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SUBROUTINE slUEEL (U, JFORMR,
: JFORM, EPOCH, ORBINC, ANODE, PERIH,
: AORQ, E, AORL, DM, JSTAT)
*+
* - - - - - -
* U E E L
* - - - - - -
*
* Transform universal elements into conventional heliocentric
* osculating elements.
*
* Given:
* U d(13) universal orbital elements (Note 1)
*
* (1) combined mass (M+m)
* (2) total energy of the orbit (alpha)
* (3) reference (osculating) epoch (t0)
* (4-6) position at reference epoch (r0)
* (7-9) velocity at reference epoch (v0)
* (10) heliocentric distance at reference epoch
* (11) r0.v0
* (12) date (t)
* (13) universal eccentric anomaly (psi) of date, approx
*
* JFORMR i requested element set (1-3; Note 3)
*
* Returned:
* JFORM d element set actually returned (1-3; Note 4)
* EPOCH d epoch of elements (TT MJD)
* ORBINC d inclination (radians)
* ANODE d longitude of the ascending node (radians)
* PERIH d longitude or argument of perihelion (radians)
* AORQ d mean distance or perihelion distance (AU)
* E d eccentricity
* AORL d mean anomaly or longitude (radians, JFORM=1,2 only)
* DM d daily motion (radians, JFORM=1 only)
* JSTAT i status: 0 = OK
* -1 = illegal combined mass
* -2 = illegal JFORMR
* -3 = position/velocity out of range
*
* Notes
*
* 1 The "universal" elements are those which define the orbit for the
* purposes of the method of universal variables (see reference 2).
* They consist of the combined mass of the two bodies, an epoch,
* and the position and velocity vectors (arbitrary reference frame)
* at that epoch. The parameter set used here includes also various
* quantities that can, in fact, be derived from the other
* information. This approach is taken to avoiding unnecessary
* computation and loss of accuracy. The supplementary quantities
* are (i) alpha, which is proportional to the total energy of the
* orbit, (ii) the heliocentric distance at epoch, (iii) the
* outwards component of the velocity at the given epoch, (iv) an
* estimate of psi, the "universal eccentric anomaly" at a given
* date and (v) that date.
*
* 2 The universal elements are with respect to the mean equator and
* equinox of epoch J2000. The orbital elements produced are with
* respect to the J2000 ecliptic and mean equinox.
*
* 3 Three different element-format options are supported:
*
* Option JFORM=1, suitable for the major planets:
*
* EPOCH = epoch of elements (TT MJD)
* ORBINC = inclination i (radians)
* ANODE = longitude of the ascending node, big omega (radians)
* PERIH = longitude of perihelion, curly pi (radians)
* AORQ = mean distance, a (AU)
* E = eccentricity, e
* AORL = mean longitude L (radians)
* DM = daily motion (radians)
*
* Option JFORM=2, suitable for minor planets:
*
* EPOCH = epoch of elements (TT MJD)
* ORBINC = inclination i (radians)
* ANODE = longitude of the ascending node, big omega (radians)
* PERIH = argument of perihelion, little omega (radians)
* AORQ = mean distance, a (AU)
* E = eccentricity, e
* AORL = mean anomaly M (radians)
*
* Option JFORM=3, suitable for comets:
*
* EPOCH = epoch of perihelion (TT MJD)
* ORBINC = inclination i (radians)
* ANODE = longitude of the ascending node, big omega (radians)
* PERIH = argument of perihelion, little omega (radians)
* AORQ = perihelion distance, q (AU)
* E = eccentricity, e
*
* 4 It may not be possible to generate elements in the form
* requested through JFORMR. The caller is notified of the form
* of elements actually returned by means of the JFORM argument:
*
* JFORMR JFORM meaning
*
* 1 1 OK - elements are in the requested format
* 1 2 never happens
* 1 3 orbit not elliptical
*
* 2 1 never happens
* 2 2 OK - elements are in the requested format
* 2 3 orbit not elliptical
*
* 3 1 never happens
* 3 2 never happens
* 3 3 OK - elements are in the requested format
*
* 5 The arguments returned for each value of JFORM (cf Note 6: JFORM
* may not be the same as JFORMR) are as follows:
*
* JFORM 1 2 3
* EPOCH t0 t0 T
* ORBINC i i i
* ANODE Omega Omega Omega
* PERIH curly pi omega omega
* AORQ a a q
* E e e e
* AORL L M -
* DM n - -
*
* where:
*
* t0 is the epoch of the elements (MJD, TT)
* T " epoch of perihelion (MJD, TT)
* i " inclination (radians)
* Omega " longitude of the ascending node (radians)
* curly pi " longitude of perihelion (radians)
* omega " argument of perihelion (radians)
* a " mean distance (AU)
* q " perihelion distance (AU)
* e " eccentricity
* L " longitude (radians, 0-2pi)
* M " mean anomaly (radians, 0-2pi)
* n " daily motion (radians)
* - means no value is set
*
* 6 At very small inclinations, the longitude of the ascending node
* ANODE becomes indeterminate and under some circumstances may be
* set arbitrarily to zero. Similarly, if the orbit is close to
* circular, the true anomaly becomes indeterminate and under some
* circumstances may be set arbitrarily to zero. In such cases,
* the other elements are automatically adjusted to compensate,
* and so the elements remain a valid description of the orbit.
*
* References:
*
* 1 Sterne, Theodore E., "An Introduction to Celestial Mechanics",
* Interscience Publishers Inc., 1960. Section 6.7, p199.
*
* 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
*
* Called: slPVEL
*
* P.T.Wallace Starlink 18 March 1999
*
* Copyright (C) 1999 Rutherford Appleton Laboratory
*
* License:
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program (see SLA_CONDITIONS); if not, write to the
* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301 USA
*
* Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
*-
IMPLICIT NONE
DOUBLE PRECISION U(13)
INTEGER JFORMR,JFORM
DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM
INTEGER JSTAT
* Gaussian gravitational constant (exact)
DOUBLE PRECISION GCON
PARAMETER (GCON=0.01720209895D0)
* Canonical days to seconds
DOUBLE PRECISION CD2S
PARAMETER (CD2S=GCON/86400D0)
INTEGER I
DOUBLE PRECISION PMASS,DATE,PV(6)
* Unpack the universal elements.
PMASS = U(1)-1D0
DATE = U(3)
DO I=1,3
PV(I) = U(I+3)
PV(I+3) = U(I+6)*CD2S
END DO
* Convert the position and velocity etc into conventional elements.
CALL slPVEL(PV,DATE,PMASS,JFORMR,JFORM,EPOCH,ORBINC,ANODE,
: PERIH,AORQ,E,AORL,DM,JSTAT)
END
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