source: Sophya/trunk/SophyaExt/XephemAstroLib/chap95.c@ 4058

/* heliocentric rectangular equatorial coordinates of Jupiter to Pluto;
 * from Chapront's expansion of DE200/extension of DE200;  mean equator J2000.0
 *
 * calculation time (milliseconds) on an HP 715/75, Jupiter to Pluto:
 * (each coordinate component counted as 1 term,
 * secular terms included for JD 2448908.5 = 1992 Oct 13.0)
 *
 *      prec    terms   rates   no rates
 *      0.0     2256    5.1     4.6
 *
 *      1e-7    792     2.6     2.4     --> nominal precision rel. to DE200
 *      1e-6    535     2.1     2.0
 *      1e-5    350     1.8     1.6
 *      1e-4    199     1.5     1.4
 *      1e-3    96      1.2     1.1
 *
 *      no drop 2256    4.5     3.9     (code without test criterion)
 */

#include <math.h>

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

#define CHAP_MAXTPOW    2       /* NB: valid for all 5 outer planets */

/* chap95()
 *
 * input:
 *      m       modified JD; days from J1900.0 = 2415020.0
 *
 *      prec    precision level, in radians.
 *              if (prec = 0.0), you get the full precision, namely
 *              a deviation of not more than 0.02 arc seconds (1e-7 rad)
 *              from the JPL DE200 integration, on which this expansion
 *              is based.
 *
 *      obj     object number as in astro.h (jupiter=3, saturn=4, ...)
 *
 * output:
 *      ret[6]  cartesian components of position and velocity
 *
 * return:
 *      0       Ok
 *      1       time out of range [CHAP_BEGIN .. CHAP_END]
 *      2       object out of range [JUPITER .. PLUTO]
 *      3       precision out of range [0.0 .. 1e-3]
 */
int
chap95 (double m, int obj, double prec, double *ret)
{
        static double a0[] = {          /* semimajor axes for precision ctrl */
            0.39, 0.72, 1.5, 5.2, 9.6, 19.2, 30.1, 39.5, 1.0
        };
        double sum[CHAP_MAXTPOW+1][6];  /* [T^0, ..][X,Y,Z,X',Y',Z'] */
        double T, t;                    /* time in centuries and years */
        double ca, sa, Nu;              /* aux vars for terms */
        double precT[CHAP_MAXTPOW+1];   /* T-augmented precision threshold */
        chap95_rec *rec;                /* term coeffs */
        int cooidx;

        /* check parameters */
        if (m < CHAP_BEGIN || m > CHAP_END)
                return (1);

        if (obj < JUPITER || obj > PLUTO)
                return (2);

        if (prec < 0.0 || prec > 1e-3)
                return (3);

        /* init the sums */
        zero_mem ((void *)sum, sizeof(sum));

        T = (m - J2000)/36525.0;        /* centuries since J2000.0 */

        /* modify precision treshold for
         * a) term storing scale
         * b) convert radians to au
         * c) account for skipped terms (more terms needed for better prec)
         *    threshold empirically established similar to VSOP; stern
         * d) augment for secular terms
         */
        precT[0] = prec * CHAP_SCALE                            /* a) */
                        * a0[obj]                               /* b) */
                        / (10. * (-log10(prec + 1e-35) - 2));   /* c) */
        t = 1./(fabs(T) + 1e-35);                               /* d) */
        precT[1] = precT[0]*t;
        precT[2] = precT[1]*t;

        t = T * 100.0;          /* YEARS since J2000.0 */

        ca = sa = Nu = 0.;      /* shut up compiler warning 'uninitialised' */

        switch (obj) {          /* set initial term record pointer */
            case JUPITER:       rec = chap95_jupiter;   break;
            case SATURN:        rec = chap95_saturn;    break;
            case URANUS:        rec = chap95_uranus;    break;
            case NEPTUNE:       rec = chap95_neptune;   break;
            case PLUTO:         rec = chap95_pluto;     break;
            default:
                return (2);     /* wrong object: severe internal trouble */
        }

        /* do the term summation into sum[T^n] slots */
        for (; rec->n >= 0; ++rec) {
            double *amp;

            /* NOTE:  The formula
             * X = SUM[i=1,Records] T**n_i*(CX_i*cos(Nu_k*t)+SX_i*sin(Nu_k*t))
             * could be rewritten as  SUM( ... A sin (B + C*t) )
             * "saving" trigonometric calls.  However, e.g. for Pluto,
             * there are only 65 distinct angles NU_k (130 trig calls).
             * With that manipulation, EVERY arg_i would be different for X,
             * Y and Z, which is 3*96 terms.  Hence, the formulation as
             * given is good (optimal?).
             */

            for (cooidx = 0, amp = rec->amp; cooidx < 3; ++cooidx) {
                double C, S, term, termdot;
                short n;                /* fast access */

                C = *amp++;
                S = *amp++;
                n = rec->n;

                /* drop term if too small
                 * this is quite expensive:  17% of loop time
                 */
                if (fabs(C) + fabs(S) < precT[n])
                        continue;

                if (n == 0 && cooidx == 0) {    /* new Nu only here */
                    double arg;

                    Nu = rec->Nu;
                    arg = Nu * t;
                    arg -= floor(arg/(2.*PI))*(2.*PI);
                    ca = cos(arg);      /* blast it - even for Nu = 0.0 */
                    sa = sin(arg);
                }

                term = C * ca + S * sa;
                sum[n][cooidx] += term;
#if CHAP_GETRATE
                termdot = (-C * sa + S * ca) * Nu;
                sum[n][cooidx+3] += termdot;
                if (n > 0) sum[n - 1][cooidx+3] += n/100.0 * term;
#endif
            } /* cooidx */
        } /* records */

        /* apply powers of time and sum up */
        for (cooidx = 0; cooidx < 6; ++cooidx) {
            ret[cooidx] = (sum[0][cooidx] +
                        T * (sum[1][cooidx] +
                        T * (sum[2][cooidx] )) )/CHAP_SCALE;
        }

        /* TEST: if the MAIN terms are dropped, get angular residue
        ret[0] = sqrt(ret[0]*ret[0] + ret[1]*ret[1] + ret[2]*ret[2])/a0[obj];
        */

#if CHAP_GETRATE
        for (cooidx = 3; cooidx < 6; ++cooidx) {
            ret[cooidx] /= 365.25;      /* yearly to daily rate */
        }
#endif

    return (0);
}

/* For RCS Only -- Do Not Edit */
static char *rcsid[2] = {(char *)rcsid, "@(#) $RCSfile: chap95.c,v $ $Date: 2011-09-21 16:17:48 $ $Revision: 1.9 $ $Name: not supported by cvs2svn $"};