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gust86.cpp
749 lines (652 loc) · 25 KB
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gust86.cpp
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/* gust86.cpp: functions for Uranian satellite coords
Copyright (C) 2010, Project Pluto
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; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/*
** gust86.cpp
** Implementation of the Lascar and Jacobson theory of the
** motion of the satellites of Uranus. Written by Chris Marriott for
** SkyMap, with some modifications by me (Bill J. Gray).
** Based on :
**
** Laskar J., Jacobson, R.: 1987, GUST86 - An analytical ephemeris of the
** Uranian satellites, Astron. Astrophys. 188, 212-224
** http://articles.adsabs.harvard.edu/cgi-bin/nph-journal_query?volume=188&plate_select=NO&page=212&plate=&cover=&journal=A%2BA..
**
** Created: 17-JUL-98
**
** $History: gust86.cpp $
**
1 Feb 2012: BJG: Revised code to avoid errors on stricter compilers
such as OpenWATCOM.
5 Nov 2008: BJG: Revised code to be more C-like and less C++-like,
did general cleanup & simplifying. Now, you can just get positions
and velocities with one relatively simple function.
** 10 Jan 2003: Bill J Gray: changed the output from B1950 to J2000,
** by replacing the Uranicentric-to-B1950 matrix in "Position( )" with
** an Uranicentric-to-J2000 one. (The original code is still available
** with #define ORIGINAL_B1950.)
**
** The individual "per-satellite" functions contained a great deal
** of code identical except for coefficient values; I put that code into
** sum_uranian_series() with the coefficients passed in as arrays.
** Most (though not all!) comments are now in English instead of French.
**
** ***************** Version 1 *****************
** User: Chris Date: 2/10/98 Time: 6:54
** Created in $/SkyMap 4.0
** Moved from solar system DLL into main project.
**
** ***************** Version 2 *****************
** User: Chris Date: 18/07/98 Time: 4:49p
** Updated in $/SkyMap 4.0/SolarSys
** Initial working version.
**
** ***************** Version 1 *****************
** User: Chris Date: 17/07/98 Time: 11:59a
** Created in $/SkyMap 4.0/SolarSys
** Initial version.
*/
#include <math.h>
#include <assert.h>
#include "gust86.h"
#define PI 3.1415926535897932384626433832795028841971693993751058209749445923
#define DEGREES_TO_RADIANS (PI/180.)
static double an[5], ae[5], ai[5]; // satellite position data
// OrbitalPosition
// Compute basic orbital position data for the satellites.
static void gust86_mean_parameters( const double jde )
{
static double curr_jde_set = -1.;
if( jde != curr_jde_set)
{
const double t0 = 2444239.5; // origin date for the theory: 1980 Jan 1
const double days_since_1980 = jde - t0; // time from origin
const double days_per_year = 365.25; // days in a year
const double years_since_1980 = days_since_1980 / days_per_year;
int i; // loop counter
static const double fqn[5] = /* mean motion at epoch in radians/day */
{
4445190.550e-06, 2492952.519e-06, 1516148.111e-06,
721718.509e-06, 466692.120e-06
};
static const double fqe[5] = /* in degrees/year */
{
20.082, 6.217, 2.865, 2.078, 0.386
};
static const double fqi[5] = /* in degrees/year */
{
-20.309, -6.288, -2.836, -1.843, -0.259
};
static const double phn[5] = /* mean longitude at epoch in radians */
{
-238051.e-06, 3098046.e-06, 2285402.e-06,
856359.e-06, -915592.e-06
};
static const double phe[5] = /* in radians */
{
0.611392, 2.408974, 2.067774, 0.735131, 0.426767
};
static const double phi[5] = /* in radians */
{
5.702313, 0.395757, 0.589326, 1.746237, 4.206896
};
// Compute the orbital data.
for( i = 0; i < 5; i++)
{
an[i] = fqn[i] * days_since_1980 + phn[i];
ae[i] = fqe[i] * DEGREES_TO_RADIANS * years_since_1980 + phe[i];
ai[i] = fqi[i] * DEGREES_TO_RADIANS * years_since_1980 + phi[i];
}
}
}
static void sum_uranian_series( double *elems,
const double *ae_series, const double *aet,
const double *ai_series, const double *ait,
const double *amplitudes, const double *phases, int n_extra_terms)
{
int i;
for( i = 2; i < 6; i++)
elems[i] = 0;
for( i = 5; i; i--)
{
elems[2] += *ae_series * cos( *aet );
elems[3] += *ae_series++ * sin( *aet++);
elems[4] += *ai_series * cos( *ait );
elems[5] += *ai_series++ * sin( *ait++);
}
while( n_extra_terms--)
{
elems[2] += *amplitudes * cos( *phases);
elems[3] += *amplitudes++ * sin( *phases++);
}
}
// miranda_elems
// Compute the orbital elements of Miranda.
static void miranda_elems( const double t, double *elems)
{
/* --- Z = K + IH ---- */
static const double ae_series[5] = { 1312.38e-6, 71.81e-6, 69.77e-6,
6.75e-6, 6.27e-6 };
static const double amplitudes[3] = {
-123.31e-6, 39.52e-6, 194.10e-6 };
double phases[3];
/* --- ZETA = Q + IP --- */
static const double ai_series[5] = { 37871.71e-06, +27.01e-06, +30.76e-06,
+12.18e-06, +5.37e-06 };
/* --- RN => mean motion (radians/day) ---- */
elems[0] = 4443522.67e-06
-34.92e-06*cos(an[0]-3.e0*an[1]+2.e0*an[2])
+8.47e-06*cos(2.*an[0]-6.*an[1]+4.*an[2])
+1.31e-06*cos(3.*an[0]-9.*an[1]+6.*an[2])
-52.28e-06*cos(an[0]-an[1])
-136.65e-06*cos(2.*an[0]-2.*an[1]);
/* --- RL => mean longitude (radians) ---- */
elems[1] = -238051.58e-06
+4445190.55e-06*t
+25472.17e-06*sin(an[0]-3.*an[1]+2.*an[2])
-3088.31e-06*sin(2.*an[0]-6.*an[1]+4.*an[2])
-318.10e-06*sin(3.*an[0]-9.*an[1]+6.*an[2])
-37.49e-06*sin(4.*an[0]-12.*an[1]+8.*an[2])
-57.85e-06*sin(an[0]-an[1])
-62.32e-06*sin(2.*an[0]-2.*an[1])
-27.95e-06*sin(3.*an[0]-3.*an[1]);
phases[0] = -an[0] + 2.*an[1];
phases[1] = -2. * an[0] + 3.*an[1];
phases[2] = an[0];
sum_uranian_series( elems, ae_series, ae, ai_series, ai,
amplitudes, phases, 3);
}
// ariel_elems
// Compute the orbital elements of Ariel.
static void ariel_elems( const double t, double *elems)
{
/* --- Z = K + IH --- */
static const double ae_series[5] = { -3.35e-6, 1187.63e-6, 861.59e-6,
71.50e-6, 55.59e-6 };
static const double ai_series[5] = { -121.75e-6, 358.25e-06, 290.08e-06,
97.78e-06, 33.97e-06 };
static const double amplitudes[4] = {
-84.60e-06, +91.81e-06, +20.03e-06, +89.77e-06 };
double phases[4];
/* --- RN => mean motion (radians/day) --- */
elems[0] = 2492542.57e-06
+2.55e-06*cos(an[0]-3.*an[1]+2.*an[2])
-42.16e-06*cos(an[1]-an[2])
-102.56e-06*cos(2.*an[1]-2.*an[2]);
/* --- RL => mean longitude (radians) --- */
elems[1] = 3098046.41e-06
+2492952.52e-06*t
-1860.50e-06*sin(an[0]-3.*an[1]+2.*an[2])
+219.99e-06*sin(2.*an[0]-6.*an[1]+4.*an[2])
+23.10e-06*sin(3.*an[0]-9.*an[1]+6.*an[2])
+4.30e-06*sin(4.*an[0]-12.*an[1]+8.*an[2])
-90.11e-06*sin(an[1]-an[2])
-91.07e-06*sin(2.*an[1]-2.*an[2])
-42.75e-06*sin(3.*an[1]-3.*an[2])
-16.49e-06*sin(2.*an[1]-2.*an[3]);
phases[0] = 2. * an[2] - an[1];
phases[1] = 3. * an[2] - 2. * an[1];
phases[2] = 2. * an[3] - an[1];
phases[3] = an[1];
sum_uranian_series( elems, ae_series, ae, ai_series, ai,
amplitudes, phases, 4);
/*
*---- ZETA = Q + IP ----------------------------------------------------
*/
}
// umbriel_elems
// Compute the orbital elements of Umbriel.
static void umbriel_elems( const double t, double *elems)
{
/* --- Z = K + IH --- */
static const double ae_series[5] = { -0.21e-6, -227.95e-6, 3904.69e-6,
309.17e-6, 221.92e-6 };
static const double ai_series[5] = { -10.86e-6, -81.51e-06, 1113.36e-06,
350.14e-06, 106.50e-06 };
static const double amplitudes[11] = {
29.34e-6, 26.20e-6, 51.19e-6, -103.86e-6, -27.16e-6,
-16.22e-6, 549.23e-6, 34.70e-6, 12.81e-6, 21.81e-6,
46.25e-6 };
double phases[11];
/* --- RN => mean motion (radians/day) --- */
elems[0] = 1515954.90e-06
+9.74e-06*cos(an[2]-2.*an[3]+ae[2])
-106.00e-06*cos(an[1]-an[2])
+54.16e-06*cos(2.*an[1]-2.*an[2])
-23.59e-06*cos(an[2]-an[3])
-70.70e-06*cos(2.*an[2]-2.*an[3])
-36.28e-06*cos(3.*an[2]-3.*an[3]);
/* --- RL => mean longitude (radians) --- */
elems[1] = 2285401.69e-06
+1516148.11e-06*t
+660.57e-06*sin(an[0]-3.*an[1]+2.*an[2])
-76.51e-06*sin(2.*an[0]-6.*an[1]+4.*an[2])
-8.96e-06*sin(3.*an[0]-9.*an[1]+6.*an[2])
-2.53e-06*sin(4.*an[0]-12.*an[1]+8.*an[2])
-52.91e-06*sin(an[2]-4.*an[3]+3.*an[4])
-7.34e-06*sin(an[2]-2.*an[3]+ae[4])
-1.83e-06*sin(an[2]-2.*an[3]+ae[3])
+147.91e-06*sin(an[2]-2.*an[3]+ae[2]);
elems[1] += -7.77e-06*sin(an[2]-2.*an[3]+ae[1])
+97.76e-06*sin(an[1]-an[2])
+73.13e-06*sin(2.*an[1]-2.*an[2])
+34.71e-06*sin(3.*an[1]-3.*an[2])
+18.89e-06*sin(4.*an[1]-4.*an[2])
-67.89e-06*sin(an[2]-an[3])
-82.86e-06*sin(2.*an[2]-2.*an[3]);
elems[1] += -33.81e-06*sin(3.*an[2]-3.*an[3])
-15.79e-06*sin(4.*an[2]-4.*an[3])
-10.21e-06*sin(an[2]-an[4])
-17.08e-06*sin(2.*an[2]-2.*an[4]);
phases[0] = an[1];
phases[1] = an[2];
phases[2] = -an[1]+2.*an[2];
phases[3] = -2.*an[1]+3.*an[2];
phases[4] = -3.*an[1]+4.*an[2];
phases[5] = an[3];
phases[6] = -an[2]+2.*an[3];
phases[7] = -2.*an[2]+3.*an[3];
phases[8] = -3.*an[2]+4.*an[3];
phases[9] = -an[2]+2.*an[4];
phases[10] = an[2];
sum_uranian_series( elems, ae_series, ae, ai_series, ai,
amplitudes, phases, 11);
/*
*---- ZETA = Q + IP ----------------------------------------------------
*/
}
// titania_elems
// Compute the orbital elements of Titania.
static void titania_elems( const double t, double *elems)
{
static const double ae_series[5] = { -0.02e-6, -1.29e-6, -324.51e-6,
932.81e-6, 1120.89e-6 };
static const double ai_series[5] = { -1.43e-6, -1.06e-06, -140.13e-06,
685.72e-06, 378.32e-06 };
static const double amplitudes[13] = {
33.86e-6, 17.46e-6, 16.58e-6, 28.89e-6, -35.86e-6,
-17.86e-6, -32.10e-6, -177.83e-6, 793.43e-6, 99.48e-6,
44.83e-6, 25.13e-6, 15.43e-6 };
double phases[13];
/* --- RN => mean motion (radians/day) --- */
elems[0] = 721663.16e-06
-2.64e-06*cos(an[2]-2.*an[3]+ae[2])
-2.16e-06*cos(2.*an[3]-3.*an[4]+ae[4])
+6.45e-06*cos(2.*an[3]-3.*an[4]+ae[3])
-1.11e-06*cos(2.*an[3]-3.*an[4]+ae[2]);
elems[0] += -62.23e-06*cos(an[1]-an[3])
-56.13e-06*cos(an[2]-an[3])
-39.94e-06*cos(an[3]-an[4])
-91.85e-06*cos(2.*an[3]-2.*an[4])
-58.31e-06*cos(3.*an[3]-3.*an[4])
-38.60e-06*cos(4.*an[3]-4.*an[4])
-26.18e-06*cos(5.*an[3]-5.*an[4])
-18.06e-06*cos(6.*an[3]-6.*an[4]);
/* --- RL => mean longitude (radians) --- */
elems[1] = 856358.79e-06
+721718.51e-06*t
+20.61e-06*sin(an[2]-4.*an[3]+3.*an[4])
-2.07e-06*sin(an[2]-2.*an[3]+ae[4])
-2.88e-06*sin(an[2]-2.*an[3]+ae[3])
-40.79e-06*sin(an[2]-2.*an[3]+ae[2])
+2.11e-06*sin(an[2]-2.*an[3]+ae[1])
-51.83e-06*sin(2.*an[3]-3.*an[4]+ae[4])
+159.87e-06*sin(2.*an[3]-3.*an[4]+ae[3]);
elems[1] += -35.05e-06*sin(2.*an[3]-3.*an[4]+ae[2])
-1.56e-06*sin(3.*an[3]-4.*an[4]+ae[4])
+40.54e-06*sin(an[1]-an[3])
+46.17e-06*sin(an[2]-an[3])
-317.76e-06*sin(an[3]-an[4])
-305.59e-06*sin(2.*an[3]-2.*an[4])
-148.36e-06*sin(3.*an[3]-3.*an[4])
-82.92e-06*sin(4.*an[3]-4.*an[4]);
elems[1] += -49.98e-06*sin(5.*an[3]-5.*an[4])
-31.56e-06*sin(6.*an[3]-6.*an[4])
-20.56e-06*sin(7.*an[3]-7.*an[4])
-13.69e-06*sin(8.*an[3]-8.*an[4]);
phases[0] = an[1];
phases[1] = an[3];
phases[2] = -an[1]+2.*an[3];
phases[3] = an[2];
phases[4] = -an[2]+2.*an[3];
phases[5] = an[3];
phases[6] = an[4];
phases[7] = -an[3]+2.*an[4];
phases[8] = -2.*an[3]+3.*an[4];
phases[9] = -3.*an[3]+4.*an[4];
phases[10] = -4.*an[3]+5.*an[4];
phases[11] = -5.*an[3]+6.*an[4];
phases[12] = -6.*an[3]+7.*an[4];
sum_uranian_series( elems, ae_series, ae, ai_series, ai,
amplitudes, phases, 13);
/*
*---- ZETA= Q + IP ----------------------------------------------------
*/
}
// oberon_elems
// Compute the orbital elements of Oberon.
static void oberon_elems( const double t, double *elems)
{
static const double ae_series[5] = { 0.00e-6, -0.35e-6, 74.53e-6,
-758.68e-6, 1397.34e-6 };
static const double ai_series[5] = { -0.44e-6, -0.31e-06, 36.89e-06,
-596.33e-06, 451.69e-06 };
static const double amplitudes[12] = {
39.00e-6, 17.66e-6, 32.42e-6, 79.75e-6, 75.66e-6, 134.04e-6,
-987.26e-6, -126.09e-6, -57.42e-6, -32.41e-6, -19.99e-6, -12.94e-6 };
double phases[12];
/* --- RN => mean motion (radians/day) --- */
elems[0] = 466580.54e-06
+2.08e-06*cos(2.*an[3]-3.*an[4]+ae[4])
-6.22e-06*cos(2.*an[3]-3.*an[4]+ae[3])
+1.07e-06*cos(2.*an[3]-3.*an[4]+ae[2])
-43.10e-06*cos(an[1]-an[4]);
elems[0] += -38.94e-06*cos(an[2]-an[4])
-80.11e-06*cos(an[3]-an[4])
+59.06e-06*cos(2.*an[3]-2.*an[4])
+37.49e-06*cos(3.*an[3]-3.*an[4])
+24.82e-06*cos(4.*an[3]-4.*an[4])
+16.84e-06*cos(5.*an[3]-5.*an[4]);
elems[1] = -915591.80e-06
+466692.12e-06*t
-7.82e-06*sin(an[2]-4.*an[3]+3.*an[4])
+51.29e-06*sin(2.*an[3]-3.*an[4]+ae[4])
-158.24e-06*sin(2.*an[3]-3.*an[4]+ae[3])
+34.51e-06*sin(2.*an[3]-3.*an[4]+ae[2])
+47.51e-06*sin(an[1]-an[4])
+38.96e-06*sin(an[2]-an[4])
+359.73e-06*sin(an[3]-an[4]);
elems[1] += 282.78e-06*sin(2.*an[3]-2.*an[4])
+138.60e-06*sin(3.*an[3]-3.*an[4])
+78.03e-06*sin(4.*an[3]-4.*an[4])
+47.29e-06*sin(5.*an[3]-5.*an[4])
+30.00e-06*sin(6.*an[3]-6.*an[4])
+19.62e-06*sin(7.*an[3]-7.*an[4])
+13.11e-06*sin(8.*an[3]-8.*an[4]);
phases[0] = an[1];
phases[1] = -an[1]+2.*an[4];
phases[2] = an[2];
phases[3] = an[3];
phases[4] = an[4];
phases[5] = -an[3]+2.*an[4];
phases[6] = -2.*an[3]+3.*an[4];
phases[7] = -3.*an[3]+4.*an[4];
phases[8] = -4.*an[3]+5.*an[4];
phases[9] = -5.*an[3]+6.*an[4];
phases[10] = -6.*an[3]+7.*an[4];
phases[11] = -7.*an[3]+8.*an[4];
sum_uranian_series( elems, ae_series, ae, ai_series, ai,
amplitudes, phases, 12);
/*
*---- ZETA = Q + IP ---------------------------------------------------
*/
}
// keplkh
// Solve Kepler's equation.
static double keplkh( const double rl, const double rk, const double rh)
{
/*
SUBROUTINE KEPLKH (RL,RK,RH,F,IT,IPRT)
*
*---- KEPLKH 1.0 12 DECEMBRE 1985 J. LASKAR --------------------------
*
* RESOLUTION DE L'EQUATION DE KEPLER EN VARIABLES LONGITUDES, K, H
*
*-----------------------------------------------------------------------
*
*/
const double eps = 1.0e-16;
double f;
double f0, e0;
const int itmax = 20;
int it;
if( rl==0.0)
return( 0.);
f0 = rl;
e0 = fabs(rl);
for( it=0; it<itmax; it++)
{
int k = 0;
const double sf = sin(f0);
const double cf = cos(f0);
double e;
const double ff0 = f0 - rk*sf + rh*cf - rl;
const double fpf0 = 1.0 - rk*cf - rh*sf;
double sdir = ff0/fpf0;
double sdir_over_2_to_the_kth = sdir;
do
{
f = f0 - sdir_over_2_to_the_kth;
e = fabs(f - f0);
if (e>e0)
{
k++;
sdir_over_2_to_the_kth *= .5;
}
}
while( e > e0);
if (k==0 && e<=eps && ff0<=eps)
it = itmax; /* time to break out of loop */
else
{
f0 = f;
e0 = e;
}
}
return( f);
}
// ellipx
// Compute rectangular coordinates from a set of orbital elements.
static void ellipx( const double ell[6], const double rmu, double xyz[6] )
{
/*
SUBROUTINE ELLIPX (ELL,RMU,XYZ,DXYZ,IDER,IPRT)
*
*---- ELLIPX 1.1 18 March 1986 J. LASKAR -----------------------------
*
* Calculate Cartesian coordinates (positions & velocities) and their
* partial derivatives with respect to orbital elements, given the
* orbital elements as input.
*
* ELL(6) : Orbital elements A: Semimajor axis
* L: Mean longitude
* K: ecc*COS(LONG asc node+ ARG PERI)
* H: ecc*SIN(LONG asc node+ ARG PERI)
* Q: SIN(Incl/2)*COS(asc node)
* P: SIN(Incl/2)*SIN(asc node)
* RMU : Constant of gravitation for the two-body problem
* RMU = G*M1*(1+M2/M1) M1 Central mass
* M2 Satellite mass
* XYZ(6) : State vector; 0..2 = position, 3..5 = velocity
* (The following three items were in the original code,
* but have been removed:)
* DXYZ(6,7) : Partial derivatives of the state vector with respect to
* the six orbital elements...
* DXYZ(I,J)=DRON(XYZ(I))/DRON(ELL(J))
* ...and with respect to the total GM:
* DXYZ(I,7)=DRON(XYZ(I))/DRON(RMU)
* IDER : 0 Get the state vector only, or...
* 1 Get the partial derivatives also
* IPRT : Print out results (not used)
*
* Subroutine used: KEPLKH
*/
double rot[2][3];
double tx1[2], tx1t[2];
double ra, rl, rk, rh, rp, rq;
double rn, phi, psi, rki;
int i, j;
double f, sf, cf;
double rlmf, umrsa, asr, rna2sr;
/*
*---- ELEMENTS UTILES --------------------------------------------------
*/
ra=ell[0];
rl=ell[1];
rk=ell[2];
rh=ell[3];
rq=ell[4];
rp=ell[5];
rn=sqrt(rmu/(ra*ra*ra));
phi=sqrt( 1.0 - rk*rk - rh*rh );
rki = sqrt( 1.0 - rq*rq - rp*rp );
psi = 1.0/(1.0 + phi);
/*
*---- Rotational matrix: ----------------------------------------------
*/
rot[0][0] = 1.0 - 2*rp*rp;
rot[1][0] = 2*rp*rq;
rot[0][1] = 2*rp*rq;
rot[1][1] = 1.0 - 2*rq*rq;
rot[0][2] = -2*rp*rki;
rot[1][2] = 2*rq*rki;
/*
*---- CALCUL DE LA LONGITUDE EXCENTRIQUE F -----------------------------
*---- F = ANOMALIE EXCENTRIQUE E + LONGITUDE DU PERIAPSE OMEGAPI -------
*/
f = keplkh( rl, rk, rh);
sf =sin(f);
cf =cos(f);
rlmf =-rk*sf+rh*cf;
umrsa =rk*cf+rh*sf;
asr =1.0/(1.0-umrsa);
rna2sr=rn*ra*asr;
/*
*---- CALCUL DE TX1 ET TX1T --------------------------------------------
tx1 = (x, y) location of satellite in the plane of its own orbit,
tx1t = (vx, vy) in similar plane, z = vz = 0.
*/
tx1[0] =ra*(cf-psi*rh*rlmf-rk);
tx1[1] =ra*(sf+psi*rk*rlmf-rh);
tx1t[0]=rna2sr*(-sf+psi*rh*umrsa);
tx1t[1]=rna2sr*( cf-psi*rk*umrsa);
/*
*---- CALCUL DE XYZ ----------------------------------------------------
Now rotate from the plane of the orbit to the plane of Uranus' equator.
*/
for (i=0; i<3; i++)
{
xyz[i] =0.0;
xyz[i+3]=0.0;
for (j=0; j<2; j++)
{
xyz[i] += rot[j][i]*tx1[j];
xyz[i+3] += rot[j][i]*tx1t[j];
}
}
}
// Position
// Compute position and velocity components for a single satellite
// at a specified time.
#define VERY_VERBOSE_OUTPUT
/* Define the above to get a "play-by-play" of what values are */
/* computed. Should make it easier to build an implementation */
/* of this theory, since you can get test values... */
#ifdef VERY_VERBOSE_OUTPUT
#include <stdio.h>
#endif
void __stdcall gust86_posn( const double jde, const int isat, double *r )
// Input arguments:
// jde Julian date, TDT
// isat Satellite index
//
// Output arguments
// r Data array [0..2] position, [3..5] velocity components.
// These are equatorial rectangular coordinates in km and
// km/sec respectively, referred to epoch J2000.0.
{
static const double gms[5] =
{ // GM of each of the five satellites
4.4, 86.1, 84.0, 230.0, 200.0 // in km^3/s^2
};
const double AU_in_km = 149597870.0; // 1AU in km
// NOTE: modern value is 149597870.7, 700 m larger
const double t0 = 2444239.5; // origin date for the theory = 1980 Jan 1
const double gmsu = 5794554.5; // Total GM of Uranus plus satellites,
// in km^3/s^2
const double gmu = gmsu - (gms[0]+gms[1]+gms[2]+gms[3]+gms[4]);
/* Above is GM of Uranus alone, without the satellites */
/* Satellite GMs sum to 604.5; gmu = 5794950.5 */
const double rmu = gmu + gms[isat];
/* Above is GM of Uranus plus the satellite we want */
const double seconds_per_day = 24. * 60. * 60.;
const double seconds_per_day_squared = seconds_per_day * seconds_per_day;
const double days_since_1980 = jde - t0;
double el[6], xu[6];
int i, j;
/*---- INITIALISATIONS --------------------------------------------------*/
/*---- Test parameters: ----------------------------------------------*/
gust86_mean_parameters( jde);
// The function to call depends on the satellite.
switch (isat)
{
case GUST86_ARIEL:
ariel_elems( days_since_1980, el);
break;
case GUST86_UMBRIEL:
umbriel_elems( days_since_1980, el);
break;
case GUST86_TITANIA:
titania_elems( days_since_1980, el);
break;
case GUST86_OBERON:
oberon_elems( days_since_1980, el);
break;
case GUST86_MIRANDA:
miranda_elems( days_since_1980, el);
break;
default: /* should never happen */
assert( 1);
return;
}
#ifdef VERY_VERBOSE_OUTPUT
printf( "Asked for satellite %d at JDE %f\n", isat, jde);
printf( "elems %f %f %f %f %f %f\n",
el[0], el[1], el[2], el[3], el[4], el[5]);
#endif
/* el[0] from the above actually gives the mean motion, in radians
per day. Use Kepler's 3rd law to convert this to a semimajor
axis in kilometers. */
el[0] = pow( rmu*seconds_per_day_squared/(el[0] * el[0]), 1.0/3.0 );
/*---- Calculate Uranicentric XYZ coordinates (position & velocity) ----- */
ellipx( el, rmu, xu );
#ifdef VERY_VERBOSE_OUTPUT
printf( " Revised el[0]: %f km\n", el[0]);
printf( " Posn/vel in Uranus' plane:\n");
printf( " %14.6f %14.6f %14.6f km\n", xu[0], xu[1], xu[2]);
printf( " %14.6f %14.6f %14.6f km/s\n", xu[3], xu[4], xu[5]);
#endif
for( i=0; i<6; i++)
r[i] = 0.0;
/* Output is in the Uranicentric frame of reference. Doing */
/* a matrix multiply by 'trans' converts to J2000. See */
/* 'gust_ref.cpp' for details as to how this matrix was made. */
for( i=0; i<3; i++)
for( j=0; j<3; j++)
{
const double trans[3][3] = {
{ 0.9753206898, -0.2207422915, 0.0047321138},
{ 0.0619432123, 0.2529905682, -0.9654837185},
{ 0.2119259083, 0.9419493686, 0.2604204221} };
r[i] += trans[j][i]*xu[j];
r[i+3] += trans[j][i]*xu[j+3];
}
#ifdef VERY_VERBOSE_OUTPUT
printf( " Posn/vel in J2000:\n");
printf( " %14.6f %14.6f %14.6f km\n", r[0], r[1], r[2]);
printf( " %14.6f %14.6f %14.6f km/s\n", r[3], r[4], r[5]);
#endif
for (i=0; i<6; i++) /* scale output to be in AU & AU/s */
r[i] /= AU_in_km;
}