/* This file contains code to calculate the libration in Lunar lat and long. * It is based entirely on code supplied to me 2 Oct 1996 by Stephen L. Moshier, * , which implements a trigonometric expansion to * approximate the librations according to JPL DE403. The following doc file * was also supplied therewith: This program calculates a trigonometric series adjusted for a best fit to the lunar librations from the Jet Propulsion Laboratory's DE403 ephemeris. lblon403.c and lblat403.c are series for the selenographic longitude and latitude of the earth. The longitude series matches DE403 with a maximum discrepancy of 2.6" (0.4" rms). The latitude has a maximum discrepancy of 1.9" (0.2" rms). The two series are valid in the Julian year interval 1600 to 2200. In both Eckhardt and DE403 the moon's principal moment of inertia axes form the lunar body coordinate system. The estimated geographic locations of these axes vary as measurements and theories gradually become more refined. There is a significant difference between Eckhardt and DE403 in the constant term of the longitude. Almanac and cartography coordinates drop the constant term (which is -64" for DE403). That practice gives librations relative to the mean selenographic longitude of the earth, for which the discrepancy from one theory to the next is small. Steve Moshier October, 1996 * Any errors in adapting this code to xephem are strictly my own. * Elwood Downey. */ #include #include #include "astro.h" #define CHAR short /* plantbl.h */ struct plantbl { /* char max_harmonic[9]; */ char max_harmonic[14]; char max_power_of_t; CHAR *arg_tbl; int *lon_tbl; int *lat_tbl; int *rad_tbl; double distance; double timescale; double trunclvl; }; /* libra403.c */ static double JD2000 = 2451545.0; /* Conversion factors between degrees and radians */ static double STR = 4.8481368110953599359e-6; /* radians per arc second */ static double ss[14][24]; static double cc[14][24]; /* Reduce arc seconds modulo 360 degrees, answer in arc seconds. */ static double mods3600 (double x) { double y; y = x - 1.296e6 * floor (x / 1.296e6); return y; } /* Prepare lookup table of sin and cos ( i * L_k ) for required multiple angles. K is the array offset corresponding to the planet. ARG is in radians. n is the highest harmonic to compute. */ static int sscc (int k, double arg, int n) { double cu, su, cv, sv, s; int i; if (n <= 0) return 0; su = sin (arg); cu = cos (arg); ss[k][0] = su; /* sin(L) */ cc[k][0] = cu; /* cos(L) */ sv = 2.0 * su * cu; cv = cu * cu - su * su; ss[k][1] = sv; /* sin(2L) */ cc[k][1] = cv; for (i = 2; i < n; i++) { s = su * cv + cu * sv; cv = cu * cv - su * sv; sv = s; ss[k][i] = sv; /* sin( i+1 L ) */ cc[k][i] = cv; } return (0); } /* Mean elements. Copied from cmoon.c, DE404 version. */ static double Jlast = -1.0e38; static double T; static int dargs (double J, struct plantbl *plan) { double T2, w; if (J == Jlast) return 0; T = (J - JD2000) / 36525.0; T2 = T * T; /* Mean anomaly of sun = l' (J. Laskar) */ w = mods3600 (129596581.038354 * T + 1287104.76154); w += (((((((( 1.62e-20 * T - 1.0390e-17) * T - 3.83508e-15) * T + 4.237343e-13) * T + 8.8555011e-11) * T - 4.77258489e-8) * T - 1.1297037031e-5) * T + 1.4732069041e-4) * T - 0.552891801772) * T2; sscc (10, STR * w, plan->max_harmonic[10]); /* Mean distance of moon from its ascending node = F */ w = mods3600 ((1739527263.0983 - 2.079419901760e-01) * T + 335779.55755); w = w + ((-9.646018347184e-06 * T2 /* F, t^4 */ - 1.138215912580e-03) * T /* F, t^3 */ - 1.312045233711e+01) * T; /* F, t^2 */ sscc (11, STR * w, plan->max_harmonic[11]); /* Mean anomaly of moon = l */ w = mods3600 ((1717915923.4728 - 2.035946368532e-01) * T + 485868.28096); w = w + ((-3.421689790404e-04 * T2 /* l, t^4 */ + 4.768357585780e-02) * T /* l, t^3 */ + 3.146734198839e+01) * T; /* l, t^2 */ sscc (9, STR * w, plan->max_harmonic[9]); /* Mean elongation of moon = D */ w = mods3600 ((1602961601.4603 + 3.962893294503e-01) * T + 1072260.73512); w = w + ((-2.905334122698e-04 * T2 /* D, t^4 */ - 5.834100476561e-03) * T /* D, t^3 */ - 6.847070905410e+00) * T; /* D, t^2 */ sscc (12, STR * w, plan->max_harmonic[12]); /* Mean longitude of moon, re mean ecliptic and equinox of date */ w = mods3600 ((1732564372.83264 - 6.784914260953e-01) * T + 785939.95571); w = w + ((-8.466472828815e-05 * T2 /* L, t^4 */ + 5.722859298199e-03) * T /* L, t^3 */ - 5.663161722088e+00) * T; /* L, t^2 */ sscc (13, STR * w, plan->max_harmonic[13]); /* Mean longitudes of planets (Laskar, Bretagnon) */ /* Venus. */ w = mods3600 (210664136.4335482 * T + 655127.283046); w += (((((((( -9.36e-023 * T - 1.95e-20) * T + 6.097e-18) * T + 4.43201e-15) * T + 2.509418e-13) * T - 3.0622898e-10) * T - 2.26602516e-9) * T - 1.4244812531e-5) * T + 0.005871373088) * T2; sscc (1, STR * w, plan->max_harmonic[1]); /* Earth. */ w = mods3600 (129597742.26669231 * T + 361679.214649); w += ((((((((-1.16e-22 * T + 2.976e-19) * T + 2.8460e-17) * T - 1.08402e-14) * T - 1.226182e-12) * T + 1.7228268e-10) * T + 1.515912254e-7) * T + 8.863982531e-6) * T - 2.0199859001e-2) * T2; sscc (2, STR * w, plan->max_harmonic[2]); /* Mars. */ w = mods3600 (68905077.59284 * T + 1279559.78866); w += (-1.043e-5 * T + 9.38012e-3) * T2; sscc (3, STR * w, plan->max_harmonic[3]); /* Jupiter. */ w = mods3600 (10925660.428608 * T + 123665.342120); w += (1.543273e-5 * T - 3.06037836351e-1) * T2; sscc (4, STR * w, plan->max_harmonic[4]); /* Saturn. */ w = mods3600 (4399609.65932 * T + 180278.89694); w += ((4.475946e-8 * T - 6.874806E-5) * T + 7.56161437443E-1) * T2; sscc (5, STR * w, plan->max_harmonic[5]); return 0; } /* Evaluate series PLAN at Julian date J. Result in arcseconds, usually. */ static double gplan (double J, struct plantbl *plan) { double su, cu, sv, cv; double t, sl; int j, k, m, k1, ip, np, nt; CHAR *p; int *pl; dargs (J, plan); /* Point to start of table of arguments. */ p = plan->arg_tbl; /* Point to tabulated cosine and sine amplitudes. */ pl = plan->lon_tbl; sl = 0.0; for (;;) { /* Find sine and cosine of argument for this term in the series. The argument has the form J_1 L_1 + J_2 L_2 + ... where J_i are integers and L_i are mean elements. */ /* Number of periodic arguments. */ np = *p++; if (np < 0) break; if (np == 0) { /* If no periodic arguments, it is a polynomial term. Evaluate A_n T^n + A_n-1 T^n-1 + ... + A_0. */ nt = *p++; cu = *pl++; for (ip = 0; ip < nt; ip++) cu = cu * T + *pl++; sl += cu; continue; } k1 = 0; cv = 0.0; sv = 0.0; for (ip = 0; ip < np; ip++) { /* What harmonic. */ j = *p++; /* Which planet. */ m = *p++ - 1; if (j) { k = j; if (j < 0) k = -k; k -= 1; /* sin(k*angle) for planet m. */ su = ss[m][k]; if (j < 0) su = -su; /* cos(k*angle) for planet m. */ cu = cc[m][k]; if (k1 == 0) { /* Set sine and cosine of first angle. */ sv = su; cv = cu; k1 = 1; } else { /* Combine angles by trigonometry. */ t = su * cv + cu * sv; cv = cu * cv - su * sv; sv = t; } } } /* Now cv = cos(arg), sv = sin(arg). Evaluate cu = (C_n T^n + C_n-1 T^n-1 + ... + C_0) cos(arg) su = (S_n T^n + S_n-1 T^n-1 + ... + S_0) sin(arg). */ /* Highest power of T. */ nt = *p++; /* Coefficients C_i, S_i. */ cu = *pl++; su = *pl++; for (ip = 0; ip < nt; ip++) { cu = cu * T + *pl++; su = su * T + *pl++; } sl += cu * cv + su * sv; } return (plan->trunclvl * sl); } /* lblat403.c */ static int lattabr[] = {-1}; static int lattabb[] = {-1}; static int lattabl[] = { 785710, -1958, 780, -178, 2850, 2243, 5927, 2714, -2911, -174, 5888, -16705, 10828, -15113, -25049, -172, 1976, 37, -13560, -40, -911, -300, 691, 3779, 722, 68, -1048, -3092, -4, 3011, -31, 250, -14293664, -149, -228, -5, -842, 62, 57967, -7, -11207, 15, -66055, -79, -71560, 8, 2998, -1062, -46, -2, 711, -5, -2, 367, -5, -353, 1, -117, 2324027, 0, -176, 19, -4, -3, -1229, 7, 4327, -2, 112, -1, -540, 73, 102982, 0, -137, 2, 239, 0, -216, 2, 3707, -1, -100, -2, 124, 0, 408, 1, 561, 0, 594, 0, 11866, -2, -229, 11, 6768, 2, 1, -2, -788, -24, 314732, -5, -3238, -2, -1263, -1, 94, -2, 206, -283, 6489836, 63, 2562, -6, 1220, 0, 135, 795, -338, -406, -101, 757, -383, -73, -31018, -5, -3010, 6, 5821, 167, 7, 2, 122623, 41, 138924, 2, 253, 0, -198, 135, 30, 2, 934, 62, -14, -531, -297537, -3, -205, 1, -393, -4, -156, -467, 90, 9, -346, -55, 1368, 4414, 2094, 480, 510, 35, 728, 6832, 6429, -2099, -3703, -9, 579, 239, 1738, 22, 968, 60260, -8929, 26, -64, 0, 0, -47, -351, 2248, -1175, 3976, 7150, 15191, 1, -15535, -143, -2308,-239959618, -45, 355, 2252, 1189, 4009, -7131, -158, 499, 776, -34, -389, 4363, 30, 28, 0, -593, 1, -1, 58, -66, 4, 1552, -1, 244, 288, 59, -276, 62, 8, 3309, 2, 1249, -156, -3, 0, -7903, -47, 154458, -710, 160, 0, 288, 328, 219514, -1, 113, -1, 1515, -20, 28493, 13, 9011, -1, 1110, -1, -103, 0, 312, 1, 360, 6, 6139, -1, 142, -1, -709, -1, -242, 67, 67200, 5, 4148, 1, 137, -15, -17969, -2, -3372, -2, -1739, 154, 116200, -1, -640, -269, -336274, 0, -1557, -1, -353, 993, 39, -1, -294, -646, -135, 750, -3, -661, 8, -163, 2591179, -1, -258, 0, 381, 6, 8272, -44, -92044, -29, 70397, -25, -17892, 1, 67, -44, -17118, 2743, 349, -4, 231, 1501, 3099, -33, 21, -1130, 97, 1263, 164, -226, -13139965, 839, -202, -1, 660, 12, -10482, 1, 17, -2, -1480, -45, -26084, 2, 259, 0, 258, -1, -1560, 32, 73046, -1, -370, -1, -77, 46, 20687, 1, 742, 1, 2399, 2, 741, 0, 52, 0, 112, 0, 297, 2, 825, 0, 161, 1, 4228, 0, 212, -1, -105, 6, 2782, 9, 37199, 3, 5045, 105, -1, -1, -179, 75, 31274, -3, -1321, -1, 363, 0, 1137, 58, 104090, -2, -2695, -1, -392, -35, -21763, -2, -205, 567, 38, -7, 117, -569, -9, 321, -1522061, -4, 276, -2, -590, 2, 632, -14, -10601, 4, 8703, -10, 16870, -4, -995, 597, -6, -386, -805403, 1025, -474, -2, 201, -95, 16, -127, 135570, 0, -173, 10, 8565, -3, 1812, -1, -108, -107, -649, 0, 151, 1, 950, 1, 312, 1, 403, 0, -576, 7, 4418, -3, -4769, -1, -769, 63, 38890, 0, -101, 0, 169, -3, -14837, 1, 372, 0, -674, -3, -1488, -36, -196300, 0, -176, -10, -4811, -2, -991, 1, 831, 1, 3138, -103, -51819, 0, -133, -4, 22171, 2, 820, 1, 149, 2227, 1277, -502, -3049, 1, 122, 0, 370, 0, 166, 2, 772, 2, 2057, -1, -486, 13, -15447, -2, -1619, 0, 335, 0, -206, 0, -104, -19, -19726, 0, 414, -8, -3425, -19, -1, 1, 546, 0, -392, 0, -2754, 0, -158, -3, -1790, -1, -230, 0, -190, 0, -366, 0, -154, }; static CHAR latargs[] = { 0, 0, 3, 1, 2, 9, 3,-20, 4, 0, 4, 1, 13, -1, 10, 3, 2, -4, 3, 2, 4, 1, 13, -1, 10, -5, 2, 9, 3, 2, 3, 9, 10, -9, 14, 1, 3, 0, 3, 1, 11, -1, 12, 1, 13, 0, 4, 1, 10, -2, 11, 1, 12, -2, 13, 0, 4, 2, 11, -1, 14, 18, 2,-18, 3, 0, 3, 1, 13, -1, 10, 1, 3, 0, 2, 1, 10, -1, 14, 0, 2, 1, 10, -1, 12, 2, 4, 1, 14,-18, 2, 16, 3, 1, 5, 0, 3, 2, 10, -1, 12, -1, 13, 0, 3, 1, 10, 1, 11, -1, 12, 0, 4, 1, 10, -1, 11, 1, 12, -2, 13, 0, 2, 1, 12, -1, 13, 0, 3, 1, 10, -1, 11, -1, 12, 0, 3, 3, 10, -1, 12, -2, 13, 0, 2, 2, 10, -2, 13, 0, 3, 1, 10, 2, 11, -1, 12, 0, 3, 1, 10, -2, 13, 1, 3, 0, 3, 1, 10, 1, 12, -2, 13, 2, 3, 1, 11, 1, 12, -1, 13, 0, 2, 2, 12, -2, 13, 0, 3, 1, 10, -2, 11, -1, 12, 0, 3, 1, 10, -3, 12, 2, 13, 0, 4, 3, 10, 1, 11, -1, 12, -2, 13, 0, 3, 2, 10, 1, 12, -3, 13, 0, 4, 1, 10, 1, 11, 1, 12, -2, 13, 0, 2, 3, 12, -3, 13, 0, 4, 1, 10, -1, 11, -3, 12, 2, 13, 0, 3, 3, 10, 1, 12, -4, 13, 0, 4, 1, 10, 2, 11, 1, 12, -2, 13, 0, 3, 1, 10, 3, 12, -4, 13, 0, 4, 1, 10, 3, 11, 1, 12, -2, 13, 0, 3, 3, 11, 1, 12, -2, 13, 0, 4, 2, 10, 1, 11, 1, 12, -4, 13, 0, 2, 3, 12, -4, 13, 0, 3, 2, 11, 1, 12, -2, 13, 0, 4, 1, 10, 1, 11, 1, 12, -3, 13, 0, 3, 2, 10, 1, 12, -4, 13, 0, 4, 1, 14, -3, 2,-16, 3, -4, 4, 0, 3, 1, 11, 1, 12, -2, 13, 1, 3, 1, 10, 1, 12, -3, 13, 0, 4, 2, 10, 1, 11, -1, 12, -2, 13, 0, 3, 2, 10, -3, 12, 2, 13, 0, 4, 1, 10, -1, 11, -1, 12, 1, 13, 0, 2, 1, 12, -2, 13, 0, 2, 2, 13, -1, 14, 0, 2, 2, 11, -1, 12, 0, 4, 1, 10, -1, 11, 1, 12, -3, 13, 0, 3, 2, 10, -3, 14, 4, 4, 0, 2, 1, 10, -2, 13, 0, 3, 1, 13, -3, 3, 4, 4, 0, 3, 2, 10, -1, 12, -2, 13, 0, 3, 2, 10, -1, 11, -1, 12, 0, 3, 1, 10, -1, 12, 1, 13, 0, 2, 1, 10, -1, 11, 0, 3, 1, 11, -1, 12, 2, 13, 0, 2, 1, 11, -1, 12, 0, 3, 1, 10, -1, 12, -1, 13, 0, 4, 2, 13, -1, 12, 2, 2, -2, 3, 0, 3, 1, 13, 2, 2, -3, 3, 0, 4, 2, 10, -1, 11, -1, 12, -2, 13, 0, 3, 1, 13, -1, 2, 2, 3, 0, 2, 2, 10, -1, 12, 0, 4, 2, 13, -1, 12, 2, 3, -2, 5, 0, 4, 2, 13, -1, 12, 3, 2, -3, 3, 0, 4, 2, 10, -2, 11, 1, 12, -2, 13, 0, 3, 1, 13, 1, 3, -2, 5, 0, 4, 1, 10, 1, 11, -1, 12, 1, 13, 0, 3, 1, 13, -5, 2, 9, 3, 0, 3, 1, 14, 2, 3, -4, 4, 0, 3, 3, 10, 4, 12, -6, 14, 0, 3, 1, 13, 3, 2, -4, 3, 0, 1, 1, 10, 0, 3, 1, 13, -3, 12, 9, 2, 0, 4, 1, 10, -1, 11, 1, 12, -1, 13, 0, 3, 2, 11, -1, 12, 2, 13, 0, 1, 1, 14, 1, 4, 1, 12, 1, 10, -1, 14, 1, 5, 0, 4, 9, 13, -9, 10, 7, 2, 10, 3, 0, 3, 1, 12, -8, 2, 13, 3, 2, 1, 1, 12, 2, 3, 1, 12, 8, 2,-13, 3, 2, 2, 1, 13, 2, 4, 0, 4, 2, 13, -1, 12, 5, 2, -6, 3, 0, 3, 1, 13, -2, 12, 1, 3, 0, 3, 1, 13, -3, 2, 6, 3, 0, 4, 1, 10, -1, 11, -1, 12, -1, 13, 0, 2, 1, 14, 2, 5, 0, 2, 1, 10, -2, 12, 0, 2, 2, 10, -3, 12, 0, 4, 2, 13, -1, 12, 4, 2, -4, 3, 0, 3, 1, 14, 4, 2, -6, 3, 0, 2, 1, 13, 1, 2, 0, 3, 2, 10, 1, 11, -1, 12, 0, 4, 2, 10, -1, 11, 1, 12, -2, 13, 0, 2, 1, 10, 1, 11, 0, 3, 1, 10, 1, 12, -1, 13, 0, 2, 1, 11, 1, 12, 0, 3, 3, 12, -2, 13, -1, 3, 0, 3, 4, 10, -1, 12, -2, 13, 0, 3, 2, 10, 1, 12, -2, 13, 0, 4, 1, 10, 1, 11, 1, 12, -1, 13, 0, 2, 2, 11, 1, 12, 0, 2, 3, 12, -2, 13, 0, 4, 2, 10, 1, 11, 1, 12, -2, 13, 0, 3, 1, 11, 3, 12, -2, 13, 0, 3, 4, 10, 1, 12, -4, 13, 0, 4, 2, 10, 2, 11, 1, 12, -2, 13, 0, 4, 1, 10, 2, 11, 1, 12, -4, 13, 0, 4, 1, 10, 1, 11, 1, 12, -4, 13, 0, 4, 1, 10, 3, 11, -1, 12, -2, 13, 0, 4, 1, 10, -2, 11, -1, 12, 2, 13, 0, 3, 1, 11, 1, 12, -3, 13, 0, 3, 1, 10, 1, 12, -4, 13, 0, 4, 1, 10, 2, 11, -1, 12, -2, 13, 0, 3, 3, 10, -1, 12, -4, 13, 0, 4, 1, 10, -1, 11, -1, 12, 2, 13, 0, 2, 1, 12, -3, 13, 0, 4, 1, 10, -1, 11, 1, 12, -4, 13, 0, 4, 1, 10, 1, 11, -1, 12, -2, 13, 0, 3, 2, 10, -1, 12, -3, 13, 0, 3, 1, 10, -1, 12, 2, 13, 0, 3, 1, 10, -2, 11, 1, 12, 0, 3, 1, 11, -1, 12, 3, 13, 0, 1, 2, 13, 0, 3, 1, 11, -1, 12, -1, 13, 0, 3, 1, 10, -3, 13, -1, 3, 0, 3, 1, 10, -1, 12, -2, 13, 2, 3, 3, 10, -1, 11, -1, 12, 0, 3, 2, 10, -1, 12, 1, 13, 0, 4, 1, 10, 1, 11, -1, 12, 2, 13, 0, 3, 1, 10, -1, 11, 1, 12, 0, 2, 1, 12, 1, 13, 0, 4, 1, 10, -1, 11, -1, 12, -2, 13, 0, 3, 1, 10, 1, 11, -3, 12, 0, 2, 3, 10, -1, 12, 0, 1, 2, 10, 0, 4, 2, 10, -1, 11, 1, 12, -1, 13, 0, 3, 1, 13, 1, 10, 1, 11, 0, 3, 2, 13, 3, 3, -2, 11, 0, 2, 1, 10, 1, 12, 2, 3, 1, 10, -3, 14, 2, 5, 0, 3, 3, 10, -1, 14, 4, 5, 0, 3, 1, 11, 1, 12, 1, 13, 0, 1, 2, 12, 0, 4, 1, 10, -2, 11, -1, 12, -2, 13, 0, 2, 1, 10, -3, 12, 0, 3, 3, 10, 1, 11, -1, 12, 0, 4, 3, 10, -1, 11, 1, 12, -2, 13, 0, 3, 2, 10, 1, 12, -1, 13, 0, 3, 1, 10, 1, 11, 1, 12, 0, 2, 3, 12, -1, 13, 0, 3, 1, 10, -1, 11, -3, 12, 0, 3, 3, 10, 1, 12, -2, 13, 0, 3, 1, 10, 2, 11, 1, 12, 0, 3, 1, 10, 3, 12, -2, 13, 0, 4, 3, 10, 1, 11, 1, 12, -2, 13, 0, 4, 1, 10, 1, 11, 3, 12, -2, 13, 0, 4, 2, 10, 1, 11, 1, 12, -6, 13, 0, 3, 2, 11, 1, 12, -4, 13, 0, 3, 2, 10, 1, 12, -6, 13, 0, 4, 2, 10, 2, 11, -1, 12, -4, 13, 0, 3, 1, 11, 1, 12, -4, 13, 0, 3, 3, 11, -1, 12, -2, 13, 0, 3, 1, 10, 1, 12, -5, 13, 0, 4, 2, 10, 1, 11, -1, 12, -4, 13, 0, 2, 1, 12, -4, 13, 0, 3, 2, 11, -1, 12, -2, 13, 0, 2, 1, 10, -4, 13, 0, 4, 1, 10, 1, 11, -1, 12, -3, 13, 0, 3, 2, 10, -1, 12, -4, 13, 0, 4, 2, 10, -1, 11, -1, 12, 2, 13, 0, 3, 1, 10, -1, 12, 3, 13, 0, 3, 1, 11, -1, 12, 4, 13, 0, 3, 1, 11, -1, 12, -2, 13, 0, 3, 1, 10, -1, 12, -3, 13, 0, 4, 2, 10, -1, 11, -1, 12, -4, 13, 0, 3, 2, 10, -1, 12, 2, 13, 0, 3, 2, 10, -2, 11, 1, 12, 0, 2, 1, 10, 2, 13, 0, 4, 1, 10, -1, 11, 1, 12, 1, 13, 0, 2, 1, 12, 2, 13, 1, 4, 1, 10, -1, 11, -1, 12, -3, 13, 0, 3, 2, 10, -3, 12, -2, 13, 0, 4, 2, 10, 1, 11, -1, 12, 2, 13, 0, 3, 2, 10, -1, 11, 1, 12, 0, 3, 1, 10, 1, 12, 1, 13, 0, 3, 1, 11, 1, 12, 2, 13, 0, 2, 4, 10, -1, 12, 0, 2, 2, 10, 1, 12, 1, 4, 1, 13, 1, 12, 10, 2, -2, 3, 0, 3, 2, 11, 1, 12, 2, 13, 0, 2, 2, 12, 1, 14, 0, 1, 3, 12, 0, 3, 3, 10, 1, 12, -1, 13, 0, 3, 2, 10, 1, 11, 1, 12, 0, 3, 4, 10, 1, 12, -2, 13, 0, 3, 2, 10, 3, 12, -2, 13, 0, 3, 4, 10, -9, 3, -1, 4, 0, 4, 1, 10, 1, 11, 1, 12, -6, 13, 0, 3, 1, 10, 1, 12, -6, 13, 0, 4, 1, 10, 2, 11, -1, 12, -4, 13, 0, 3, 3, 10, -1, 12, -6, 13, 0, 4, 1, 10, -1, 11, -1, 12, 4, 13, 0, 4, 1, 10, 1, 11, -1, 12, -4, 13, 0, 3, 1, 10, -1, 12, 4, 13, 0, 4, 1, 10, -2, 11, 1, 12, 2, 13, 0, 3, 1, 10, -1, 12, -4, 13, 0, 4, 3, 10, -1, 11, -1, 12, 2, 13, 0, 4, 1, 10, 1, 11, -1, 12, 4, 13, 0, 4, 1, 10, -1, 11, 1, 12, 2, 13, 0, 2, 1, 12, 3, 13, 0, 4, 1, 10, -1, 11, -1, 12, -4, 13, 0, 3, 3, 10, -1, 12, 2, 13, 0, 3, 1, 10, 1, 12, 2, 13, 0, 3, 1, 11, 1, 12, 3, 13, 0, 3, 1, 10, -3, 12, -2, 13, 0, 3, 3, 10, -1, 11, 1, 12, 0, 3, 2, 10, 1, 12, 1, 13, 0, 4, 1, 10, 1, 11, 1, 12, 2, 13, 0, 2, 3, 10, 1, 12, 0, 4, 2, 10, 1, 11, 1, 12, 1, 13, 0, 2, 1, 10, 3, 12, 0, 3, 3, 10, 1, 11, 1, 12, 0, 3, 5, 10, 1, 12, -2, 13, 0, 3, 4, 14, -4, 2, 8, 3, 0, 3, 5, 10, -9, 3, -1, 4, 0, 4, 2, 10, 1, 11, -1, 12, -6, 13, 0, 2, 1, 12, -6, 13, 0, 3, 2, 11, -1, 12, -4, 13, 0, 3, 2, 10, -1, 12, -6, 13, 0, 3, 1, 11, -1, 12, -4, 13, 0, 3, 2, 10, -1, 12, 4, 13, 0, 2, 1, 12, 4, 13, 0, 4, 2, 10, -1, 11, 1, 12, 2, 13, 0, 3, 1, 11, 1, 12, 4, 13, 0, 3, 1, 11, -3, 12, -2, 13, 0, 3, 4, 10, -1, 12, 2, 13, 0, 3, 2, 10, 1, 12, 2, 13, 0, 4, 2, 10, 1, 11, 1, 12, 2, 13, 0, 2, 4, 10, 1, 12, 0, 3, 7, 12, -2, 10, -4, 5, 0, 3, 1, 10, -1, 12, -6, 13, 0, 4, 1, 10, -1, 11, 1, 12, 4, 13, 0, 3, 1, 10, 1, 12, 4, 13, 0, 4, 3, 10, -1, 11, 1, 12, 2, 13, 0, 3, 3, 10, 1, 12, 2, 13, 0, 2, 5, 10, 1, 12, 0, 2, 1, 12, 6, 13, 0, 3, 2, 10, 1, 12, 4, 13, 0, 3, 4, 10, 1, 12, 2, 13, 0, -1 }; /* Total terms = 254, small = 254 */ static struct plantbl liblat = { /* { 0, 18, 18, 20, 4, 0, 0, 0, 0, 9, 3, 7, 9, 9,}, */ /* Use max of liblon, liblat. */ { 0, 18, 18, 20, 4, 2, 0, 0, 0, 9, 16, 7, 9, 9,}, 2, latargs, lattabl, lattabb, lattabr, 3.850000e+05, 36525.0, 1.0e-4, }; /* lblon403.c */ static int lontabr[] = {-1}; static int lontabb[] = {-1}; static int lontabl[] = { -640001, -19, 3, -1, 0, -3, 17, 2, -9, 2, 3, 141, 1816, 2, -76, 78, -81, 3, 1, 50, -13, -12, 18, -6, 74, 19, 10, -19, 701, -26, 37, 36, -122, 131, -71, -40, 1, 61463, 12853, 5, -29, 354, 201, 94, -5, 31, 25, -73, -22, 673, 1435, 3844, 44, -44, -8, 195, -16, -827, -171768, 7051, -4116, 1036, 616, -2034, 6300, -13786, -3808, -118, -536, -1246, 771, 2555, 3214, 203, 26, 2975, -715, -743, 1286, -232, -50, 4, 234, -139, 475, 0, -98, -3, -11848, 0, 118, -202, 146, -33673, 7601, -150, 88, -1720, 1002, -293, 481, -2078, 1, 199, 220655, 137, 7459, -127, 28, -10, 2259, 4, 450, -26, 30, -76, 19043, 215, -7577830, -65, -45, -5, -14189, -6, -496, 9, 3265, 0, -131, 48, -90, -9, -155, -2, 21, 151, 19, -101, -516, -827, 3, 796, 2, 134, -2215850, -11, -1908, 0, 451, -2, 1399, 3, 7, -163, 5, -1582, 61, -22, -77215, 167, -471084, -85, -28, 1, -473, -1, 444, 4, 89, 6, -88, -157, -87813, 3, 274, -3, -1036, 7, -17005, -1, -332, 0, 50, -1, -228, -5, -2986, -1, -334, 1, -452, 0, 4, 0, -247, -3, -2493, -4, -1000, 0, -160, 0, -3163, -75, -74207, 13, 829, 32, 481, -33, -11859, -2, -3634, 7, -1611, 3, 520, -1, 2534, 5, -446, -471, 8, 399, 5160, 201, -2057189, 83, -2106, 11, 12240, 3, -270, 248, 1112, -63, -61809, -183, 594, 27, 25844, -3, 5594, 8, 571, -23, -1855, 477, -466, 0, -1257, 247, 1550, -10178, -175, 9570, -423, 2610, -45917681, -51, 937, -1001, 168, -168, 882, 1260, -2894, 4306, -1515, 7, 402, 0, 36, -280, -373, -19, 840, -1227, -138, 3486, 1478247, 1649, -644, 840, 377, 47, -1464, 167, -1251123, -194, -713, 133, 284429, 0, -191, -3, 1534, -700, 918, -7, -633, -221, -559, 1, 99, -17, -3513, -30, 14, -602, -5006, 908, 4178, 542, -379, 1568, 782, 528, 2761, -38994, -25804, 1696398, -324306, 47292, 71061, 457883, 52470, 159777, 224906030, -13068, -18508, -104, 3754, 541, 614, -290, 1412, -48, 162, 42, -50, -609, -4969, 44, -11435, -473, -412, 22, -6389, -87, 44, -39, 180182, -4186, -2227, -503, -208, 976, -512, -1016, -4403, 16, 25357, 565, -891, 28, 38836, -659, -855, -200, 619, 1, -1780, 24, 17531, 1053, 335, 502, 2745, -309, -1094576, -1, -263, 3, -394, 0, 4152, -1, -467, -339, -132142, -14, -11676, 29, 63360, 0, 129, -12, -4802, -1, -180, 2, 3424, 0, 45, -1, -155, -1, -74, 0, -134, -4, -1588, -1, -3424, 2, 119, -57, -27417, 0, 168, 0, 206, -21, -80823, 8, 2324, -4, 835, 396, -6, -244, -308040, 0, -294, -56, -1332, 2, -110, 306, 4060, -58, -1644587, -155, -210, 67, -1642, 27, 32070, 9, 3592, -8, -17, -1, 2, -9, -4580, 5, 1940, 5, -1217, 62, -862, -522, -1163, 0, 0, -1646, 1, 1169, 109, 1395, 23634968, 2, 0, -512, 1148, -9, 32, 0, -2749, 969, -4, 2, 351, 1, 105, 152, 97075, -55, -84524, -49, 607, 29, -242117, 4, 6518, 5, -77, 1, -39, 9, 1, 5, -231, 2296, -10, -2453, 3, 138, 7689964, 0, -689, 1, 12635, 5444, 372, 9, -1843, 3485, -560, 909, 3, -742, -1, -66, -6945414, 8, -7, -3, -181, 1, 1282, -115, -76497, 3, -90, 1, -142, -5, 10263, -33, -9479, 0, -657, 19, 15040, -2, 1084, -1, -295, -161, 403, 0, -175, -1, -392, -4, -3096, -9, -2928, 1, 332, -56, -43733, 1, 572, 2, -660, 4, 7540, 4, -659, -505, -382941, -3, 256, 2, 30, 76, 145296, -4, 4115, 9, 6329, 11, 6962, 0, -338, 1, 153, 2, -147, -270, 211, -519, 97, 385, 1912268, -1, 1495, -3, 223, 254, 152832, 15, 6709, -8, -5835, -12, -29016, 0, -5641, -2, 4217, -2, -1176, -496, 4, 331, 360972, 1, 918, -2, -136, -111, -762309, 2, -610, 1, 96, -11, -5468, 0, 4856, 0, -2, -16, -668, 20, 1963, -1, -95, 0, -83, 0, -96, -2, -902, 0, -1523, -14, -5691, -10, -18650, 0, 131, 0, 128, 0, 243, 1, 644, -76, 138046, -1, 316, 8, 2703, 15, 11758, -1, 16, 2, -2867, 5, 6504, 180, 143085, -1, 224, 86, -96384, 1, 471, 0, -407, -3, -2886, -1, -919, 0, 742, -2, 1145, 59, 19306, 0, 67, -61, -67569, -14, 11725, -1, -395, 1, 772, -1, -49, 563, 871, 1951, -22, -1, -711, 0, 240, -6, -3912, 1, 2812, 0, 106, 0, 378, 4, 19609, 6, 3331, 2, 930, 0, -37, 0, -502, 0, -1257, 21, 10531, 2, -16662, 0, -267, -1, 22, 6, 1104, -14, -5544, 1, -250, -1, 1248, 0, 325, 2, 2163, 2, -1421, 0, 73, -1, -67, 2, 771, -1, -2085, 0, 67, 1, 226, 1, 212, 0, 56, }; static CHAR lonargs[] = { 0, 0, 4, 1, 10, 3, 11,-18, 2, 13, 3, 0, 4, -2, 12, 2, 13, 5, 2, -6, 3, 0, 4, 2, 10, -2, 13, -2, 3, 3, 5, 0, 3, 1, 10, -1, 14, 1, 5, 0, 4, -2, 10, 2, 13, -5, 3, -6, 4, 0, 2, 1, 12, -1, 14, 0, 4, -2, 10, 2, 13, 2, 3, -2, 5, 0, 2, 1, 3, -2, 4, 0, 4, -1, 12, 1, 13, -3, 2, 6, 3, 0, 1, 1, 5, 0, 4, -1, 10, 2, 13,-15, 2, 13, 3, 0, 4, 2, 10, -2, 13, -3, 2, 3, 3, 0, 2, 2, 12, -2, 14, 0, 3, 1, 10, -1, 11, -1, 13, 0, 2, 11, 2,-18, 3, 0, 2, 3, 2, -5, 3, 0, 2, 2, 3, -4, 4, 0, 2, 5, 2, -8, 3, 0, 2, 1, 10, -1, 12, 0, 4, -1, 12, 1, 14, 3, 2, -5, 3, 0, 3, 6, 12, -6, 13, -4, 2, 0, 2, 3, 3, -6, 4, 0, 2, 5, 3, -9, 4, 0, 4, -1, 10, 2, 13,-18, 2, 18, 3, 0, 3, 2, 10, -2, 3, -2, 13, 0, 2, 2, 2, -3, 3, 0, 4, 2, 10, -2, 13, -4, 2, 5, 3, 0, 2, 4, 3, -7, 4, 0, 2, 2, 10, -2, 12, 0, 2, 3, 3, -5, 4, 0, 3, 3, 2, -4, 3, -1, 4, 2, 3, 1, 2, -5, 3, 7, 4, 2, 4, -2, 10, 2, 13, 5, 2, -6, 3, 0, 2, 1, 2, -2, 3, 0, 2, 2, 3, -3, 4, 0, 4, -1, 12, 1, 14, 4, 2, -6, 3, 0, 2, 1, 3, -1, 4, 0, 2, 4, 2, -6, 3, 0, 4, 2, 10, -2, 13, -2, 2, 2, 3, 0, 2, 1, 2, -1, 3, 0, 3, 2, 10, 1, 11, -2, 12, 0, 2, 1, 3, -3, 5, 0, 3, 2, 10, -1, 3, -2, 13, 0, 2, 4, 3, -6, 4, 0, 2, 1, 3, -2, 5, 0, 2, 3, 3, -4, 4, 0, 2, 3, 2, -4, 3, 0, 2, 1, 10, -1, 13, 0, 2, 1, 3, -1, 5, 0, 2, 1, 3, -2, 6, 0, 2, 2, 3, -2, 4, 0, 2, 1, 3, -1, 6, 0, 1, 1, 11, 2, 2, 1, 3, 1, 5, 0, 3, 1, 11, -2, 12, 2, 13, 0, 3, 1, 10, -2, 12, 1, 13, 0, 2, 2, 2, -2, 3, 0, 3, 2, 10, -1, 11, -2, 12, 0, 2, 4, 3, -5, 4, 0, 2, 3, 3, -3, 4, 0, 3, 4, 10, -2, 12, -2, 13, 0, 1, 1, 2, 0, 2, 2, 3, -3, 5, 0, 2, 2, 10, -2, 13, 2, 2, 2, 3, -2, 5, 0, 2, 3, 3, -3, 2, 0, 3, 1, 10, 1, 11, -1, 13, 0, 3, 3, 3, -1, 2, 1, 4, 0, 2, 2, 3, -1, 5, 0, 3, 1, 10, 1, 12, -2, 13, 0, 1, 2, 11, 0, 2, 2, 12, -2, 13, 0, 2, 2, 2, -1, 3, 0, 2, 4, 2, -4, 3, 0, 2, 3, 10, -3, 13, 0, 4, 2, 10, -2, 13, 1, 3, -1, 5, 0, 2, 3, 3, -3, 5, 0, 3, 2, 10, 1, 11, -2, 13, 0, 3, 1, 10, 2, 12, -3, 13, 0, 1, 3, 11, 0, 3, 1, 11, 2, 12, -2, 13, 0, 2, 5, 2, -5, 3, 0, 2, 4, 10, -4, 13, 0, 2, 6, 2, -6, 3, 0, 3, 2, 10, 2, 11, -2, 13, 0, 3, 2, 10, 2, 12, -4, 13, 0, 3, 2, 11, 2, 12, -2, 13, 0, 3, 4, 10, 1, 11, -4, 13, 0, 4, 1, 10, 1, 11, 2, 12, -4, 13, 0, 3, 1, 10, 3, 11, -2, 13, 0, 3, 3, 10, 1, 11, -4, 13, 0, 4, 1, 10, -2, 11, -2, 12, 2, 13, 0, 3, 1, 10, 2, 12, -4, 13, 0, 3, 1, 10, 2, 11, -2, 13, 0, 3, 2, 10, 1, 11, -3, 13, 0, 3, 1, 13, -2, 2, 1, 4, 0, 2, 3, 10, -4, 13, 0, 4, 1, 10, -1, 11, -2, 12, 2, 13, 0, 4, -1, 10, 2, 13, -2, 2, 2, 3, 0, 2, 1, 10, -3, 11, 0, 2, 2, 12, -3, 13, 0, 2, 2, 11, -1, 13, 0, 3, 1, 10, 1, 11, -2, 13, 2, 4, -1, 10, 2, 13, -1, 3, 1, 5, 0, 2, 2, 10, -3, 13, 0, 3, 3, 10, -1, 11, -4, 13, 0, 3, 4, 11, 2, 13,-11, 2, 0, 3, 1, 10, -2, 12, 2, 13, 0, 3, 1, 12, -2, 13, 1, 5, 0, 2, 1, 10, -2, 11, 0, 2, 1, 11, -1, 13, 0, 3, 1, 10, -2, 13, 1, 5, 0, 3, 1, 10, -2, 3, 2, 5, 0, 3, 18, 2,-18, 3, 2, 5, 0, 3, 1, 10, -3, 2, 3, 3, 0, 3, 2, 13, 16, 11,-18, 2, 0, 2, 1, 10, -2, 13, 2, 3, 1, 13, -2, 10, 5, 4, 0, 3, 2, 12, -2, 14, 7, 2, 0, 3, 1, 10, -2, 3, 3, 5, 0, 3, 1, 12, -1, 3, -2, 5, 1, 3, 2, 10, -1, 11, -3, 13, 0, 3, 3, 10, -2, 12, -2, 13, 0, 2, 8, 2, -1, 3, 0, 4, 1, 10, 1, 11, -2, 12, 2, 13, 0, 3, 1, 12, -2, 14, 2, 4, 0, 2, 1, 10, -1, 11, 0, 3, 8, 2, -5, 3, 8, 4, 0, 2, 18, 2,-17, 3, 0, 3, 1, 10, -1, 3, 1, 5, 0, 1, 1, 13, 0, 3, 1, 10, -1, 11, -2, 13, 1, 3, 1, 10, 1, 11, -2, 12, 0, 3, 1, 10, -1, 2, 1, 3, 0, 3, 2, 13, -8, 2, 1, 3, 0, 2, 3, 10, -2, 12, 0, 3, 2, 10, -1, 12, -1, 5, 0, 3, 3, 10, -2, 11, -2, 13, 0, 3, 2, 10, -1, 11, -1, 13, 0, 3, 2, 10, 1, 3, -2, 4, 0, 3, 1, 12, -1, 10, -1, 14, 0, 4, -1, 10, 2, 13, 2, 3, -3, 5, 0, 3, 2, 13, -4, 2, -5, 3, 0, 3, 2, 12, 2, 10, -3, 14, 1, 2, 1, 12, -2, 5, 0, 2, 10, 2, -3, 11, 0, 1, 1, 10, 2, 3, 1, 12, -2, 10, -2, 5, 0, 2, 18, 2,-16, 3, 0, 2, 2, 12, -3, 14, 1, 3, 1, 13,-17, 2, 2, 11, 0, 3, 1, 10, 1, 2, -3, 4, 0, 3, 1, 12, 1, 10, -1, 14, 0, 4, -1, 10, 2, 13, 2, 3, -2, 5, 0, 3, 1, 10, -1, 3, 2, 4, 0, 4, -1, 10, 2, 13, 3, 2, -3, 3, 0, 4, 1, 10, -2, 11, 2, 12, -2, 13, 0, 2, 1, 11, 1, 13, 0, 3, 8, 2, 2, 3, -3, 4, 0, 1, 1, 12, 0, 3, 6, 2, 9, 3,-10, 4, 1, 3, 1, 10, -2, 11, -2, 13, 0, 2, 8, 2, 1, 4, 0, 2, 1, 10, -2, 12, 0, 2, 11, 2, -4, 3, 0, 3, 3, 11, -2, 14, 6, 2, 0, 3, 3, 10, -1, 11, -2, 13, 0, 2, 2, 10, -1, 13, 0, 3, 1, 12, -2, 2, 4, 3, 0, 2, 1, 10, 1, 11, 1, 4, 1, 10, -1, 11, 2, 12, -2, 13, 0, 2, 2, 11, 1, 13, 0, 2, 2, 12, -1, 13, 0, 3, 1, 10, -1, 11, -2, 12, 0, 2, 3, 10, -2, 13, 0, 2, 1, 10, 2, 11, 0, 3, 1, 10, 2, 12, -2, 13, 0, 3, 1, 11, 2, 12, -1, 13, 0, 3, 3, 10, 1, 11, -2, 13, 0, 2, 1, 10, 3, 11, 0, 4, 1, 10, 1, 11, 2, 12, -2, 13, 0, 2, 5, 10, -4, 13, 0, 3, 3, 10, 2, 11, -2, 13, 0, 3, 3, 10, 2, 12, -4, 13, 0, 2, 4, 11, -2, 13, 0, 3, 2, 10, 2, 11, -4, 13, 0, 2, 3, 11, -2, 13, 0, 3, 1, 10, 2, 11, -3, 13, 0, 3, 2, 10, 1, 11, -4, 13, 0, 2, 3, 10, -5, 13, 0, 2, 2, 12, -4, 13, 0, 2, 2, 11, -2, 13, 0, 3, 1, 10, 1, 11, -3, 13, 0, 3, 2, 13, -2, 3, 2, 5, 0, 2, 2, 10, -4, 13, 1, 4, 2, 10, -1, 11, -2, 12, 2, 13, 0, 2, 2, 14, -2, 2, 0, 3, 1, 10, -2, 12, 3, 13, 0, 2, 1, 11, -2, 13, 1, 3, 2, 14, -2, 2, 3, 5, 0, 3, 2, 13, -1, 3, 1, 5, 0, 2, 1, 10, -3, 13, 0, 3, 2, 10, -1, 11, -4, 13, 0, 4, 2, 10, 1, 11, -2, 12, -2, 13, 0, 3, 2, 13, 1, 14, -8, 2, 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13, 0, 3, 1, 10, -1, 11, -6, 13, 0, 4, 1, 10, 1, 11, -2, 12, -4, 13, 0, 2, 1, 10, 4, 13, 0, 3, 1, 10, -2, 12, -4, 13, 0, 3, 3, 10, -1, 11, 2, 13, 0, 2, 2, 10, 3, 13, 0, 3, 1, 10, 1, 11, 4, 13, 0, 4, 1, 10, -1, 11, 2, 12, 2, 13, 0, 2, 3, 10, 2, 13, 0, 3, 1, 10, 2, 12, 2, 13, 0, 3, 3, 10, 1, 11, 2, 13, 0, 3, 1, 10, -1, 11, 4, 12, 0, 1, 5, 10, 0, 2, 3, 10, 2, 12, 0, 2, 1, 11, -6, 13, 0, 1, 6, 13, 0, 3, 2, 10, -1, 11, 4, 13, 0, 2, 2, 10, 4, 13, 0, 2, 2, 12, 4, 13, 0, 3, 4, 10, -1, 11, 2, 13, 0, 3, 2, 10, 1, 11, 4, 13, 0, 2, 4, 10, 2, 13, 0, 3, 2, 10, 2, 12, 2, 13, 0, 1, 6, 10, 0, 2, 1, 10, 6, 13, 0, 2, 3, 10, 4, 13, 0, 2, 5, 10, 2, 13, 0, -1 }; /* Total terms = 356, small = 356 */ static struct plantbl liblon = { /* { 0, 18, 18, 10, 3, 2, 0, 0, 0, 6, 16, 6, 6, 3,}, */ /* Use max of liblon, liblat. */ { 0, 18, 18, 20, 4, 2, 0, 0, 0, 9, 16, 7, 9, 9,}, 2, lonargs, lontabl, lontabb, lontabr, 3.850000e+05, 36525.0, 1.0e-4, }; /* given a Julian date, return the lunar libration in lat and long, in rads. */ void llibration (double JD, double *llatp, double *llonp) { double lg, lt; /* arc seconds */ lg = gplan (JD, &liblon); lt = gplan (JD, &liblat); *llonp = degrad (lg/3600.0); *llatp = degrad (lt/3600.0); }