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slalib/el2ue.f
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328
slalib/el2ue.f
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SUBROUTINE sla_EL2UE (DATE, JFORM, EPOCH, ORBINC, ANODE,
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: PERIH, AORQ, E, AORL, DM,
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: U, JSTAT)
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*+
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* - - - - - -
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* E L 2 U E
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* - - - - - -
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*
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* Transform conventional osculating orbital elements into "universal"
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* form.
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*
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* Given:
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* DATE d epoch (TT MJD) of osculation (Note 3)
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* JFORM i choice of element set (1-3, Note 6)
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* EPOCH d epoch (TT MJD) of the elements
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* ORBINC d inclination (radians)
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* ANODE d longitude of the ascending node (radians)
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* PERIH d longitude or argument of perihelion (radians)
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* AORQ d mean distance or perihelion distance (AU)
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* E d eccentricity
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* AORL d mean anomaly or longitude (radians, JFORM=1,2 only)
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* DM d daily motion (radians, JFORM=1 only)
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*
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* Returned:
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* U d(13) universal orbital elements (Note 1)
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*
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* (1) combined mass (M+m)
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* (2) total energy of the orbit (alpha)
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* (3) reference (osculating) epoch (t0)
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* (4-6) position at reference epoch (r0)
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* (7-9) velocity at reference epoch (v0)
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* (10) heliocentric distance at reference epoch
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* (11) r0.v0
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* (12) date (t)
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* (13) universal eccentric anomaly (psi) of date, approx
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*
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* JSTAT i status: 0 = OK
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* -1 = illegal JFORM
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* -2 = illegal E
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* -3 = illegal AORQ
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* -4 = illegal DM
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* -5 = numerical error
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*
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* Called: sla_UE2PV, sla_PV2UE
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*
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* Notes
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*
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* 1 The "universal" elements are those which define the orbit for the
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* purposes of the method of universal variables (see reference).
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* They consist of the combined mass of the two bodies, an epoch,
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* and the position and velocity vectors (arbitrary reference frame)
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* at that epoch. The parameter set used here includes also various
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* quantities that can, in fact, be derived from the other
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* information. This approach is taken to avoiding unnecessary
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* computation and loss of accuracy. The supplementary quantities
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* are (i) alpha, which is proportional to the total energy of the
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* orbit, (ii) the heliocentric distance at epoch, (iii) the
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* outwards component of the velocity at the given epoch, (iv) an
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* estimate of psi, the "universal eccentric anomaly" at a given
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* date and (v) that date.
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*
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* 2 The companion routine is sla_UE2PV. This takes the set of numbers
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* that the present routine outputs and uses them to derive the
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* object's position and velocity. A single prediction requires one
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* call to the present routine followed by one call to sla_UE2PV;
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* for convenience, the two calls are packaged as the routine
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* sla_PLANEL. Multiple predictions may be made by again calling the
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* present routine once, but then calling sla_UE2PV multiple times,
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* which is faster than multiple calls to sla_PLANEL.
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*
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* 3 DATE is the epoch of osculation. It is in the TT timescale
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* (formerly Ephemeris Time, ET) and is a Modified Julian Date
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* (JD-2400000.5).
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*
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* 4 The supplied orbital elements are with respect to the J2000
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* ecliptic and equinox. The position and velocity parameters
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* returned in the array U are with respect to the mean equator and
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* equinox of epoch J2000, and are for the perihelion prior to the
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* specified epoch.
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*
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* 5 The universal elements returned in the array U are in canonical
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* units (solar masses, AU and canonical days).
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*
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* 6 Three different element-format options are available:
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*
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* Option JFORM=1, suitable for the major planets:
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*
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* EPOCH = epoch of elements (TT MJD)
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* ORBINC = inclination i (radians)
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* ANODE = longitude of the ascending node, big omega (radians)
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* PERIH = longitude of perihelion, curly pi (radians)
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* AORQ = mean distance, a (AU)
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* E = eccentricity, e (range 0 to <1)
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* AORL = mean longitude L (radians)
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* DM = daily motion (radians)
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*
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* Option JFORM=2, suitable for minor planets:
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*
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* EPOCH = epoch of elements (TT MJD)
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* ORBINC = inclination i (radians)
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* ANODE = longitude of the ascending node, big omega (radians)
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* PERIH = argument of perihelion, little omega (radians)
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* AORQ = mean distance, a (AU)
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* E = eccentricity, e (range 0 to <1)
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* AORL = mean anomaly M (radians)
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*
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* Option JFORM=3, suitable for comets:
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*
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* EPOCH = epoch of perihelion (TT MJD)
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* ORBINC = inclination i (radians)
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* ANODE = longitude of the ascending node, big omega (radians)
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* PERIH = argument of perihelion, little omega (radians)
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* AORQ = perihelion distance, q (AU)
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* E = eccentricity, e (range 0 to 10)
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*
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* 7 Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
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* not accessed.
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*
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* 8 The algorithm was originally adapted from the EPHSLA program of
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* D.H.P.Jones (private communication, 1996). The method is based
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* on Stumpff's Universal Variables.
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*
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* Reference: Everhart & Pitkin, Am.J.Phys. 51, 712 (1983).
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*
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* Last revision: 8 September 2005
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*
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* Copyright P.T.Wallace. All rights reserved.
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*
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* License:
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program (see SLA_CONDITIONS); if not, write to the
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* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
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* Boston, MA 02111-1307 USA
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*
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*-
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IMPLICIT NONE
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DOUBLE PRECISION DATE
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INTEGER JFORM
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DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM,U(13)
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INTEGER JSTAT
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* Gaussian gravitational constant (exact)
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DOUBLE PRECISION GCON
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PARAMETER (GCON=0.01720209895D0)
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* Sin and cos of J2000 mean obliquity (IAU 1976)
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DOUBLE PRECISION SE,CE
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PARAMETER (SE=0.3977771559319137D0,
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: CE=0.9174820620691818D0)
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INTEGER J
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DOUBLE PRECISION PHT,ARGPH,Q,W,CM,ALPHA,PHS,SW,CW,SI,CI,SO,CO,
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: X,Y,Z,PX,PY,PZ,VX,VY,VZ,DT,FC,FP,PSI,
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: UL(13),PV(6)
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* Validate arguments.
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IF (JFORM.LT.1.OR.JFORM.GT.3) THEN
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JSTAT = -1
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GO TO 9999
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END IF
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IF (E.LT.0D0.OR.E.GT.10D0.OR.(E.GE.1D0.AND.JFORM.NE.3)) THEN
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JSTAT = -2
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GO TO 9999
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END IF
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IF (AORQ.LE.0D0) THEN
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JSTAT = -3
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GO TO 9999
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END IF
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IF (JFORM.EQ.1.AND.DM.LE.0D0) THEN
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JSTAT = -4
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GO TO 9999
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END IF
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*
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* Transform elements into standard form:
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*
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* PHT = epoch of perihelion passage
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* ARGPH = argument of perihelion (little omega)
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* Q = perihelion distance (q)
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* CM = combined mass, M+m (mu)
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IF (JFORM.EQ.1) THEN
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* Major planet.
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PHT = EPOCH-(AORL-PERIH)/DM
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ARGPH = PERIH-ANODE
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Q = AORQ*(1D0-E)
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W = DM/GCON
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CM = W*W*AORQ*AORQ*AORQ
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ELSE IF (JFORM.EQ.2) THEN
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* Minor planet.
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PHT = EPOCH-AORL*SQRT(AORQ*AORQ*AORQ)/GCON
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ARGPH = PERIH
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Q = AORQ*(1D0-E)
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CM = 1D0
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ELSE
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* Comet.
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PHT = EPOCH
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ARGPH = PERIH
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Q = AORQ
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CM = 1D0
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END IF
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* The universal variable alpha. This is proportional to the total
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* energy of the orbit: -ve for an ellipse, zero for a parabola,
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* +ve for a hyperbola.
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ALPHA = CM*(E-1D0)/Q
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* Speed at perihelion.
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PHS = SQRT(ALPHA+2D0*CM/Q)
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* In a Cartesian coordinate system which has the x-axis pointing
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* to perihelion and the z-axis normal to the orbit (such that the
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* object orbits counter-clockwise as seen from +ve z), the
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* perihelion position and velocity vectors are:
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*
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* position [Q,0,0]
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* velocity [0,PHS,0]
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*
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* To express the results in J2000 equatorial coordinates we make a
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* series of four rotations of the Cartesian axes:
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*
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* axis Euler angle
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*
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* 1 z argument of perihelion (little omega)
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* 2 x inclination (i)
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* 3 z longitude of the ascending node (big omega)
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* 4 x J2000 obliquity (epsilon)
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*
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* In each case the rotation is clockwise as seen from the +ve end of
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* the axis concerned.
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* Functions of the Euler angles.
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SW = SIN(ARGPH)
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CW = COS(ARGPH)
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SI = SIN(ORBINC)
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CI = COS(ORBINC)
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SO = SIN(ANODE)
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CO = COS(ANODE)
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* Position at perihelion (AU).
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X = Q*CW
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Y = Q*SW
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Z = Y*SI
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Y = Y*CI
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PX = X*CO-Y*SO
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Y = X*SO+Y*CO
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PY = Y*CE-Z*SE
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PZ = Y*SE+Z*CE
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* Velocity at perihelion (AU per canonical day).
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X = -PHS*SW
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Y = PHS*CW
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Z = Y*SI
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Y = Y*CI
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VX = X*CO-Y*SO
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Y = X*SO+Y*CO
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VY = Y*CE-Z*SE
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VZ = Y*SE+Z*CE
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* Time from perihelion to date (in Canonical Days: a canonical day
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* is 58.1324409... days, defined as 1/GCON).
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DT = (DATE-PHT)*GCON
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* First approximation to the Universal Eccentric Anomaly, PSI,
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* based on the circle (FC) and parabola (FP) values.
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FC = DT/Q
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W = (3D0*DT+SQRT(9D0*DT*DT+8D0*Q*Q*Q))**(1D0/3D0)
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FP = W-2D0*Q/W
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PSI = (1D0-E)*FC+E*FP
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* Assemble local copy of element set.
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UL(1) = CM
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UL(2) = ALPHA
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UL(3) = PHT
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UL(4) = PX
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UL(5) = PY
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UL(6) = PZ
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UL(7) = VX
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UL(8) = VY
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UL(9) = VZ
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UL(10) = Q
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UL(11) = 0D0
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UL(12) = DATE
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UL(13) = PSI
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* Predict position+velocity at epoch of osculation.
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CALL sla_UE2PV(DATE,UL,PV,J)
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IF (J.NE.0) GO TO 9010
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* Convert back to universal elements.
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CALL sla_PV2UE(PV,DATE,CM-1D0,U,J)
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IF (J.NE.0) GO TO 9010
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* OK exit.
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JSTAT = 0
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GO TO 9999
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* Quasi-impossible numerical errors.
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9010 CONTINUE
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JSTAT = -5
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9999 CONTINUE
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END
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