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slalib/ue2el.f
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211
slalib/ue2el.f
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SUBROUTINE sla_UE2EL (U, JFORMR,
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: JFORM, EPOCH, ORBINC, ANODE, PERIH,
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: AORQ, E, AORL, DM, JSTAT)
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*+
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* - - - - - -
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* U E 2 E L
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* - - - - - -
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*
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* Transform universal elements into conventional heliocentric
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* osculating elements.
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*
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* Given:
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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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* JFORMR i requested element set (1-3; Note 3)
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*
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* Returned:
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* JFORM d element set actually returned (1-3; Note 4)
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* EPOCH d epoch of elements (TT MJD)
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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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* JSTAT i status: 0 = OK
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* -1 = illegal combined mass
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* -2 = illegal JFORMR
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* -3 = position/velocity out of range
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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 2).
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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 universal elements are with respect to the mean equator and
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* equinox of epoch J2000. The orbital elements produced are with
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* respect to the J2000 ecliptic and mean equinox.
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*
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* 3 Three different element-format options are supported:
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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
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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
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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
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*
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* 4 It may not be possible to generate elements in the form
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* requested through JFORMR. The caller is notified of the form
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* of elements actually returned by means of the JFORM argument:
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*
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* JFORMR JFORM meaning
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*
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* 1 1 OK - elements are in the requested format
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* 1 2 never happens
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* 1 3 orbit not elliptical
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*
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* 2 1 never happens
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* 2 2 OK - elements are in the requested format
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* 2 3 orbit not elliptical
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*
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* 3 1 never happens
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* 3 2 never happens
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* 3 3 OK - elements are in the requested format
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*
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* 5 The arguments returned for each value of JFORM (cf Note 6: JFORM
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* may not be the same as JFORMR) are as follows:
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*
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* JFORM 1 2 3
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* EPOCH t0 t0 T
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* ORBINC i i i
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* ANODE Omega Omega Omega
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* PERIH curly pi omega omega
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* AORQ a a q
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* E e e e
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* AORL L M -
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* DM n - -
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*
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* where:
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*
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* t0 is the epoch of the elements (MJD, TT)
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* T " epoch of perihelion (MJD, TT)
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* i " inclination (radians)
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* Omega " longitude of the ascending node (radians)
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* curly pi " longitude of perihelion (radians)
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* omega " argument of perihelion (radians)
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* a " mean distance (AU)
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* q " perihelion distance (AU)
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* e " eccentricity
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* L " longitude (radians, 0-2pi)
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* M " mean anomaly (radians, 0-2pi)
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* n " daily motion (radians)
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* - means no value is set
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*
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* 6 At very small inclinations, the longitude of the ascending node
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* ANODE becomes indeterminate and under some circumstances may be
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* set arbitrarily to zero. Similarly, if the orbit is close to
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* circular, the true anomaly becomes indeterminate and under some
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* circumstances may be set arbitrarily to zero. In such cases,
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* the other elements are automatically adjusted to compensate,
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* and so the elements remain a valid description of the orbit.
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*
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* References:
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*
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* 1 Sterne, Theodore E., "An Introduction to Celestial Mechanics",
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* Interscience Publishers Inc., 1960. Section 6.7, p199.
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*
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* 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
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*
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* Called: sla_PV2EL
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*
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* P.T.Wallace Starlink 18 March 1999
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*
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* Copyright (C) 1999 Rutherford Appleton Laboratory
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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 U(13)
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INTEGER JFORMR,JFORM
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DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM
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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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* Canonical days to seconds
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DOUBLE PRECISION CD2S
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PARAMETER (CD2S=GCON/86400D0)
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INTEGER I
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DOUBLE PRECISION PMASS,DATE,PV(6)
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* Unpack the universal elements.
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PMASS = U(1)-1D0
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DATE = U(3)
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DO I=1,3
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PV(I) = U(I+3)
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PV(I+3) = U(I+6)*CD2S
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END DO
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* Convert the position and velocity etc into conventional elements.
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CALL sla_PV2EL(PV,DATE,PMASS,JFORMR,JFORM,EPOCH,ORBINC,ANODE,
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: PERIH,AORQ,E,AORL,DM,JSTAT)
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END
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