| 1 | /* rewritten for Bureau des Longitude theories by Bretagnon and Chapront
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| 2 | * Michael Sternberg <sternberg@physik.tu-chemnitz.de>
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| 3 | */
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| 4 | #include <stdio.h>
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| 5 | #include <math.h>
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| 6 |
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| 7 | #include "astro.h"
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| 8 | #include "vsop87.h"
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| 9 | #include "chap95.h"
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| 10 |
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| 11 | static void pluto_ell (double mj, double *ret);
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| 12 | static void chap_trans (double mj, double *ret);
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| 13 | static void planpos (double mj, int obj, double prec, double *ret);
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| 14 |
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| 15 | /* coordinate transformation
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| 16 | * from:
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| 17 | * J2000.0 rectangular equatoreal ret[{0,1,2}] = {x,y,z}
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| 18 | * to:
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| 19 | * mean equinox of date spherical ecliptical ret[{0,1,2}] = {l,b,r}
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| 20 | */
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| 21 | static void
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| 22 | chap_trans (
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| 23 | double mj, /* destination epoch */
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| 24 | double *ret) /* vector to be transformed _IN PLACE_ */
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| 25 | {
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| 26 | double ra, dec, r, eps;
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| 27 | double sr, cr, sd, cd, se, ce;
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| 28 |
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| 29 | cartsph(ret[0], ret[1], ret[2], &ra, &dec, &r);
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| 30 | precess(J2000, mj, &ra, &dec);
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| 31 | obliquity(mj, &eps);
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| 32 | sr = sin(ra); cr = cos(ra);
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| 33 | sd = sin(dec); cd = cos(dec);
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| 34 | se = sin(eps); ce = cos(eps);
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| 35 | ret[0] = atan2( sr * ce + sd/cd * se, cr); /* long */
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| 36 | ret[1] = asin( sd * ce - cd * se * sr); /* lat */
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| 37 | ret[2] = r; /* radius */
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| 38 | }
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| 39 |
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| 40 | /* low precision ecliptic coordinates of Pluto from mean orbit.
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| 41 | * Only for sake of completeness outside available perturbation theories.
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| 42 | */
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| 43 | static void
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| 44 | pluto_ell (
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| 45 | double mj, /* epoch */
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| 46 | double *ret) /* ecliptic coordinates {l,b,r} at equinox of date */
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| 47 | {
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| 48 | /* mean orbital elements of Pluto.
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| 49 | * The origin of these is somewhat obscure.
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| 50 | */
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| 51 | double a = 39.543, /* semimajor axis, au */
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| 52 | e = 0.2490, /* excentricity */
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| 53 | inc0 = 17.140, /* inclination, deg */
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| 54 | Om0 = 110.307, /* long asc node, deg */
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| 55 | omeg0 = 113.768, /* arg of perihel, deg */
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| 56 | mjp = 2448045.539 - MJD0, /* epoch of perihel */
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| 57 | mjeq = J2000, /* equinox of elements */
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| 58 | n = 144.9600/36525.; /* daily motion, deg */
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| 59 |
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| 60 | double inc, Om, omeg; /* orbital elements at epoch of date */
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| 61 | double ma, ea, nu; /* mean, excentric and true anomaly */
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| 62 | double lo, slo, clo; /* longitude in orbit from asc node */
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| 63 |
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| 64 | reduce_elements(mjeq, mj, degrad(inc0), degrad(omeg0), degrad(Om0),
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| 65 | &inc, &omeg, &Om);
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| 66 | ma = degrad((mj - mjp) * n);
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| 67 | anomaly(ma, e, &nu, &ea);
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| 68 | ret[2] = a * (1.0 - e*cos(ea)); /* r */
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| 69 | lo = omeg + nu;
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| 70 | slo = sin(lo);
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| 71 | clo = cos(lo);
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| 72 | ret[1] = asin(slo * sin(inc)); /* b */
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| 73 | ret[0] = atan2(slo * cos(inc), clo) + Om; /* l */
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| 74 | }
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| 75 |
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| 76 | /*************************************************************/
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| 77 |
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| 78 | /* geometric heliocentric position of planet, mean ecliptic of date
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| 79 | * (not corrected for light-time)
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| 80 | */
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| 81 | static void
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| 82 | planpos (double mj, int obj, double prec, double *ret)
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| 83 | {
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| 84 | if (mj >= CHAP_BEGIN && mj <= CHAP_END) {
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| 85 | if (obj >= JUPITER) { /* prefer Chapront */
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| 86 | chap95(mj, obj, prec, ret);
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| 87 | chap_trans (mj, ret);
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| 88 | } else { /* VSOP for inner planets */
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| 89 | vsop87(mj, obj, prec, ret);
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| 90 | }
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| 91 | } else { /* outside Chapront time: */
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| 92 | if (obj != PLUTO) { /* VSOP for all but Pluto */
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| 93 | vsop87(mj, obj, prec, ret);
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| 94 | } else { /* Pluto mean elliptic orbit */
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| 95 | pluto_ell(mj, ret);
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| 96 | }
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| 97 | }
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| 98 | }
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| 99 |
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| 100 | /*************************************************************/
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| 101 |
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| 102 | /* visual elements of planets
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| 103 | * [planet][0] = angular size at 1 AU
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| 104 | * [planet][1] = magnitude at 1 AU from sun and earth and 0 deg phase angle
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| 105 | * [planet][2] = A
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| 106 | * [planet][3] = B
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| 107 | * [planet][4] = C
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| 108 | * where mag correction = A*(i/100) + B*(i/100)^2 + C*(i/100)^3
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| 109 | * i = angle between sun and earth from planet, degrees
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| 110 | * from Explanatory Supplement, 1992
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| 111 | */
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| 112 | static double vis_elements[8][5] = {
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| 113 | /* Mercury */ { 6.74, -0.36, 3.8, -2.73, 2.00},
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| 114 | /* Venus */ { 16.92, -4.29, 0.09, 2.39, -.65},
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| 115 | /* Mars */ { 9.36, -1.52, 1.60, 0., 0.},
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| 116 | /* Jupiter */ { 196.74, -9.25, 0.50, 0., 0.},
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| 117 | /* Saturn */ { 165.6, -8.88, 4.40, 0., 0.},
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| 118 | /* Uranus */ { 65.8, -7.19, 0.28, 0., 0.},
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| 119 | /* Neptune */ { 62.2, -6.87, 0., 0., 0.},
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| 120 | /* Pluto */ { 8.2, -1.01, 4.1, 0., 0.}
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| 121 | };
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| 122 |
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| 123 | /* given a modified Julian date, mj, and a planet, p, find:
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| 124 | * lpd0: heliocentric longitude,
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| 125 | * psi0: heliocentric latitude,
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| 126 | * rp0: distance from the sun to the planet,
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| 127 | * rho0: distance from the Earth to the planet,
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| 128 | * none corrected for light time, ie, they are the true values for the
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| 129 | * given instant.
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| 130 | * lam: geocentric ecliptic longitude,
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| 131 | * bet: geocentric ecliptic latitude,
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| 132 | * each corrected for light time, ie, they are the apparent values as
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| 133 | * seen from the center of the Earth for the given instant.
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| 134 | * dia: angular diameter in arcsec at 1 AU,
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| 135 | * mag: visual magnitude
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| 136 | *
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| 137 | * all angles are in radians, all distances in AU.
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| 138 | *
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| 139 | * corrections for nutation and abberation must be made by the caller. The RA
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| 140 | * and DEC calculated from the fully-corrected ecliptic coordinates are then
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| 141 | * the apparent geocentric coordinates. Further corrections can be made, if
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| 142 | * required, for atmospheric refraction and geocentric parallax.
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| 143 | */
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| 144 | void
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| 145 | plans (double mj, PLCode p, double *lpd0, double *psi0, double *rp0,
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| 146 | double *rho0, double *lam, double *bet, double *dia, double *mag)
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| 147 | {
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| 148 | static double lastmj = -10000;
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| 149 | static double lsn, bsn, rsn; /* geocentric coords of sun */
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| 150 | static double xsn, ysn, zsn; /* cartesian " */
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| 151 | double lp, bp, rp; /* heliocentric coords of planet */
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| 152 | double xp, yp, zp, rho; /* rect. coords and geocentric dist. */
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| 153 | double dt; /* light time */
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| 154 | double *vp; /* vis_elements[p] */
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| 155 | double ci, i; /* sun/earth angle: cos, degrees */
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| 156 | int pass;
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| 157 |
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| 158 | /* get sun cartesian; needed only once at mj */
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| 159 | if (mj != lastmj) {
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| 160 | sunpos (mj, &lsn, &rsn, &bsn);
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| 161 | sphcart (lsn, bsn, rsn, &xsn, &ysn, &zsn);
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| 162 | lastmj = mj;
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| 163 | }
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| 164 |
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| 165 | /* first find the true position of the planet at mj.
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| 166 | * then repeat a second time for a slightly different time based
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| 167 | * on the position found in the first pass to account for light-travel
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| 168 | * time.
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| 169 | */
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| 170 | dt = 0.0;
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| 171 | for (pass = 0; pass < 2; pass++) {
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| 172 | double ret[6];
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| 173 |
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| 174 | /* get spherical coordinates of planet from precision routines,
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| 175 | * retarded for light time in second pass;
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| 176 | * alternative option: vsop allows calculating rates.
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| 177 | */
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| 178 | planpos(mj - dt, p, 0.0, ret);
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| 179 |
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| 180 | lp = ret[0];
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| 181 | bp = ret[1];
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| 182 | rp = ret[2];
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| 183 |
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| 184 | sphcart (lp, bp, rp, &xp, &yp, &zp);
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| 185 | cartsph (xp + xsn, yp + ysn, zp + zsn, lam, bet, &rho);
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| 186 |
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| 187 | if (pass == 0) {
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| 188 | /* save heliocentric coordinates at first pass since, being
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| 189 | * true, they are NOT to be corrected for light-travel time.
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| 190 | */
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| 191 | *lpd0 = lp;
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| 192 | range (lpd0, 2.*PI);
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| 193 | *psi0 = bp;
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| 194 | *rp0 = rp;
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| 195 | *rho0 = rho;
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| 196 | }
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| 197 |
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| 198 | /* when we view a planet we see it in the position it occupied
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| 199 | * dt days ago, where rho is the distance between it and earth,
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| 200 | * in AU. use this as the new time for the next pass.
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| 201 | */
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| 202 | dt = rho * 5.7755183e-3;
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| 203 | }
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| 204 |
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| 205 | vp = vis_elements[p];
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| 206 | *dia = vp[0];
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| 207 |
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| 208 | /* solve plane triangle, assume sun/earth dist == 1 */
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| 209 | ci = (rp*rp + rho*rho - 1)/(2*rp*rho);
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| 210 |
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| 211 | /* expl supp equation for mag */
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| 212 | if (ci < -1) ci = -1;
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| 213 | if (ci > 1) ci = 1;
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| 214 | i = raddeg(acos(ci))/100.;
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| 215 | *mag = vp[1] + 5*log10(rho*rp) + i*(vp[2] + i*(vp[3] + i*vp[4]));
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| 216 |
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| 217 | /* rings contribution if SATURN */
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| 218 | if (p == SATURN) {
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| 219 | double et, st, set;
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| 220 | satrings (bp, lp, rp, lsn+PI, rsn, mj+MJD0, &et, &st);
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| 221 | set = sin(fabs(et));
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| 222 | *mag += (-2.60 + 1.25*set)*set;
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| 223 | }
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| 224 | }
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| 225 |
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| 226 | /* For RCS Only -- Do Not Edit */
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| 227 | static char *rcsid[2] = {(char *)rcsid, "@(#) $RCSfile: plans.c,v $ $Date: 2009-07-16 10:34:38 $ $Revision: 1.8 $ $Name: not supported by cvs2svn $"};
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