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/*
*+
* Name:
* palEl2ue
* Purpose:
* Transform conventional elements into "universal" form
* Language:
* Starlink ANSI C
* Type of Module:
* Library routine
* Invocation:
* void palEl2ue ( double date, int jform, double epoch, double orbinc,
* double anode, double perih, double aorq, double e,
* double aorl, double dm, double u[13], int *jstat );
* Arguments:
* date = double (Given)
* Epoch (TT MJD) of osculation (Note 3)
* jform = int (Given)
* Element set actually returned (1-3; Note 6)
* epoch = double (Given)
* Epoch of elements (TT MJD)
* orbinc = double (Given)
* inclination (radians)
* anode = double (Given)
* longitude of the ascending node (radians)
* perih = double (Given)
* longitude or argument of perihelion (radians)
* aorq = double (Given)
* mean distance or perihelion distance (AU)
* e = double (Given)
* eccentricity
* aorl = double (Given)
* mean anomaly or longitude (radians, JFORM=1,2 only)
* dm = double (Given)
* daily motion (radians, JFORM=1 only)
* u = double [13] (Returned)
* Universal orbital elements (Note 1)
* - (0) combined mass (M+m)
* - (1) total energy of the orbit (alpha)
* - (2) reference (osculating) epoch (t0)
* - (3-5) position at reference epoch (r0)
* - (6-8) velocity at reference epoch (v0)
* - (9) heliocentric distance at reference epoch
* - (10) r0.v0
* - (11) date (t)
* - (12) universal eccentric anomaly (psi) of date, approx
* jstat = int * (Returned)
* status: 0 = OK
* - -1 = illegal JFORM
* - -2 = illegal E
* - -3 = illegal AORQ
* - -4 = illegal DM
* - -5 = numerical error
* Description:
* Transform conventional osculating elements into "universal" form.
* Authors:
* PTW: Pat Wallace (STFC)
* TIMJ: Tim Jenness (JAC, Hawaii)
* {enter_new_authors_here}
* Notes:
* - The "universal" elements are those which define the orbit for the
* purposes of the method of universal variables (see reference).
* 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.
* - The companion routine is palUe2pv. This takes the set of numbers
* that the present routine outputs and uses them to derive the
* object's position and velocity. A single prediction requires one
* call to the present routine followed by one call to palUe2pv;
* for convenience, the two calls are packaged as the routine
* palPlanel. Multiple predictions may be made by again calling the
* present routine once, but then calling palUe2pv multiple times,
* which is faster than multiple calls to palPlanel.
* - DATE is the epoch of osculation. It is in the TT timescale
* (formerly Ephemeris Time, ET) and is a Modified Julian Date
* (JD-2400000.5).
* - The supplied orbital elements are with respect to the J2000
* ecliptic and equinox. The position and velocity parameters
* returned in the array U are with respect to the mean equator and
* equinox of epoch J2000, and are for the perihelion prior to the
* specified epoch.
* - The universal elements returned in the array U are in canonical
* units (solar masses, AU and canonical days).
* - Three different element-format options are available:
*
* 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 (range 0 to <1)
* 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 (range 0 to <1)
* 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 (range 0 to 10)
*
* - Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
* not accessed.
* - The algorithm was originally adapted from the EPHSLA program of
* D.H.P.Jones (private communication, 1996). The method is based
* on Stumpff's Universal Variables.
*
* See Also:
* Everhart & Pitkin, Am.J.Phys. 51, 712 (1983).
* History:
* 2012-03-12 (TIMJ):
* Initial version taken directly from SLA/F.
* Adapted with permission from the Fortran SLALIB library.
* {enter_further_changes_here}
* Copyright:
* Copyright (C) 2005 Patrick T. Wallace
* Copyright (C) 2012 Science and Technology Facilities Council.
* All Rights Reserved.
* Licence:
* 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 3 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; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02110-1301, USA.
* Bugs:
* {note_any_bugs_here}
*-
*/
#include <math.h>
#include "pal.h"
#include "palmac.h"
void palEl2ue ( double date, int jform, double epoch, double orbinc,
double anode, double perih, double aorq, double e,
double aorl, double dm, double u[13], int *jstat ) {
/* Sin and cos of J2000 mean obliquity (IAU 1976) */
const double SE=0.3977771559319137;
const double CE=0.9174820620691818;
int J;
double PHT,ARGPH,Q,W,CM,ALPHA,PHS,SW,CW,SI,CI,SO,CO,
X,Y,Z,PX,PY,PZ,VX,VY,VZ,DT,FC,FP,PSI,
UL[13],PV[6];
/* Validate arguments. */
if (jform < 1 || jform > 3) {
*jstat = -1;
return;
}
if (e < 0.0 || e > 10.0 || (e >= 1.0 && jform != 3)) {
*jstat = -2;
return;
}
if (aorq <= 0.0) {
*jstat = -3;
return;
}
if (jform == 1 && dm <= 0.0) {
*jstat = -4;
return;
}
/*
* Transform elements into standard form:
*
* PHT = epoch of perihelion passage
* ARGPH = argument of perihelion (little omega)
* Q = perihelion distance (q)
* CM = combined mass, M+m (mu)
*/
if (jform == 1) {
/* Major planet. */
PHT = epoch-(aorl-perih)/dm;
ARGPH = perih-anode;
Q = aorq*(1.0-e);
W = dm/PAL__GCON;
CM = W*W*aorq*aorq*aorq;
} else if (jform == 2) {
/* Minor planet. */
PHT = epoch-aorl*sqrt(aorq*aorq*aorq)/PAL__GCON;
ARGPH = perih;
Q = aorq*(1.0-e);
CM = 1.0;
} else {
/* Comet. */
PHT = epoch;
ARGPH = perih;
Q = aorq;
CM = 1.0;
}
/* The universal variable alpha. This is proportional to the total
* energy of the orbit: -ve for an ellipse, zero for a parabola,
* +ve for a hyperbola. */
ALPHA = CM*(e-1.0)/Q;
/* Speed at perihelion. */
PHS = sqrt(ALPHA+2.0*CM/Q);
/* In a Cartesian coordinate system which has the x-axis pointing
* to perihelion and the z-axis normal to the orbit (such that the
* object orbits counter-clockwise as seen from +ve z), the
* perihelion position and velocity vectors are:
*
* position [Q,0,0]
* velocity [0,PHS,0]
*
* To express the results in J2000 equatorial coordinates we make a
* series of four rotations of the Cartesian axes:
*
* axis Euler angle
*
* 1 z argument of perihelion (little omega)
* 2 x inclination (i)
* 3 z longitude of the ascending node (big omega)
* 4 x J2000 obliquity (epsilon)
*
* In each case the rotation is clockwise as seen from the +ve end of
* the axis concerned.
*/
/* Functions of the Euler angles. */
SW = sin(ARGPH);
CW = cos(ARGPH);
SI = sin(orbinc);
CI = cos(orbinc);
SO = sin(anode);
CO = cos(anode);
/* Position at perihelion (AU). */
X = Q*CW;
Y = Q*SW;
Z = Y*SI;
Y = Y*CI;
PX = X*CO-Y*SO;
Y = X*SO+Y*CO;
PY = Y*CE-Z*SE;
PZ = Y*SE+Z*CE;
/* Velocity at perihelion (AU per canonical day). */
X = -PHS*SW;
Y = PHS*CW;
Z = Y*SI;
Y = Y*CI;
VX = X*CO-Y*SO;
Y = X*SO+Y*CO;
VY = Y*CE-Z*SE;
VZ = Y*SE+Z*CE;
/* Time from perihelion to date (in Canonical Days: a canonical day
* is 58.1324409... days, defined as 1/PAL__GCON). */
DT = (date-PHT)*PAL__GCON;
/* First approximation to the Universal Eccentric Anomaly, PSI,
* based on the circle (FC) and parabola (FP) values. */
FC = DT/Q;
W = pow(3.0*DT+sqrt(9.0*DT*DT+8.0*Q*Q*Q), 1.0/3.0);
FP = W-2.0*Q/W;
PSI = (1.0-e)*FC+e*FP;
/* Assemble local copy of element set. */
UL[0] = CM;
UL[1] = ALPHA;
UL[2] = PHT;
UL[3] = PX;
UL[4] = PY;
UL[5] = PZ;
UL[6] = VX;
UL[7] = VY;
UL[8] = VZ;
UL[9] = Q;
UL[10] = 0.0;
UL[11] = date;
UL[12] = PSI;
/* Predict position+velocity at epoch of osculation. */
palUe2pv( date, UL, PV, &J );
if (J != 0) {
*jstat = -5;
return;
}
/* Convert back to universal elements. */
palPv2ue( PV, date, CM-1.0, u, &J );
if (J != 0) {
*jstat = -5;
return;
}
/* OK exit. */
*jstat = 0;
}
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