source: Sophya/trunk/SophyaExt/XephemAstroLib/plans.c@ 2996

/* rewritten for Bureau des Longitude theories by Bretagnon and Chapront
 * Michael Sternberg <sternberg@physik.tu-chemnitz.de>
 */
#include <stdio.h>
#include <math.h>

#include "astro.h"
#include "vsop87.h"
#include "chap95.h"

static void pluto_ell (double mj, double *ret);
static void chap_trans (double mj, double *ret);
static void planpos (double mj, int obj, double prec, double *ret);

/* coordinate transformation
 * from:
 *      J2000.0 rectangular equatoreal                  ret[{0,1,2}] = {x,y,z}
 * to:
 *      mean equinox of date spherical ecliptical       ret[{0,1,2}] = {l,b,r}
 */
static void
chap_trans (
double mj,      /* destination epoch */
double *ret)    /* vector to be transformed _IN PLACE_ */
{
        double ra, dec, r, eps;
        double sr, cr, sd, cd, se, ce;

        cartsph(ret[0], ret[1], ret[2], &ra, &dec, &r);
        precess(J2000, mj, &ra, &dec);
        obliquity(mj, &eps);
        sr = sin(ra); cr = cos(ra);
        sd = sin(dec); cd = cos(dec);
        se = sin(eps); ce = cos(eps);
        ret[0] = atan2( sr * ce + sd/cd * se, cr);      /* long */
        ret[1] = asin( sd * ce - cd * se * sr);         /* lat */
        ret[2] = r;                                     /* radius */
}

/* low precision ecliptic coordinates of Pluto from mean orbit.
 * Only for sake of completeness outside available perturbation theories.
 */
static void
pluto_ell (
double mj,      /* epoch */
double *ret)    /* ecliptic coordinates {l,b,r} at equinox of date */
{
        /* mean orbital elements of Pluto.
         * The origin of these is somewhat obscure.
         */
        double  a = 39.543,                     /* semimajor axis, au */
                e = 0.2490,                     /* excentricity */
                inc0 = 17.140,                  /* inclination, deg */
                Om0 = 110.307,                  /* long asc node, deg */
                omeg0 = 113.768,                /* arg of perihel, deg */
                mjp = 2448045.539 - MJD0,       /* epoch of perihel */
                mjeq = J2000,                   /* equinox of elements */
                n = 144.9600/36525.;            /* daily motion, deg */

        double inc, Om, omeg;   /* orbital elements at epoch of date */
        double ma, ea, nu;      /* mean, excentric and true anomaly */
        double lo, slo, clo;    /* longitude in orbit from asc node */

        reduce_elements(mjeq, mj, degrad(inc0), degrad(omeg0), degrad(Om0),
                                &inc, &omeg, &Om);
        ma = degrad((mj - mjp) * n);
        anomaly(ma, e, &nu, &ea);
        ret[2] = a * (1.0 - e*cos(ea));                 /* r */
        lo = omeg + nu;
        slo = sin(lo);
        clo = cos(lo);
        ret[1] = asin(slo * sin(inc));                  /* b */
        ret[0] = atan2(slo * cos(inc), clo) + Om;       /* l */
}

/*************************************************************/

/* geometric heliocentric position of planet, mean ecliptic of date
 * (not corrected for light-time)
 */
static void
planpos (double mj, int obj, double prec, double *ret)
{
        if (mj >= CHAP_BEGIN && mj <= CHAP_END) {
            if (obj >= JUPITER) {               /* prefer Chapront */
                chap95(mj, obj, prec, ret);
                chap_trans (mj, ret);
            } else {                            /* VSOP for inner planets */
                vsop87(mj, obj, prec, ret);
            }
        } else {                                /* outside Chapront time: */
            if (obj != PLUTO) {                 /* VSOP for all but Pluto */
                vsop87(mj, obj, prec, ret);
            } else {                            /* Pluto mean elliptic orbit */
                pluto_ell(mj, ret);
            }
        }
}

/*************************************************************/

/* visual elements of planets
 * [planet][0] = angular size at 1 AU
 * [planet][1] = magnitude at 1 AU from sun and earth and 0 deg phase angle
 * [planet][2] = A
 * [planet][3] = B
 * [planet][4] = C
 *   where mag correction = A*(i/100) + B*(i/100)^2 + C*(i/100)^3
 *      i = angle between sun and earth from planet, degrees
 * from Explanatory Supplement, 1992
 */
static double vis_elements[8][5] = {
        /* Mercury */   { 6.74, -0.36, 3.8, -2.73, 2.00},
        /* Venus */     { 16.92, -4.29, 0.09, 2.39, -.65},
        /* Mars */      { 9.36, -1.52, 1.60, 0., 0.},
        /* Jupiter */   { 196.74, -9.25, 0.50, 0., 0.},
        /* Saturn */    { 165.6, -8.88, 4.40, 0., 0.},
        /* Uranus */    { 65.8, -7.19, 0.28, 0., 0.},
        /* Neptune */   { 62.2, -6.87, 0., 0., 0.},
        /* Pluto */     { 8.2, -1.01, 4.1, 0., 0.}
};

/* given a modified Julian date, mj, and a planet, p, find:
 *   lpd0: heliocentric longitude, 
 *   psi0: heliocentric latitude,
 *   rp0:  distance from the sun to the planet, 
 *   rho0: distance from the Earth to the planet,
 *         none corrected for light time, ie, they are the true values for the
 *         given instant.
 *   lam:  geocentric ecliptic longitude, 
 *   bet:  geocentric ecliptic latitude,
 *         each corrected for light time, ie, they are the apparent values as
 *         seen from the center of the Earth for the given instant.
 *   dia:  angular diameter in arcsec at 1 AU, 
 *   mag:  visual magnitude
 *
 * all angles are in radians, all distances in AU.
 *
 * corrections for nutation and abberation must be made by the caller. The RA 
 *   and DEC calculated from the fully-corrected ecliptic coordinates are then
 *   the apparent geocentric coordinates. Further corrections can be made, if
 *   required, for atmospheric refraction and geocentric parallax.
 */
void
plans (double mj, PLCode p, double *lpd0, double *psi0, double *rp0,
double *rho0, double *lam, double *bet, double *dia, double *mag)
{
        static double lastmj = -10000;
        static double lsn, bsn, rsn;    /* geocentric coords of sun */
        static double xsn, ysn, zsn;    /* cartesian " */
        double lp, bp, rp;              /* heliocentric coords of planet */
        double xp, yp, zp, rho;         /* rect. coords and geocentric dist. */
        double dt;                      /* light time */
        double *vp;                     /* vis_elements[p] */
        double ci, i;                   /* sun/earth angle: cos, degrees */
        int pass;

        /* get sun cartesian; needed only once at mj */
        if (mj != lastmj) {
            sunpos (mj, &lsn, &rsn, &bsn);
            sphcart (lsn, bsn, rsn, &xsn, &ysn, &zsn);
            lastmj = mj;
        }

        /* first find the true position of the planet at mj.
         * then repeat a second time for a slightly different time based
         * on the position found in the first pass to account for light-travel
         * time.
         */
        dt = 0.0;
        for (pass = 0; pass < 2; pass++) {
            double ret[6];

            /* get spherical coordinates of planet from precision routines,
             * retarded for light time in second pass;
             * alternative option:  vsop allows calculating rates.
             */
            planpos(mj - dt, p, 0.0, ret);

            lp = ret[0];
            bp = ret[1];
            rp = ret[2];

            sphcart (lp, bp, rp, &xp, &yp, &zp);
            cartsph (xp + xsn, yp + ysn, zp + zsn, lam, bet, &rho);

            if (pass == 0) {
                /* save heliocentric coordinates at first pass since, being
                 * true, they are NOT to be corrected for light-travel time.
                 */
                *lpd0 = lp;
                range (lpd0, 2.*PI);
                *psi0 = bp;
                *rp0 = rp;
                *rho0 = rho;
            }

            /* when we view a planet we see it in the position it occupied
             * dt days ago, where rho is the distance between it and earth,
             * in AU. use this as the new time for the next pass.
             */
            dt = rho * 5.7755183e-3;
        }

        vp = vis_elements[p];
        *dia = vp[0];

        /* solve plane triangle, assume sun/earth dist == 1 */
        ci = (rp*rp + rho*rho - 1)/(2*rp*rho);

        /* expl supp equation for mag */
        if (ci < -1) ci = -1;
        if (ci >  1) ci =  1;
        i = raddeg(acos(ci))/100.;
        *mag = vp[1] + 5*log10(rho*rp) + i*(vp[2] + i*(vp[3] + i*vp[4]));

        /* rings contribution if SATURN */
        if (p == SATURN) {
            double et, st, set;
            satrings (bp, lp, rp, lsn+PI, rsn, mj+MJD0, &et, &st);
            set = sin(fabs(et));
            *mag += (-2.60 + 1.25*set)*set;
        }
}

/* For RCS Only -- Do Not Edit */
static char *rcsid[2] = {(char *)rcsid, "@(#) $RCSfile: plans.c,v $ $Date: 2005-08-21 10:02:39 $ $Revision: 1.5 $ $Name: not supported by cvs2svn $"};