the average, being only a fraction of a km (negligible for the Sun).
To give you a better idea of the accuracy of the data, they are
consistent with a time of closest approach of 1986/03/14 00:02:59.5 UTC
and a miss distance of 629 km. (In March 1986 we did some detailed
analysis, not reflected by the data on the orbit files, and made a best
estimate of 1986/03/14 00:03:00.4 UTC +/- 2 s (1-sigma) and
610 km +/- 40 km (1-sigma)). According to W. Curdt et al. in A & A 191,
L1-L3, 1998, using the HMC data the best estimates are
1986/03/14 00:03:01.84 UTC +/- 0.2 s and 596 km +/- 2 km.
Trevor Morley
ESOC
*************************************************************************
Appendix A1
The Position Data File
1992 40.3000000000D+01 208 325
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Appendix A2
Source Module for Subroutine GIODAT
C-----------------------------------------------------------------------
SUBROUTINE GIODAT(TUTC,PVG,PVH,PVE,PVS,IERR)
C-------------------------------------------------
C S.J ISSUE 04 - 14.01.85
C------------------------
C
************ SUBROUTINE IDENTIFICATION ************
* *
* GIODAT IS AN INTERFACE ROUTINE TO THE EXPERIMENTER SUPPORT DATA *
* FILE ON LOGICAL UNIT 7 WHICH CONTAINS POSITION DATA FOR THE *
* GIOTTO PROBE, HALLEYS COMET, THE EARTH AND THE SUN GIVEN IN THE *
* BARYCENTRIC REFERENCE FRAME OF 1950 ( UNITS = KM ) *
* THE APPROXIMATE VELOCITIES FOR THE FOUR BODIES WILL BE DERIVED *
* FROM THE POSITION DATA AND GIVEN IN KM/S. *
* *
************************************************************************
* *
************ VARIABLE IDENTIFICATIONS *************
* *
***** INPUT VARIABLES ( ARGUMENT LIST ) ***
* *
* TUTC - UNIVERSAL COORDINATED TIME *
* *
***** OUTPUT VARIABLES ( ARGUMENT LIST ) ***
* *
* PVG(1-3) - POSITION OF THE GIOTTO PROBE AT TIME TUTC *
* PVG(4-6) - VELOCITY OF THE GIOTTO PROBE AT TIME TUTC *
* PVH(1-3) *
* PVH(4-6) - DITTO FOR HALLEYS COMET *
* PVE(1-3) *
* PVE(4-6) - DITTO FOR THE EARTH *
* PVS(1-3) *
* PVS(4-6) - DITTO FOR THE SUN *
* IERR - ERROR CODE *
* =0 : NO ERROR *
* =1 : TUTC TOO EARLY *
* =2 : TUTC TOO LATE *
* *
***** LOCAL VARIABLES ***
* *
* ET - MODIFIED JULIAN DAY ( 1950.0 ) *
* PGI(3,3) - TO STORE POSITION DATA FOR THREE SAMPLES FOR THE *
* GIOTTO PROBE. USED IN THE QUADRATIC INTERPOLATION *
* PHI(3,3) - DITTO FOR HALLEYS COMET *
* PEI(3,3) - DITTO FOR THE EARTH *
* PSI(3,3) - DITTO FOR THE SUN *
* T(3) - TO STORE REFERENCE TIME T0 FOR THE INTERPOLATION. *
* SKIP(3) - USED FOR SKIPPING RECORDS ON THE DATA FILE *
* *
***** CONSTANT IDENTIFICATION ***
* *
* HSEC - (STEP SIZE)*86400 *
* LUN - LOGICAL UNIT NUMBER OF FILE/TAPE CONTAINING *
* THE POSITION DATA. *
* STPUTC - STEP IN UTC AT TIME SUTC *
* *
***** TEMPORARY VARIABLES ***
* *
* (1) *
* TMP(1) - 0.5*(P-1)*(P-2) *
* TMP(2) - P*(P-2) *
* TMP(3) - 0.5*P*(P-1) *
* (2) *
* TMP(1) - (P-1.5)/HSEC *
* TMP(2) - (2*P-2)/HSEC *
* TMP(3) - (P-0.5)/HSEC *
* WHERE ET(P) IS THE EPOCH FOR WHICH THE POSITIONS ARE REQUIRED. *
* ( RANGE OF P : 0:2 ) *
* *
************************************************************************
* *
************ TYPE DECLARATION AND STORAGE ALLOCATION ************
* *
IMPLICIT REAL*8(A-H,O-Z)
LOGICAL FIRST
CHARACTER*1 SKIP(3)
DIMENSION PVG(6),PVH(6),PVE(6),PVS(6),PGI(3,3),
& PHI(3,3),PEI(3,3),PSI(3,3),T(3),TMP(3)
DATA FIRST/.TRUE./
DATA LUN/7/
* *
************************************************************************
* *
************ INITIALISE AND VERIFY INPUT DATA ***BLOCK0000
* *
IERR=0
C IF FIRST CALL READ CONTROL RECORD AND SET CONSTANTS
IF(FIRST)THEN
READ(LUN,10) IYGEN,MOGEN,DGEN,NS,NR,ET1,ET2,SUTC,ETUTC1,ETUTC2
10 FORMAT(2I5,D16.10,2I5,/,5D16.10)
C DETERMINE STEP IN UTC AT TIME SUTC
STPUTC=ETUTC2-ETUTC1
C DETERMINE STEP SIZE
H=(ET2-ET1)/(DFLOAT(NR)-1.D0)
HSEC=H*86400.D0
FIRST=.FALSE.
ENDIF
C DETERMINE ET ( MODIFIED JULIAN DAY )
ET=TUTC+ETUTC1
IF(ET.GE.SUTC)ET=ET+STPUTC
C VERIFY EPOCH ON FILE
IF(ET.LT.ET1-1.D-4)GOTO 910
IF(ET.GT.ET2+1.D-4)GOTO 920
DO 20 I=1,6
PVG(I)=0.D0
PVH(I)=0.D0
PVE(I)=0.D0
PVS(I)=0.D0
20 CONTINUE
* *
************************************************************************
* *
******* DETERMINE THE POSITION VECTORS FOR EPOCH ET **BLOCK0100
* *
C FIND RECORD NUMBER
IREC=DINT((ET-ET1)/H)+1
110 CONTINUE
C POSITION THE T0 SAMPLE TO ENSURE T1 AND T2 AVAILABLE
IF(NR-IREC.LT.2)THEN
IREC=IREC-1
GOTO 110
ENDIF
IF(FIRST)THEN
IF(IREC.EQ.1)GOTO 135
DO 130 I=1,IREC-1
READ(LUN,120)SKIP
120 FORMAT(A1)
130 CONTINUE
GOTO 135
ENDIF
IDIF=IREC-IRECOL-1
IF(IDIF.EQ.0)GOTO 135
ISKP=ABS(IDIF)
IF(IDIF.LT.0)THEN
DO 131 I=1,ISKP*3
BACKSPACE LUN
131 CONTINUE
ELSE
DO 132 I=1,ISKP
READ(LUN,120)SKIP
132 CONTINUE
ENDIF
135 CONTINUE
IRECOL=IREC+2
DO 150 I=1,3
READ(LUN,140)T(I),(PGI(I,J),J=1,3),(PHI(I,J),J=1,3),
& (PEI(I,J),J=1,3),(PSI(I,J),J=1,3)
140 FORMAT(5D16.10)
150 CONTINUE
* *
* *
************************************************************************
* *
******* DETERMINE POSITIONS USING QUADRATIC INTERPOLATION **BLOCK0200
* *
P=(ET-T(1))/H
TMP(1)=0.5*(P-1.D0)*(P-2.D0)
TMP(2)=P*(2.D0-P)
TMP(3)=0.5D0*P*(P-1.D0)
DO 220 I=1,3
DO 210 J=1,3
PVG(I)=PVG(I)+PGI(J,I)*TMP(J)
PVH(I)=PVH(I)+PHI(J,I)*TMP(J)
PVE(I)=PVE(I)+PEI(J,I)*TMP(J)
PVS(I)=PVS(I)+PSI(J,I)*TMP(J)
210 CONTINUE
220 CONTINUE
* *
************************************************************************
* *
******* DETERMINE VELOCITIES FROM DERIVATIVES OF POSITIONS **BLOCK0300
* *
TMP(1)=(P-1.5D0)/HSEC
TMP(2)=(2.D0-2.D0*P)/HSEC
TMP(3)=(P-0.5D0)/HSEC
DO 320 I=1,3
I1=I+3
DO 310 J=1,3
PVG(I1)=PVG(I1)+PGI(J,I)*TMP(J)
PVH(I1)=PVH(I1)+PHI(J,I)*TMP(J)
PVE(I1)=PVE(I1)+PEI(J,I)*TMP(J)
PVS(I1)=PVS(I1)+PSI(J,I)*TMP(J)
310 CONTINUE
320 CONTINUE
* *
************************************************************************
* *
************ ERROR MESSAGE BLOCK ***BLOCK0900
* *
GOTO 1000
910 CONTINUE
IERR=1
WRITE(6,911)
911 FORMAT(/' GIOPOS : ET TOO EARLY ')
GOTO 1000
920 CONTINUE
IERR=2
WRITE(6,921)
921 FORMAT(/' GIOPOS : ET TOO LATE ')
1000 CONTINUE
RETURN
END
Appendix A3
Source Module for Subroutine TRAVEL
C-----------------------------------------------------------------------
SUBROUTINE TRAVEL(TUTC,S,DTG,P,G,IER)
C-------------------------------------------------
C ISSUE 01 - 18.01.85
C----------------------
C
************ SUBROUTINE IDENTIFICATION ************
* *
* TRAVEL PROVIDES THE FOLLOWING GIOTTO EXPERIMENTER SUPPORT DATA: *
* - SIGNAL TRAVEL TIME BETWEEN THE GIOTTO S/C AND A STATION ON EARTH *
* - POSITIONS OF STATION AND S/C IN THE HELIOCENTRIC EME50 *
* AT SIGNAL RECEPTION AND TRANSMISSION TIMES INVOLVED. *
* STATION COORDINATES ARE COMPUTED WITHOUT PRECESSION, I.E. *
* THE TRAVEL TIMES GIVEN ARE ACCURATE TO ABOUT 1 MSEC. *
* TRAVEL RETRIEVES THE STATES OF THE PARTICIPATING BODIES FROM *
* THE POSITION DATA FILE BY MEANS OF THE INTERFACE ROUTINE GIODAT. *
* *
************************************************************************
* *
************ VARIABLE IDENTIFICATIONS *************
* *
***** INPUT VARIABLES ( ARGUMENT LIST ) ***
* *
* TUTC - SIGNAL RECEPTION TIME (UTC DAYS SINCE 1950.0) *
* S(1-3) - CARTESIAN COORDINATES OF STATION IN BODY-FIXED SYSTEM *
* *
***** OUTPUT VARIABLES ( ARGUMENT LIST ) ***
* *
* DTG - SIGNAL TRAVEL TIME(SEC) GIOTTO S/C - STATION *
* P(1-3) - POSITION OF STATION AT TUTC IN HELIOCENTRIC EME50 *
* G(1-3) - POSITION OF GIOTTO AT TUTC-DTG IN HELIOCENTRIC EME50 *
* IER - ERROR CODE *
* =0 : NO ERROR *
* =1 : TUTC TOO EARLY, NO DATA ON POSITION DATA FILE *
* =2 : TUTC TOO LATE , NO DATA ON POSITION DATA FILE *
* =3 : NO CONVERGENCE IN SOLUTION OF LIGHT TIME EQUATION*
* *
***** LOCAL VARIABLES OF SPECIAL INTEREST ***
* *
* SG(6) GIOTTO STATE IN BARYCENTRIC EME50 *
* SH(6) - DITTO FOR HALLEYS COMET *
* SU(6) - DITTO FOR SUN *
* *
***** CONSTANT IDENTIFICATION ***
* *
* RJ,RK,RL - COEFFICIENTS IN FORMULA FOR SIDERIAL ANGLE *
* C - VELOCITY OF LIGHT *
* TWOPI - TWO PI *
* *
************************************************************************
* *
************ TYPE DECLARATION AND STORAGE ALLOCATION ************
* *
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION S(3),P(3),G(3),SS(6),SG(6),SH(6),SU(6)
* *
************************************************************************
* *
************ SET CONSTANTS ***BLOCK0000
DATA RJ,RK,RL /0.2769194D0,100.0021359028D0,0.107523D-5/
DATA C,TWOPI /299792.458D0,6.283185307179587D0/
* *
************************************************************************
* *
******* STATION STATE AT TUTC **BLOCK0100
* *
CALL GIODAT(TUTC,SG,SH,SS,SU,IER)
IF(IER.NE.0) RETURN
Y=0.5D0+TUTC/36525.D0
IT=TUTC
X=TUTC-IT
X=(X+RJ+(RK+RL*Y)*Y)*TWOPI
Y=DCOS(X)
Z=DSIN(X)
P(1)=S(1)*Y-S(2)*Z+SS(1)
P(2)=S(1)*Z+S(2)*Y+SS(2)
P(3)=S(3)+SS(3)
G(1)=SU(1)
G(2)=SU(2)
G(3)=SU(3)
* *
************************************************************************
* *
******* SOLUTION OF LIGHT TIME EQUATION **BLOCK0200
* *
DTG=0.D0
DO 210 I=1,5
X=SG(1)-P(1)
Y=SG(2)-P(2)
Z=SG(3)-P(3)
DGB=DSQRT(X*X+Y*Y+Z*Z)
Z=(X*SG(4)+Y*SG(5)+Z*SG(6))/DGB
Y=(DTG-DGB/C)/(1.D0-Z/C)
DTG=DTG-Y
IF(DABS(Y).LT.1.D-4) GOTO 1000
X=TUTC-DTG/864.D2
CALL GIODAT(X,SG,SH,SS,SU,IER)
IF(IER.NE.0) RETURN
210 CONTINUE
* *
************************************************************************
* *
******* ERROR MESSAGES **BLOCK0900
* *
IER=3
WRITE(6,910) IER
910 FORMAT(' TRAVEL ERROR MESSAGE',I3/
&' = NO CONVERGENCE AFTER 5 ITERATIONS'/
&' IN SOLUTION OF LIGHT TIME EQUATION')
* *
************************************************************************
* *
******* SET OUTPUT VARIABLES AND RETURN **BLOCK1000
* *
1000 P(1)=P(1)-G(1)
P(2)=P(2)-G(2)
P(3)=P(3)-G(3)
G(1)=SG(1)-SU(1)
G(2)=SG(2)-SU(2)
G(3)=SG(3)-SU(3)
RETURN
END
Appendix A4
Source Module for Suroutine PETRA
SUBROUTINE PETRA(XMUP,X,INIT,KODE,T,Y,RY,AUT)
CP GIVES STATE VECTOR OF AN ELLIPTICAL, PARABOLICAL OR
CP HYPERBOLICAL TRAJECTORY CENTRED AT THE ORIGIN OF THE COORD. SYST.
C SAME AS 'TRAJEC', EXCEPT FOR ADDITIONAL INPUT: 'XMUP'.
C
CI XMUP = GRAVITY POTENTIAL OF CENTRAL BODY
CI X( ) = POSITION (X(1)..X(3)) AND VELOCITY (X(4)..X(6)), (KM,KM/SEC)
CI INIT = 0 FOR EACH NEW X. OLD VALUE SHOULD HAVE INIT.GT.0
CI KODE = 1 ONLY POSITION IN Y(1)..Y(3)
CI = 2 POSITION + VELOCITY IN Y(1)..Y(6)
CI E = 14: AS 2 + OUTPUT VECTOR AUT(14) FOR PARTIAL DERIVATIVES.
CI T = TIME DIFFERENCE (SEC) BETWEEN X AND Y
C
CO Y( ) = STATE VECTOR AFTER TIME T
CO RY = SQRT(Y(1)**2+Y(2)**2+Y(3)**2) ONLY IF KODE.GE.2
CO AUT(1) = INVERSE SEMI-MAJ.AXIS; NEGATIVE FOR HYPERBOLAE.
CO AUT(2)...AUT(14) = INPUT TO SUBROUTINE 'PEDER' FOR PARTIAL
CO DERIVATIVES. ONLY IF KODE.GE.3
C
IMPLICIT REAL*8(A-H,O-Z)
DIMENSION X(6),Y(6),AUT(KODE),C2(7),C3(7)
DATA KNIT/0/
COEFFICIENTS FOR STUMPFF-FUNCTIONS
DATA C3/0.7650283228592385 D-12,-0.1605953765319026 D-9,
& 0.2505210785999854 D-7,-0.2755731919939401 D-5,
& 0.1984126984129264 D-3, -0.8333333333333568D-2,
& 0.166666666666666665 D0/,C2/0.1147134108311665 D-10,
& -0.2087759200397967 D-8,0.2755731917059028 D-6,
& -0.2480158725995993 D-4,0.1388888888888999 D-2,
& -0.4166666666667176 D-1,0.4999999999999998 D0/
IF(INIT*KNIT .GT. 0) GOTO 115
KNIT = 1
WMUP = DSQRT(XMUP)
RX = DSQRT(X(1)**2+X(2)**2+X(3)**2)
A = 2.D0/RX -(X(4)**2+X(5)**2+X(6)**2)/XMUP
QA = DSQRT(DABS(A))
RVWM= (X(1)*X(4)+X(2)*X(5)+X(3)*X(6))/WMUP
115 TM = T*WMUP
C FIND SUITABLE INITIAL VALUE FOR B AND FOR MAXIMUM STEP LENGTH:
DBMAX = DMAX1(DABS(A*TM),DABS(TM)/RX)
C IF WE ARE FAR OUT ON A PARABOLA:
ATM6 = 6.D0*DABS(TM)
IF(DBMAX**3.LT.ATM6) DBMAX = ATM6**(1.D0/3.D0)
IF(A.GE.-1.D-30) GOTO 135
C IF WE ARE FAR OUT ON A HYPERBOLA:
UP = DABS(TM*QA*A*2.D0)
DO = 1.D0 - A*RX
IF(UP.LE.DO) GOTO 135
DBMAX = DMIN1(DBMAX,DLOG(UP/DO)/QA)
135 B = DSIGN(DBMAX,TM)
C MAXIMUM STEP = 1 RAD FOR A PARABOLA:
IF(A*DBMAX.GT.QA) DBMAX = 1.D0/QA
DB = 0.D0
C END OF INITIALISATION, START NEWTON'S ITERATION FOR ECC. ANOM.
155 W = B*QA
C USE STUMPFF-SERIES WHEN CLOSE TO 0:
IF(DABS(W).GE.0.3D0) GOTO 242
BB = B*B
WW = BB*A
G2 = C2(1)
G3 = C3(1)
DO 221 I=2,7
G2 = G2*WW + C2(I)
221 G3 = G3*WW + C3(I)
G2 = G2*BB
G3 = G3*BB*B
GO = 1.D0-A*G2
G1 = B-A*G3
GOTO 595
242 IF(A.LT.0.D0) GOTO 511
C ONLY ELLIPSES
GO = DCOS(W)
G1 = DSIN(W)/QA
GOTO 553
C ONLY HYPERBOLAE:
511 GO = DCOSH(W)
G1 = DSINH(W)/QA
553 G2 = (1.D0-GO)/A
G3 = (B-G1)/A
595 DOLD = DB
DB = (TM-RX*G1-RVWM*G2-G3
& )/(RX*GO+RVWM*G1+G2)
C DECREASE MAX STEP IF WE HAVE ALTERNATING SIGNS:
IF(DB*DOLD.LT.-1.D-20) DBMAX = DBMAX*0.5D0
C PUT A LIMIT TO THE STEP LENGTH:
DB = DMAX1(-DBMAX,DMIN1(DBMAX,DB))
B = B + DB
CHECK IF WE HAVE CONVERGED:
IF(DABS(DB).GT.DABS(B)*1.D-8) GOTO 155
C ITERATION END; UPDATE THE G'S LINEARLY FROM LAST STEP.
GO = GO-DB*G1*A
G1 = G1+DB*GO
G2 = G2+DB*G1
G3 = G3+DB*G2
FX = 1.D0-G2/RX
GX = T-G3/WMUP
DO 635 J = 1,3
635 Y(J) = FX*X(J)+GX*X(J+3)
AUT(1) = A
IF(KODE .LE. 1) RETURN
RY = DSQRT(Y(1)**2+Y(2)**2+Y(3)**2)
FT = -WMUP*G1/(RX*RY)
GT = 1.D0-G2/RY
DO 660 J=4,6
660 Y(J) = FT*X(J-3)+GT*X(J)
IF(KODE .LE. 2) RETURN
C PREPARATION OF PARTIAL DERIVATIVES
AUT(2)=B
AUT(3)=RVWM
AUT(4)=GO
AUT(5)=G1
AUT(6)=G2
AUT(7)=G3
AUT(8)=RX
AUT(9)=FX
AUT(10)=GX
AUT(11)=FT
AUT(12)=GT
AUT(13)=XMUP
AUT(14)=WMUP
RETURN
END
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