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swemmoon.c
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/* SWISSEPH
$Header: swemmoon.c,v 1.27 98/12/02 19:18:02 dieter Exp $
*
* Steve Moshier's analytical lunar ephemeris
*/
/* Copyright (C) 1997, 1998 Astrodienst AG, Switzerland. All rights reserved.
This file is part of Swiss Ephemeris Free Edition.
Swiss Ephemeris is distributed with NO WARRANTY OF ANY KIND. No author
or distributor accepts any responsibility for the consequences of using it,
or for whether it serves any particular purpose or works at all, unless he
or she says so in writing. Refer to the Swiss Ephemeris Public License
("SEPL" or the "License") for full details.
Every copy of Swiss Ephemeris must include a copy of the License,
normally in a plain ASCII text file named LICENSE. The License grants you
the right to copy, modify and redistribute Swiss Ephemeris, but only
under certain conditions described in the License. Among other things, the
License requires that the copyright notices and this notice be preserved on
all copies.
For uses of the Swiss Ephemeris which do not fall under the definitions
laid down in the Public License, the Swiss Ephemeris Professional Edition
must be purchased by the developer before he/she distributes any of his
software or makes available any product or service built upon the use of
the Swiss Ephemeris.
Authors of the Swiss Ephemeris: Dieter Koch and Alois Treindl
The authors of Swiss Ephemeris have no control or influence over any of
the derived works, i.e. over software or services created by other
programmers which use Swiss Ephemeris functions.
The names of the authors or of the copyright holder (Astrodienst) must not
be used for promoting any software, product or service which uses or contains
the Swiss Ephemeris. This copyright notice is the ONLY place where the
names of the authors can legally appear, except in cases where they have
given special permission in writing.
The trademarks 'Swiss Ephemeris' and 'Swiss Ephemeris inside' may be used
for promoting such software, products or services.
*/
/*
* Expansions for the geocentric ecliptic longitude,
* latitude, and distance of the Moon referred to the mean equinox
* and ecliptic of date.
*
* This version of cmoon.c adjusts the ELP2000-85 analytical Lunar
* theory of Chapront-Touze and Chapront to fit the Jet Propulsion
* Laboratory's DE404 long ephemeris on the interval from 3000 B.C.
* to 3000 A.D.
*
* The fit is much better in the remote past and future if
* secular terms are included in the arguments of the oscillatory
* perturbations. Such adjustments cannot easily be incorporated
* into the 1991 lunar tables. In this program the traditional
* literal arguments are used instead, with mean elements adjusted
* for a best fit to the reference ephemeris.
*
* This program omits many oscillatory terms from the analytical
* theory which, if they were included, would yield a much higher
* accuracy for modern dates. Detailed statistics of the precision
* are given in the table below. Comparing at 64-day intervals
* over the period -3000 to +3000, the maximum discrepancies noted
* were 7" longitude, 5" latitude, and 5 x 10^-8 au radius.
* The expressions used for precession in this comparision were
* those of Simon et al (1994).
*
* The adjusted coefficients were found by an unweighted least squares
* fit to the numerical ephemeris in the mentioned test interval.
* The approximation error increases rapidly outside this interval.
* J. Chapront (1994) has described the basic fitting procedure.
*
* A major change from DE200 to DE404 is in the coefficient
* of tidal acceleration of the Moon, which causes the Moon's
* longitude to depart by about -0.9" per century squared
* from DE200. Uncertainty in this quantity continues to
* be the limiting factor in long term projections of the Moon's
* ephemeris.
*
* Since the Lunar theory is cast in the ecliptic of date, it makes
* some difference what formula you use for precession. The adjustment
* to DE404 was carried out relative to the mean equinox and ecliptic
* of date as defined in Williams (1994). An earlier version of this
* program used the precession given by Simon et al (1994). The difference
* between these two precession formulas amounts to about 12" in Lunar
* longitude at 3000 B.C.
*
* Maximum deviations between DE404 and this program
* in a set of 34274 samples spaced 64 days apart
*
* Interval Longitude Latitude Radius
* Julian Year arc sec arc sec 10^-8 au
* -3000 to -2500 5.66 4.66 4.93
* -2500 to -2000 5.49 3.98 4.56
* -2000 to -1500 6.98 4.17 4.81
* -1500 to -1000 5.74 3.53 4.87
* -1000 to -500 5.95 3.42 4.67
* -500 to 0 4.94 3.07 4.04
* 0 to 500 4.42 2.65 4.55
* 500 to 1000 5.68 3.30 3.99
* 1000 to 1500 4.32 3.21 3.83
* 1500 to 2000 2.70 2.69 3.71
* 2000 to 2500 3.35 2.32 3.85
* 2500 to 3000 4.62 2.39 4.11
*
*
*
* References:
*
* James G. Williams, "Contributions to the Earth's obliquity rate,
* precession, and nutation," Astron. J. 108, 711-724 (1994)
*
* DE403 and DE404 ephemerides by E. M. Standish, X. X. Newhall, and
* J. G. Williams are at the JPL computer site navigator.jpl.nasa.gov.
*
* J. L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touze', G. Francou,
* and J. Laskar, "Numerical Expressions for precession formulae and
* mean elements for the Moon and the planets," Astronomy and Astrophysics
* 282, 663-683 (1994)
*
* P. Bretagnon and Francou, G., "Planetary theories in rectangular
* and spherical variables. VSOP87 solutions," Astronomy and
* Astrophysics 202, 309-315 (1988)
*
* M. Chapront-Touze' and J. Chapront, "ELP2000-85: a semi-analytical
* lunar ephemeris adequate for historical times," Astronomy and
* Astrophysics 190, 342-352 (1988).
*
* M. Chapront-Touze' and J. Chapront, _Lunar Tables and
* Programs from 4000 B.C. to A.D. 8000_, Willmann-Bell (1991)
*
* J. Laskar, "Secular terms of classical planetary theories
* using the results of general theory," Astronomy and Astrophysics
* 157, 59070 (1986)
*
* S. L. Moshier, "Comparison of a 7000-year lunar ephemeris
* with analytical theory," Astronomy and Astrophysics 262,
* 613-616 (1992)
*
* J. Chapront, "Representation of planetary ephemerides by frequency
* analysis. Application to the five outer planets," Astronomy and
* Astrophysics Suppl. Ser. 109, 181-192 (1994)
*
*
* Entry swi_moshmoon2() returns the geometric position of the Moon
* relative to the Earth. Its calling procedure is as follows:
*
* double JD; input Julian Ephemeris Date
* double pol[3]; output ecliptic polar coordinatees in radians and au
* pol[0] longitude, pol[1] latitude, pol[2] radius
* swi_moshmoon2( JD, pol );
*
* - S. L. Moshier, August, 1991
* DE200 fit: July, 1992
* DE404 fit: October, 1995
*
* Dieter Koch: adaptation to SWISSEPH, April 1996
*/
#include <string.h>
#include "swephexp.h"
#include "sweph.h"
#include "swephlib.h"
static void mean_elements(void);
static double mods3600(double x);
#ifndef NO_MOSHIER
static void ecldat_equ2000(double tjd, double *xpm);
static void chewm(short *pt, int nlines, int nangles,
int typflg, double *ans );
static void sscc(int k, double arg, int n );
static void moon1(void);
static void moon2(void);
static void moon3(void);
static void moon4(void);
#endif
/* The following coefficients were calculated by a simultaneous least
* squares fit between the analytical theory and DE404 on the finite
* interval from -3000 to +3000.
* The coefficients were estimated from 34,247 Lunar positions.
*/
static double FAR z[] = {
/* The following are scaled in arc seconds, time in Julian centuries.
They replace the corresponding terms in the mean elements. */
-1.312045233711e+01, /* F, t^2 */
-1.138215912580e-03, /* F, t^3 */
-9.646018347184e-06, /* F, t^4 */
3.146734198839e+01, /* l, t^2 */
4.768357585780e-02, /* l, t^3 */
-3.421689790404e-04, /* l, t^4 */
-6.847070905410e+00, /* D, t^2 */
-5.834100476561e-03, /* D, t^3 */
-2.905334122698e-04, /* D, t^4 */
-5.663161722088e+00, /* L, t^2 */
5.722859298199e-03, /* L, t^3 */
-8.466472828815e-05, /* L, t^4 */
/* The following longitude terms are in arc seconds times 10^5. */
-8.429817796435e+01, /* t^2 cos(18V - 16E - l) */
-2.072552484689e+02, /* t^2 sin(18V - 16E - l) */
7.876842214863e+00, /* t^2 cos(10V - 3E - l) */
1.836463749022e+00, /* t^2 sin(10V - 3E - l) */
-1.557471855361e+01, /* t^2 cos(8V - 13E) */
-2.006969124724e+01, /* t^2 sin(8V - 13E) */
2.152670284757e+01, /* t^2 cos(4E - 8M + 3J) */
-6.179946916139e+00, /* t^2 sin(4E - 8M + 3J) */
-9.070028191196e-01, /* t^2 cos(18V - 16E) */
-1.270848233038e+01, /* t^2 sin(18V - 16E) */
-2.145589319058e+00, /* t^2 cos(2J - 5S) */
1.381936399935e+01, /* t^2 sin(2J - 5S) */
-1.999840061168e+00, /* t^3 sin(l') */
};
#ifndef NO_MOSHIER
/* Perturbation tables
*/
#define NLR 118
static short FAR LR[8*NLR] = {
/*
Longitude Radius
D l' l F 1" .0001" 1km .0001km */
0, 0, 1, 0, 22639, 5858,-20905,-3550,
2, 0,-1, 0, 4586, 4383, -3699,-1109,
2, 0, 0, 0, 2369, 9139, -2955,-9676,
0, 0, 2, 0, 769, 257, -569,-9251,
0, 1, 0, 0, -666,-4171, 48, 8883,
0, 0, 0, 2, -411,-5957, -3,-1483,
2, 0,-2, 0, 211, 6556, 246, 1585,
2,-1,-1, 0, 205, 4358, -152,-1377,
2, 0, 1, 0, 191, 9562, -170,-7331,
2,-1, 0, 0, 164, 7285, -204,-5860,
0, 1,-1, 0, -147,-3213, -129,-6201,
1, 0, 0, 0, -124,-9881, 108, 7427,
0, 1, 1, 0, -109,-3803, 104, 7552,
2, 0, 0,-2, 55, 1771, 10, 3211,
0, 0, 1, 2, -45, -996, 0, 0,
0, 0, 1,-2, 39, 5333, 79, 6606,
4, 0,-1, 0, 38, 4298, -34,-7825,
0, 0, 3, 0, 36, 1238, -23,-2104,
4, 0,-2, 0, 30, 7726, -21,-6363,
2, 1,-1, 0, -28,-3971, 24, 2085,
2, 1, 0, 0, -24,-3582, 30, 8238,
1, 0,-1, 0, -18,-5847, -8,-3791,
1, 1, 0, 0, 17, 9545, -16,-6747,
2,-1, 1, 0, 14, 5303, -12,-8314,
2, 0, 2, 0, 14, 3797, -10,-4448,
4, 0, 0, 0, 13, 8991, -11,-6500,
2, 0,-3, 0, 13, 1941, 14, 4027,
0, 1,-2, 0, -9,-6791, -7, -27,
2, 0,-1, 2, -9,-3659, 0, 7740,
2,-1,-2, 0, 8, 6055, 10, 562,
1, 0, 1, 0, -8,-4531, 6, 3220,
2,-2, 0, 0, 8, 502, -9,-8845,
0, 1, 2, 0, -7,-6302, 5, 7509,
0, 2, 0, 0, -7,-4475, 1, 657,
2,-2,-1, 0, 7, 3712, -4,-9501,
2, 0, 1,-2, -6,-3832, 4, 1311,
2, 0, 0, 2, -5,-7416, 0, 0,
4,-1,-1, 0, 4, 3740, -3,-9580,
0, 0, 2, 2, -3,-9976, 0, 0,
3, 0,-1, 0, -3,-2097, 3, 2582,
2, 1, 1, 0, -2,-9145, 2, 6164,
4,-1,-2, 0, 2, 7319, -1,-8970,
0, 2,-1, 0, -2,-5679, -2,-1171,
2, 2,-1, 0, -2,-5212, 2, 3536,
2, 1,-2, 0, 2, 4889, 0, 1437,
2,-1, 0,-2, 2, 1461, 0, 6571,
4, 0, 1, 0, 1, 9777, -1,-4226,
0, 0, 4, 0, 1, 9337, -1,-1169,
4,-1, 0, 0, 1, 8708, -1,-5714,
1, 0,-2, 0, -1,-7530, -1,-7385,
2, 1, 0,-2, -1,-4372, 0,-1357,
0, 0, 2,-2, -1,-3726, -4,-4212,
1, 1, 1, 0, 1, 2618, 0,-9333,
3, 0,-2, 0, -1,-2241, 0, 8624,
4, 0,-3, 0, 1, 1868, 0,-5142,
2,-1, 2, 0, 1, 1770, 0,-8488,
0, 2, 1, 0, -1,-1617, 1, 1655,
1, 1,-1, 0, 1, 777, 0, 8512,
2, 0, 3, 0, 1, 595, 0,-6697,
2, 0, 1, 2, 0,-9902, 0, 0,
2, 0,-4, 0, 0, 9483, 0, 7785,
2,-2, 1, 0, 0, 7517, 0,-6575,
0, 1,-3, 0, 0,-6694, 0,-4224,
4, 1,-1, 0, 0,-6352, 0, 5788,
1, 0, 2, 0, 0,-5840, 0, 3785,
1, 0, 0,-2, 0,-5833, 0,-7956,
6, 0,-2, 0, 0, 5716, 0,-4225,
2, 0,-2,-2, 0,-5606, 0, 4726,
1,-1, 0, 0, 0,-5569, 0, 4976,
0, 1, 3, 0, 0,-5459, 0, 3551,
2, 0,-2, 2, 0,-5357, 0, 7740,
2, 0,-1,-2, 0, 1790, 8, 7516,
3, 0, 0, 0, 0, 4042, -1,-4189,
2,-1,-3, 0, 0, 4784, 0, 4950,
2,-1, 3, 0, 0, 932, 0, -585,
2, 0, 2,-2, 0,-4538, 0, 2840,
2,-1,-1, 2, 0,-4262, 0, 373,
0, 0, 0, 4, 0, 4203, 0, 0,
0, 1, 0, 2, 0, 4134, 0,-1580,
6, 0,-1, 0, 0, 3945, 0,-2866,
2,-1, 0, 2, 0,-3821, 0, 0,
2,-1, 1,-2, 0,-3745, 0, 2094,
4, 1,-2, 0, 0,-3576, 0, 2370,
1, 1,-2, 0, 0, 3497, 0, 3323,
2,-3, 0, 0, 0, 3398, 0,-4107,
0, 0, 3, 2, 0,-3286, 0, 0,
4,-2,-1, 0, 0,-3087, 0,-2790,
0, 1,-1,-2, 0, 3015, 0, 0,
4, 0,-1,-2, 0, 3009, 0,-3218,
2,-2,-2, 0, 0, 2942, 0, 3430,
6, 0,-3, 0, 0, 2925, 0,-1832,
2, 1, 2, 0, 0,-2902, 0, 2125,
4, 1, 0, 0, 0,-2891, 0, 2445,
4,-1, 1, 0, 0, 2825, 0,-2029,
3, 1,-1, 0, 0, 2737, 0,-2126,
0, 1, 1, 2, 0, 2634, 0, 0,
1, 0, 0, 2, 0, 2543, 0, 0,
3, 0, 0,-2, 0,-2530, 0, 2010,
2, 2,-2, 0, 0,-2499, 0,-1089,
2,-3,-1, 0, 0, 2469, 0,-1481,
3,-1,-1, 0, 0,-2314, 0, 2556,
4, 0, 2, 0, 0, 2185, 0,-1392,
4, 0,-1, 2, 0,-2013, 0, 0,
0, 2,-2, 0, 0,-1931, 0, 0,
2, 2, 0, 0, 0,-1858, 0, 0,
2, 1,-3, 0, 0, 1762, 0, 0,
4, 0,-2, 2, 0,-1698, 0, 0,
4,-2,-2, 0, 0, 1578, 0,-1083,
4,-2, 0, 0, 0, 1522, 0,-1281,
3, 1, 0, 0, 0, 1499, 0,-1077,
1,-1,-1, 0, 0,-1364, 0, 1141,
1,-3, 0, 0, 0,-1281, 0, 0,
6, 0, 0, 0, 0, 1261, 0, -859,
2, 0, 2, 2, 0,-1239, 0, 0,
1,-1, 1, 0, 0,-1207, 0, 1100,
0, 0, 5, 0, 0, 1110, 0, -589,
0, 3, 0, 0, 0,-1013, 0, 213,
4,-1,-3, 0, 0, 998, 0, 0,
};
#define NMB 77
static short FAR MB[6*NMB] = {
/*
Latitude
D l' l F 1" .0001" */
0, 0, 0, 1,18461, 2387,
0, 0, 1, 1, 1010, 1671,
0, 0, 1,-1, 999, 6936,
2, 0, 0,-1, 623, 6524,
2, 0,-1, 1, 199, 4837,
2, 0,-1,-1, 166, 5741,
2, 0, 0, 1, 117, 2607,
0, 0, 2, 1, 61, 9120,
2, 0, 1,-1, 33, 3572,
0, 0, 2,-1, 31, 7597,
2,-1, 0,-1, 29, 5766,
2, 0,-2,-1, 15, 5663,
2, 0, 1, 1, 15, 1216,
2, 1, 0,-1, -12, -941,
2,-1,-1, 1, 8, 8681,
2,-1, 0, 1, 7, 9586,
2,-1,-1,-1, 7, 4346,
0, 1,-1,-1, -6,-7314,
4, 0,-1,-1, 6, 5796,
0, 1, 0, 1, -6,-4601,
0, 0, 0, 3, -6,-2965,
0, 1,-1, 1, -5,-6324,
1, 0, 0, 1, -5,-3684,
0, 1, 1, 1, -5,-3113,
0, 1, 1,-1, -5, -759,
0, 1, 0,-1, -4,-8396,
1, 0, 0,-1, -4,-8057,
0, 0, 3, 1, 3, 9841,
4, 0, 0,-1, 3, 6745,
4, 0,-1, 1, 2, 9985,
0, 0, 1,-3, 2, 7986,
4, 0,-2, 1, 2, 4139,
2, 0, 0,-3, 2, 1863,
2, 0, 2,-1, 2, 1462,
2,-1, 1,-1, 1, 7660,
2, 0,-2, 1, -1,-6244,
0, 0, 3,-1, 1, 5813,
2, 0, 2, 1, 1, 5198,
2, 0,-3,-1, 1, 5156,
2, 1,-1, 1, -1,-3178,
2, 1, 0, 1, -1,-2643,
4, 0, 0, 1, 1, 1919,
2,-1, 1, 1, 1, 1346,
2,-2, 0,-1, 1, 859,
0, 0, 1, 3, -1, -194,
2, 1, 1,-1, 0,-8227,
1, 1, 0,-1, 0, 8042,
1, 1, 0, 1, 0, 8026,
0, 1,-2,-1, 0,-7932,
2, 1,-1,-1, 0,-7910,
1, 0, 1, 1, 0,-6674,
2,-1,-2,-1, 0, 6502,
0, 1, 2, 1, 0,-6388,
4, 0,-2,-1, 0, 6337,
4,-1,-1,-1, 0, 5958,
1, 0, 1,-1, 0,-5889,
4, 0, 1,-1, 0, 4734,
1, 0,-1,-1, 0,-4299,
4,-1, 0,-1, 0, 4149,
2,-2, 0, 1, 0, 3835,
3, 0, 0,-1, 0,-3518,
4,-1,-1, 1, 0, 3388,
2, 0,-1,-3, 0, 3291,
2,-2,-1, 1, 0, 3147,
0, 1, 2,-1, 0,-3129,
3, 0,-1,-1, 0,-3052,
0, 1,-2, 1, 0,-3013,
2, 0, 1,-3, 0,-2912,
2,-2,-1,-1, 0, 2686,
0, 0, 4, 1, 0, 2633,
2, 0,-3, 1, 0, 2541,
2, 0,-1, 3, 0,-2448,
2, 1, 1, 1, 0,-2370,
4,-1,-2, 1, 0, 2138,
4, 0, 1, 1, 0, 2126,
3, 0,-1, 1, 0,-2059,
4, 1,-1,-1, 0,-1719,
};
#define NLRT 38
static short FAR LRT[8*NLRT] = {
/*
Multiply by T
Longitude Radius
D l' l F .1" .00001" .1km .00001km */
0, 1, 0, 0, 16, 7680, -1,-2302,
2,-1,-1, 0, -5,-1642, 3, 8245,
2,-1, 0, 0, -4,-1383, 5, 1395,
0, 1,-1, 0, 3, 7115, 3, 2654,
0, 1, 1, 0, 2, 7560, -2,-6396,
2, 1,-1, 0, 0, 7118, 0,-6068,
2, 1, 0, 0, 0, 6128, 0,-7754,
1, 1, 0, 0, 0,-4516, 0, 4194,
2,-2, 0, 0, 0,-4048, 0, 4970,
0, 2, 0, 0, 0, 3747, 0, -540,
2,-2,-1, 0, 0,-3707, 0, 2490,
2,-1, 1, 0, 0,-3649, 0, 3222,
0, 1,-2, 0, 0, 2438, 0, 1760,
2,-1,-2, 0, 0,-2165, 0,-2530,
0, 1, 2, 0, 0, 1923, 0,-1450,
0, 2,-1, 0, 0, 1292, 0, 1070,
2, 2,-1, 0, 0, 1271, 0,-6070,
4,-1,-1, 0, 0,-1098, 0, 990,
2, 0, 0, 0, 0, 1073, 0,-1360,
2, 0,-1, 0, 0, 839, 0, -630,
2, 1, 1, 0, 0, 734, 0, -660,
4,-1,-2, 0, 0, -688, 0, 480,
2, 1,-2, 0, 0, -630, 0, 0,
0, 2, 1, 0, 0, 587, 0, -590,
2,-1, 0,-2, 0, -540, 0, -170,
4,-1, 0, 0, 0, -468, 0, 390,
2,-2, 1, 0, 0, -378, 0, 330,
2, 1, 0,-2, 0, 364, 0, 0,
1, 1, 1, 0, 0, -317, 0, 240,
2,-1, 2, 0, 0, -295, 0, 210,
1, 1,-1, 0, 0, -270, 0, -210,
2,-3, 0, 0, 0, -256, 0, 310,
2,-3,-1, 0, 0, -187, 0, 110,
0, 1,-3, 0, 0, 169, 0, 110,
4, 1,-1, 0, 0, 158, 0, -150,
4,-2,-1, 0, 0, -155, 0, 140,
0, 0, 1, 0, 0, 155, 0, -250,
2,-2,-2, 0, 0, -148, 0, -170,
};
#define NBT 16
static short FAR BT[5*NBT] = {
/*
Multiply by T
Latitude
D l' l F .00001" */
2,-1, 0,-1, -7430,
2, 1, 0,-1, 3043,
2,-1,-1, 1, -2229,
2,-1, 0, 1, -1999,
2,-1,-1,-1, -1869,
0, 1,-1,-1, 1696,
0, 1, 0, 1, 1623,
0, 1,-1, 1, 1418,
0, 1, 1, 1, 1339,
0, 1, 1,-1, 1278,
0, 1, 0,-1, 1217,
2,-2, 0,-1, -547,
2,-1, 1,-1, -443,
2, 1,-1, 1, 331,
2, 1, 0, 1, 317,
2, 0, 0,-1, 295,
};
#define NLRT2 25
static short FAR LRT2[6*NLRT2] = {
/*
Multiply by T^2
Longitude Radius
D l' l F .00001" .00001km */
0, 1, 0, 0, 487, -36,
2,-1,-1, 0, -150, 111,
2,-1, 0, 0, -120, 149,
0, 1,-1, 0, 108, 95,
0, 1, 1, 0, 80, -77,
2, 1,-1, 0, 21, -18,
2, 1, 0, 0, 20, -23,
1, 1, 0, 0, -13, 12,
2,-2, 0, 0, -12, 14,
2,-1, 1, 0, -11, 9,
2,-2,-1, 0, -11, 7,
0, 2, 0, 0, 11, 0,
2,-1,-2, 0, -6, -7,
0, 1,-2, 0, 7, 5,
0, 1, 2, 0, 6, -4,
2, 2,-1, 0, 5, -3,
0, 2,-1, 0, 5, 3,
4,-1,-1, 0, -3, 3,
2, 0, 0, 0, 3, -4,
4,-1,-2, 0, -2, 0,
2, 1,-2, 0, -2, 0,
2,-1, 0,-2, -2, 0,
2, 1, 1, 0, 2, -2,
2, 0,-1, 0, 2, 0,
0, 2, 1, 0, 2, 0,
};
#define NBT2 12
static short FAR BT2[5*NBT2] = {
/*
Multiply by T^2
Latitiude
D l' l F .00001" */
2,-1, 0,-1, -22,
2, 1, 0,-1, 9,
2,-1, 0, 1, -6,
2,-1,-1, 1, -6,
2,-1,-1,-1, -5,
0, 1, 0, 1, 5,
0, 1,-1,-1, 5,
0, 1, 1, 1, 4,
0, 1, 1,-1, 4,
0, 1, 0,-1, 4,
0, 1,-1, 1, 4,
2,-2, 0,-1, -2,
};
/* The following times are set up by update() and refer
* to the same instant. The distinction between them
* is required by altaz().
*/
static double FAR ss[5][8];
static double FAR cc[5][8];
static double l; /* Moon's ecliptic longitude */
static double B; /* Ecliptic latitude */
static double moonpol[3];
#endif /* NO_MOSHIER */
/* Orbit calculation begins.
*/
static double LP;
static double M;
static double MP;
static double D;
static double NF;
static double T;
static double T2;
#ifndef NO_MOSHIER
static double T3;
static double T4;
static double f;
static double g;
static double Ve;
static double Ea;
static double Ma;
static double Ju;
static double Sa;
static double cg;
static double sg;
static double l1;
static double l2;
static double l3;
static double l4;
/* Calculate geometric coordinates of Moon
* without light time or nutation correction.
*/
int swi_moshmoon2(double J, double *pol)
{
int i;
T = (J-J2000)/36525.0;
T2 = T*T;
mean_elements();
moon1();
moon2();
moon3();
moon4();
for( i=0; i<3; i++ )
pol[i] = moonpol[i];
return(0);
}
/* Moshier's moom
* tjd julian day
* xpm array of 6 doubles for moon's position and speed vectors
* serr pointer to error string
*/
int swi_moshmoon(double tjd, AS_BOOL do_save, double *xpmret, char *serr)
{
int i;
double a, b, x1[6], x2[6], t;
double xx[6], *xpm;
struct plan_data *pdp = &swed.pldat[SEI_MOON];
char s[AS_MAXCH];
if (do_save)
xpm = pdp->x;
else
xpm = xx;
if (tjd < MOSHLUEPH_START || tjd > MOSHLUEPH_END) {
if (serr != NULL) {
sprintf(s, "jd %f beyond Moshier eph. limits %f and %f ",
tjd, MOSHLUEPH_START, MOSHLUEPH_END);
if (strlen(serr) + strlen(s) < AS_MAXCH)
strcat(serr, s);
}
return(ERR);
}
/* if moon has already been computed */
if (tjd == pdp->teval && pdp->iephe == SEFLG_MOSEPH) {
if (xpmret != NULL)
for (i = 0; i <= 5; i++)
xpmret[i] = pdp->x[i];
return(OK);
}
/* else compute moon */
swi_moshmoon2(tjd, xpm);
if (do_save) {
pdp->teval = tjd;
pdp->xflgs = -1;
pdp->iephe = SEFLG_MOSEPH;
}
/* Moshier moon is referred to ecliptic of date. But we need
* equatorial positions for several reasons.
* e.g. computation of earth from emb and moon
* of heliocentric moon
* Besides, this helps to keep the program structure simpler
*/
ecldat_equ2000(tjd, xpm);
/* speed */
/* from 2 other positions. */
/* one would be good enough for computation of osculating node,
* but not for osculating apogee */
t = tjd + MOON_SPEED_INTV;
swi_moshmoon2(t, x1);
ecldat_equ2000(t, x1);
t = tjd - MOON_SPEED_INTV;
swi_moshmoon2(t, x2);
ecldat_equ2000(t, x2);
for (i = 0; i <= 2; i++) {
#if 0
xpm[i+3] = (x1[i] - x2[i]) / MOON_SPEED_INTV / 2;
#else
b = (x1[i] - x2[i]) / 2;
a = (x1[i] + x2[i]) / 2 - xpm[i];
xpm[i+3] = (2 * a + b) / MOON_SPEED_INTV;
#endif
}
if (xpmret != NULL)
for (i = 0; i <= 5; i++)
xpmret[i] = xpm[i];
return(OK);
}
static void moon1()
{
double a;
/* Mean longitudes of planets (Laskar, Bretagnon) */
Ve = mods3600( 210664136.4335482 * T + 655127.283046 );
Ve += ((((((((
-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;
Ea = mods3600( 129597742.26669231 * T + 361679.214649 );
Ea += (((((((( -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;
Ma = mods3600( 68905077.59284 * T + 1279559.78866 );
Ma += (-1.043e-5*T + 9.38012e-3)*T2;
Ju = mods3600( 10925660.428608 * T + 123665.342120 );
Ju += (1.543273e-5*T - 3.06037836351e-1)*T2;
Sa = mods3600( 4399609.65932 * T + 180278.89694 );
Sa += (( 4.475946e-8*T - 6.874806E-5 ) * T + 7.56161437443E-1)*T2;
sscc( 0, STR*D, 6 );
sscc( 1, STR*M, 4 );
sscc( 2, STR*MP, 4 );
sscc( 3, STR*NF, 4 );
moonpol[0] = 0.0;
moonpol[1] = 0.0;
moonpol[2] = 0.0;
/* terms in T^2, scale 1.0 = 10^-5" */
chewm( LRT2, NLRT2, 4, 2, moonpol );
chewm( BT2, NBT2, 4, 4, moonpol );
f = 18 * Ve - 16 * Ea;
g = STR*(f - MP ); /* 18V - 16E - l */
cg = cos(g);
sg = sin(g);
l = 6.367278 * cg + 12.747036 * sg; /* t^0 */
l1 = 23123.70 * cg - 10570.02 * sg; /* t^1 */
l2 = z[12] * cg + z[13] * sg; /* t^2 */
moonpol[2] += 5.01 * cg + 2.72 * sg;
g = STR * (10.*Ve - 3.*Ea - MP);
cg = cos(g);
sg = sin(g);
l += -0.253102 * cg + 0.503359 * sg;
l1 += 1258.46 * cg + 707.29 * sg;
l2 += z[14] * cg + z[15] * sg;
g = STR*(8.*Ve - 13.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.187231 * cg - 0.127481 * sg;
l1 += -319.87 * cg - 18.34 * sg;
l2 += z[16] * cg + z[17] * sg;
a = 4.0*Ea - 8.0*Ma + 3.0*Ju;
g = STR * a;
cg = cos(g);
sg = sin(g);
l += -0.866287 * cg + 0.248192 * sg;
l1 += 41.87 * cg + 1053.97 * sg;
l2 += z[18] * cg + z[19] * sg;
g = STR*(a - MP);
cg = cos(g);
sg = sin(g);
l += -0.165009 * cg + 0.044176 * sg;
l1 += 4.67 * cg + 201.55 * sg;
g = STR*f; /* 18V - 16E */
cg = cos(g);
sg = sin(g);
l += 0.330401 * cg + 0.661362 * sg;
l1 += 1202.67 * cg - 555.59 * sg;
l2 += z[20] * cg + z[21] * sg;
g = STR*(f - 2.0*MP ); /* 18V - 16E - 2l */
cg = cos(g);
sg = sin(g);
l += 0.352185 * cg + 0.705041 * sg;
l1 += 1283.59 * cg - 586.43 * sg;
g = STR * (2.0*Ju - 5.0*Sa);
cg = cos(g);
sg = sin(g);
l += -0.034700 * cg + 0.160041 * sg;
l2 += z[22] * cg + z[23] * sg;
g = STR * (LP - NF);
cg = cos(g);
sg = sin(g);
l += 0.000116 * cg + 7.063040 * sg;
l1 += 298.8 * sg;
/* T^3 terms */
sg = sin( STR * M );
/* l3 += z[24] * sg; moshier! l3 not initialized! */
l3 = z[24] * sg;
l4 = 0;
g = STR * (2.0*D - M);
sg = sin(g);
cg = cos(g);
moonpol[2] += -0.2655 * cg * T;
g = STR * (M - MP);
moonpol[2] += -0.1568 * cos( g ) * T;
g = STR * (M + MP);
moonpol[2] += 0.1309 * cos( g ) * T;
g = STR * (2.0*(D + M) - MP);
sg = sin(g);
cg = cos(g);
moonpol[2] += 0.5568 * cg * T;
l2 += moonpol[0];
g = STR*(2.0*D - M - MP);
moonpol[2] += -0.1910 * cos( g ) * T;
moonpol[1] *= T;
moonpol[2] *= T;
/* terms in T */
moonpol[0] = 0.0;
chewm( BT, NBT, 4, 4, moonpol );
chewm( LRT, NLRT, 4, 1, moonpol );
g = STR*(f - MP - NF - 2355767.6); /* 18V - 16E - l - F */
moonpol[1] += -1127. * sin(g);
g = STR*(f - MP + NF - 235353.6); /* 18V - 16E - l + F */
moonpol[1] += -1123. * sin(g);
g = STR*(Ea + D + 51987.6);
moonpol[1] += 1303. * sin(g);
g = STR*LP;
moonpol[1] += 342. * sin(g);
g = STR*(2.*Ve - 3.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.343550 * cg - 0.000276 * sg;
l1 += 105.90 * cg + 336.53 * sg;
g = STR*(f - 2.*D); /* 18V - 16E - 2D */
cg = cos(g);
sg = sin(g);
l += 0.074668 * cg + 0.149501 * sg;
l1 += 271.77 * cg - 124.20 * sg;
g = STR*(f - 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.073444 * cg + 0.147094 * sg;
l1 += 265.24 * cg - 121.16 * sg;
g = STR*(f + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.072844 * cg + 0.145829 * sg;
l1 += 265.18 * cg - 121.29 * sg;
g = STR*(f + 2.*(D - MP));
cg = cos(g);
sg = sin(g);
l += 0.070201 * cg + 0.140542 * sg;
l1 += 255.36 * cg - 116.79 * sg;
g = STR*(Ea + D - NF);
cg = cos(g);
sg = sin(g);
l += 0.288209 * cg - 0.025901 * sg;
l1 += -63.51 * cg - 240.14 * sg;
g = STR*(2.*Ea - 3.*Ju + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.077865 * cg + 0.438460 * sg;
l1 += 210.57 * cg + 124.84 * sg;
g = STR*(Ea - 2.*Ma);
cg = cos(g);
sg = sin(g);
l += -0.216579 * cg + 0.241702 * sg;
l1 += 197.67 * cg + 125.23 * sg;
g = STR*(a + MP);
cg = cos(g);
sg = sin(g);
l += -0.165009 * cg + 0.044176 * sg;
l1 += 4.67 * cg + 201.55 * sg;
g = STR*(a + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += -0.133533 * cg + 0.041116 * sg;
l1 += 6.95 * cg + 187.07 * sg;
g = STR*(a - 2.*D + MP);
cg = cos(g);
sg = sin(g);
l += -0.133430 * cg + 0.041079 * sg;
l1 += 6.28 * cg + 169.08 * sg;
g = STR*(3.*Ve - 4.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.175074 * cg + 0.003035 * sg;
l1 += 49.17 * cg + 150.57 * sg;
g = STR*(2.*(Ea + D - MP) - 3.*Ju + 213534.);
l1 += 158.4 * sin(g);
l1 += moonpol[0];
a = 0.1 * T; /* set amplitude scale of 1.0 = 10^-4 arcsec */
moonpol[1] *= a;
moonpol[2] *= a;
}
static void moon2()
{
/* terms in T^0 */
g = STR*(2*(Ea-Ju+D)-MP+648431.172);
l += 1.14307 * sin(g);
g = STR*(Ve-Ea+648035.568);
l += 0.82155 * sin(g);
g = STR*(3*(Ve-Ea)+2*D-MP+647933.184);
l += 0.64371 * sin(g);
g = STR*(Ea-Ju+4424.04);
l += 0.63880 * sin(g);
g = STR*(LP + MP - NF + 4.68);
l += 0.49331 * sin(g);
g = STR*(LP - MP - NF + 4.68);
l += 0.4914 * sin(g);
g = STR*(LP+NF+2.52);
l += 0.36061 * sin(g);
g = STR*(2.*Ve - 2.*Ea + 736.2);
l += 0.30154 * sin(g);
g = STR*(2.*Ea - 3.*Ju + 2.*D - 2.*MP + 36138.2);
l += 0.28282 * sin(g);
g = STR*(2.*Ea - 2.*Ju + 2.*D - 2.*MP + 311.0);
l += 0.24516 * sin(g);
g = STR*(Ea - Ju - 2.*D + MP + 6275.88);
l += 0.21117 * sin(g);
g = STR*(2.*(Ea - Ma) - 846.36);
l += 0.19444 * sin(g);
g = STR*(2.*(Ea - Ju) + 1569.96);
l -= 0.18457 * sin(g);
g = STR*(2.*(Ea - Ju) - MP - 55.8);
l += 0.18256 * sin(g);
g = STR*(Ea - Ju - 2.*D + 6490.08);
l += 0.16499 * sin(g);
g = STR*(Ea - 2.*Ju - 212378.4);
l += 0.16427 * sin(g);
g = STR*(2.*(Ve - Ea - D) + MP + 1122.48);
l += 0.16088 * sin(g);
g = STR*(Ve - Ea - MP + 32.04);
l -= 0.15350 * sin(g);
g = STR*(Ea - Ju - MP + 4488.88);
l += 0.14346 * sin(g);
g = STR*(2.*(Ve - Ea + D) - MP - 8.64);
l += 0.13594 * sin(g);
g = STR*(2.*(Ve - Ea - D) + 1319.76);
l += 0.13432 * sin(g);
g = STR*(Ve - Ea - 2.*D + MP - 56.16);
l -= 0.13122 * sin(g);
g = STR*(Ve - Ea + MP + 54.36);
l -= 0.12722 * sin(g);
g = STR*(3.*(Ve - Ea) - MP + 433.8);
l += 0.12539 * sin(g);
g = STR*(Ea - Ju + MP + 4002.12);
l += 0.10994 * sin(g);
g = STR*(20.*Ve - 21.*Ea - 2.*D + MP - 317511.72);
l += 0.10652 * sin(g);
g = STR*(26.*Ve - 29.*Ea - MP + 270002.52);
l += 0.10490 * sin(g);
g = STR*(3.*Ve - 4.*Ea + D - MP - 322765.56);
l += 0.10386 * sin(g);
g = STR*(LP+648002.556);
B = 8.04508 * sin(g);
g = STR*(Ea+D+996048.252);
B += 1.51021 * sin(g);
g = STR*(f - MP + NF + 95554.332);
B += 0.63037 * sin(g);
g = STR*(f - MP - NF + 95553.792);
B += 0.63014 * sin(g);
g = STR*(LP - MP + 2.9);
B += 0.45587 * sin(g);
g = STR*(LP + MP + 2.5);
B += -0.41573 * sin(g);
g = STR*(LP - 2.0*NF + 3.2);
B += 0.32623 * sin(g);
g = STR*(LP - 2.0*D + 2.5);
B += 0.29855 * sin(g);
}
static void moon3()
{
/* terms in T^0 */
moonpol[0] = 0.0;
chewm( LR, NLR, 4, 1, moonpol );
chewm( MB, NMB, 4, 3, moonpol );
l += (((l4 * T + l3) * T + l2) * T + l1) * T * 1.0e-5;
moonpol[0] = LP + l + 1.0e-4 * moonpol[0];
moonpol[1] = 1.0e-4 * moonpol[1] + B;
moonpol[2] = 1.0e-4 * moonpol[2] + 385000.52899; /* kilometers */
}
/* Compute final ecliptic polar coordinates
*/
static void moon4()
{
moonpol[2] /= AUNIT / 1000;
moonpol[0] = STR * mods3600( moonpol[0] );
moonpol[1] = STR * moonpol[1];
}
#endif /* NO_MOSHIER */
/* mean lunar node
* J julian day
* pol return array for position and velocity
* (polar coordinates of ecliptic of date)
*/
int swi_mean_node(double J, double *pol, char *serr)
{
#if 0
double a, b, c;
#endif
char s[AS_MAXCH];
T = (J-J2000)/36525.0;
T2 = T*T;
#ifndef NO_MOSHIER
T3 = T*T2;
T4 = T2*T2;
#endif /* NO_MOSHIER */