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swephlib.cpp
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/* SWISSEPH
SWISSEPH modules that may be useful for other applications
e.g. chopt.c, venus.c, swetest.c
Authors: Dieter Koch and Alois Treindl, Astrodienst Zurich
coordinate transformations
obliquity of ecliptic
nutation
precession
delta t
sidereal time
setting or getting of tidal acceleration of moon
chebyshew interpolation
ephemeris file name generation
cyclic redundancy checksum CRC
modulo and normalization functions
**************************************************************/
/* Copyright (C) 1997 - 2008 Astrodienst AG, Switzerland. All rights reserved.
License conditions
------------------
This file is part of Swiss Ephemeris.
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.
Swiss Ephemeris is made available by its authors under a dual licensing
system. The software developer, who uses any part of Swiss Ephemeris
in his or her software, must choose between one of the two license models,
which are
a) GNU public license version 2 or later
b) Swiss Ephemeris Professional License
The choice must be made before the software developer distributes software
containing parts of Swiss Ephemeris to others, and before any public
service using the developed software is activated.
If the developer choses the GNU GPL software license, he or she must fulfill
the conditions of that license, which includes the obligation to place his
or her whole software project under the GNU GPL or a compatible license.
See http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
If the developer choses the Swiss Ephemeris Professional license,
he must follow the instructions as found in http://www.astro.com/swisseph/
and purchase the Swiss Ephemeris Professional Edition from Astrodienst
and sign the corresponding license contract.
The License grants you the right to use, 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.
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.
*/
#include "astrolog.h"
#undef MM
#undef DD
#ifdef SWISS
#include <string.h>
#include <ctype.h>
#include "swephexp.h"
#include "sweph.h"
#include "swephlib.h"
#if MSDOS
# include <process.h>
# define strdup _strdup
#endif
#ifdef TRACE
void swi_open_trace(char *serr);
TLS FILE *swi_fp_trace_c = NULL;
TLS FILE *swi_fp_trace_out = NULL;
TLS int32 swi_trace_count = 0;
#endif
static void init_crc32(void);
static int init_dt(void);
static double adjust_for_tidacc(double ans, double Y, double tid_acc, double tid_acc0, AS_BOOL adjust_after_1955);
static double deltat_espenak_meeus_1620(double tjd, double tid_acc);
static double deltat_stephenson_etc_2016(double tjd, double tid_acc);
static double deltat_longterm_morrison_stephenson(double tjd);
static double deltat_stephenson_morrison_2004_1600(double tjd, double tid_acc);
static double deltat_stephenson_morrison_1997_1600(double tjd, double tid_acc);
static double deltat_aa(double tjd, double tid_acc);
#define SEFLG_EPHMASK (SEFLG_JPLEPH|SEFLG_SWIEPH|SEFLG_MOSEPH)
/* Reduce x modulo 360 degrees
*/
double CALL_CONV swe_degnorm(double x)
{
double y;
y = fmod(x, 360.0);
if (fabs(y) < 1e-13) y = 0; /* Alois fix 11-dec-1999 */
if( y < 0.0 ) y += 360.0;
return(y);
}
/* Reduce x modulo TWOPI degrees
*/
double CALL_CONV swe_radnorm(double x)
{
double y;
y = fmod(x, TWOPI);
if (fabs(y) < 1e-13) y = 0; /* Alois fix 11-dec-1999 */
if( y < 0.0 ) y += TWOPI;
return(y);
}
double CALL_CONV swe_deg_midp(double x1, double x0)
{
double d, y;
d = swe_difdeg2n(x1, x0); /* arc from x0 to x1 */
y = swe_degnorm(x0 + d / 2);
return(y);
}
double CALL_CONV swe_rad_midp(double x1, double x0)
{
return DEGTORAD * swe_deg_midp(x1 * RADTODEG, x0 * RADTODEG);
}
/* Reduce x modulo 2*PI
*/
double swi_mod2PI(double x)
{
double y;
y = fmod(x, TWOPI);
if( y < 0.0 ) y += TWOPI;
return(y);
}
double swi_angnorm(double x)
{
if (x < 0.0 )
return x + TWOPI;
else if (x >= TWOPI)
return x - TWOPI;
else
return x;
}
void swi_cross_prod(double *a, double *b, double *x)
{
x[0] = a[1]*b[2] - a[2]*b[1];
x[1] = a[2]*b[0] - a[0]*b[2];
x[2] = a[0]*b[1] - a[1]*b[0];
}
/* Evaluates a given chebyshev series coef[0..ncf-1]
* with ncf terms at x in [-1,1]. Communications of the ACM, algorithm 446,
* April 1973 (vol. 16 no.4) by Dr. Roger Broucke.
*/
double swi_echeb(double x, double *coef, int ncf)
{
int j;
double x2, br, brp2, brpp;
x2 = x * 2.;
br = 0.;
brp2 = 0.; /* dummy assign to silence gcc warning */
brpp = 0.;
for (j = ncf - 1; j >= 0; j--) {
brp2 = brpp;
brpp = br;
br = x2 * brpp - brp2 + coef[j];
}
return (br - brp2) * .5;
}
/*
* evaluates derivative of chebyshev series, see echeb
*/
double swi_edcheb(double x, double *coef, int ncf)
{
double bjpl, xjpl;
int j;
double x2, bf, bj, dj, xj, bjp2, xjp2;
x2 = x * 2.;
bf = 0.; /* dummy assign to silence gcc warning */
bj = 0.; /* dummy assign to silence gcc warning */
xjp2 = 0.;
xjpl = 0.;
bjp2 = 0.;
bjpl = 0.;
for (j = ncf - 1; j >= 1; j--) {
dj = (double) (j + j);
xj = coef[j] * dj + xjp2;
bj = x2 * bjpl - bjp2 + xj;
bf = bjp2;
bjp2 = bjpl;
bjpl = bj;
xjp2 = xjpl;
xjpl = xj;
}
return (bj - bf) * .5;
}
/*
* conversion between ecliptical and equatorial polar coordinates.
* for users of SWISSEPH, not used by our routines.
* for ecl. to equ. eps must be negative.
* for equ. to ecl. eps must be positive.
* xpo, xpn are arrays of 3 doubles containing position.
* attention: input must be in degrees!
*/
void CALL_CONV swe_cotrans(double *xpo, double *xpn, double eps)
{
int i;
double x[6], e = eps * DEGTORAD;
for(i = 0; i <= 1; i++)
x[i] = xpo[i];
x[0] *= DEGTORAD;
x[1] *= DEGTORAD;
x[2] = 1;
for(i = 3; i <= 5; i++)
x[i] = 0;
swi_polcart(x, x);
swi_coortrf(x, x, e);
swi_cartpol(x, x);
xpn[0] = x[0] * RADTODEG;
xpn[1] = x[1] * RADTODEG;
xpn[2] = xpo[2];
}
/*
* conversion between ecliptical and equatorial polar coordinates
* with speed.
* for users of SWISSEPH, not used by our routines.
* for ecl. to equ. eps must be negative.
* for equ. to ecl. eps must be positive.
* xpo, xpn are arrays of 6 doubles containing position and speed.
* attention: input must be in degrees!
*/
void CALL_CONV swe_cotrans_sp(double *xpo, double *xpn, double eps)
{
int i;
double x[6], e = eps * DEGTORAD;
for (i = 0; i <= 5; i++)
x[i] = xpo[i];
x[0] *= DEGTORAD;
x[1] *= DEGTORAD;
x[2] = 1; /* avoids problems with polcart(), if x[2] = 0 */
x[3] *= DEGTORAD;
x[4] *= DEGTORAD;
swi_polcart_sp(x, x);
swi_coortrf(x, x, e);
swi_coortrf(x+3, x+3, e);
swi_cartpol_sp(x, xpn);
xpn[0] *= RADTODEG;
xpn[1] *= RADTODEG;
xpn[2] = xpo[2];
xpn[3] *= RADTODEG;
xpn[4] *= RADTODEG;
xpn[5] = xpo[5];
}
/*
* conversion between ecliptical and equatorial cartesian coordinates
* for ecl. to equ. eps must be negative
* for equ. to ecl. eps must be positive
*/
void swi_coortrf(double *xpo, double *xpn, double eps)
{
double sineps, coseps;
double x[3];
sineps = sin(eps);
coseps = cos(eps);
x[0] = xpo[0];
x[1] = xpo[1] * coseps + xpo[2] * sineps;
x[2] = -xpo[1] * sineps + xpo[2] * coseps;
xpn[0] = x[0];
xpn[1] = x[1];
xpn[2] = x[2];
}
/*
* conversion between ecliptical and equatorial cartesian coordinates
* sineps sin(eps)
* coseps cos(eps)
* for ecl. to equ. sineps must be -sin(eps)
*/
void swi_coortrf2(double *xpo, double *xpn, double sineps, double coseps)
{
double x[3];
x[0] = xpo[0];
x[1] = xpo[1] * coseps + xpo[2] * sineps;
x[2] = -xpo[1] * sineps + xpo[2] * coseps;
xpn[0] = x[0];
xpn[1] = x[1];
xpn[2] = x[2];
}
/* conversion of cartesian (x[3]) to polar coordinates (l[3]).
* x = l is allowed.
* if |x| = 0, then lon, lat and rad := 0.
*/
void swi_cartpol(double *x, double *l)
{
double rxy;
double ll[3];
if (x[0] == 0 && x[1] == 0 && x[2] == 0) {
l[0] = l[1] = l[2] = 0;
return;
}
rxy = x[0]*x[0] + x[1]*x[1];
ll[2] = sqrt(rxy + x[2]*x[2]);
rxy = sqrt(rxy);
ll[0] = atan2(x[1], x[0]);
if (ll[0] < 0.0) ll[0] += TWOPI;
if (rxy == 0) {
if (x[2] >= 0)
ll[1] = PI / 2;
else
ll[1] = -(PI / 2);
} else {
ll[1] = atan(x[2] / rxy);
}
l[0] = ll[0];
l[1] = ll[1];
l[2] = ll[2];
}
/* conversion from polar (l[3]) to cartesian coordinates (x[3]).
* x = l is allowed.
*/
void swi_polcart(double *l, double *x)
{
double xx[3];
double cosl1;
cosl1 = cos(l[1]);
xx[0] = l[2] * cosl1 * cos(l[0]);
xx[1] = l[2] * cosl1 * sin(l[0]);
xx[2] = l[2] * sin(l[1]);
x[0] = xx[0];
x[1] = xx[1];
x[2] = xx[2];
}
/* conversion of position and speed.
* from cartesian (x[6]) to polar coordinates (l[6]).
* x = l is allowed.
* if position is 0, function returns direction of
* motion.
*/
void swi_cartpol_sp(double *x, double *l)
{
int i;
double xx[6], ll[6];
double rxy, coslon, sinlon, coslat, sinlat;
/* zero position */
if (x[0] == 0 && x[1] == 0 && x[2] == 0) {
ll[0] = ll[1] = ll[3] = ll[4] = 0;
ll[5] = sqrt(square_sum((x+3)));
swi_cartpol(x+3, ll);
ll[2] = 0;
for (i = 0; i <= 5; i++)
l[i] = ll[i];
return;
}
/* zero speed */
if (x[3] == 0 && x[4] == 0 && x[5] == 0) {
l[3] = l[4] = l[5] = 0;
swi_cartpol(x, l);
return;
}
/* position */
rxy = x[0]*x[0] + x[1]*x[1];
ll[2] = sqrt(rxy + x[2]*x[2]);
rxy = sqrt(rxy);
ll[0] = atan2(x[1], x[0]);
if (ll[0] < 0.0) ll[0] += TWOPI;
ll[1] = atan(x[2] / rxy);
/* speed:
* 1. rotate coordinate system by longitude of position about z-axis,
* so that new x-axis = position radius projected onto x-y-plane.
* in the new coordinate system
* vy'/r = dlong/dt, where r = sqrt(x^2 +y^2).
* 2. rotate coordinate system by latitude about new y-axis.
* vz"/r = dlat/dt, where r = position radius.
* vx" = dr/dt
*/
coslon = x[0] / rxy; /* cos(l[0]); */
sinlon = x[1] / rxy; /* sin(l[0]); */
coslat = rxy / ll[2]; /* cos(l[1]); */
sinlat = x[2] / ll[2]; /* sin(ll[1]); */
xx[3] = x[3] * coslon + x[4] * sinlon;
xx[4] = -x[3] * sinlon + x[4] * coslon;
l[3] = xx[4] / rxy; /* speed in longitude */
xx[4] = -sinlat * xx[3] + coslat * x[5];
xx[5] = coslat * xx[3] + sinlat * x[5];
l[4] = xx[4] / ll[2]; /* speed in latitude */
l[5] = xx[5]; /* speed in radius */
l[0] = ll[0]; /* return position */
l[1] = ll[1];
l[2] = ll[2];
}
/* conversion of position and speed
* from polar (l[6]) to cartesian coordinates (x[6])
* x = l is allowed
* explanation s. swi_cartpol_sp()
*/
void swi_polcart_sp(double *l, double *x)
{
double sinlon, coslon, sinlat, coslat;
double xx[6], rxy, rxyz;
/* zero speed */
if (l[3] == 0 && l[4] == 0 && l[5] == 0) {
x[3] = x[4] = x[5] = 0;
swi_polcart(l, x);
return;
}
/* position */
coslon = cos(l[0]);
sinlon = sin(l[0]);
coslat = cos(l[1]);
sinlat = sin(l[1]);
xx[0] = l[2] * coslat * coslon;
xx[1] = l[2] * coslat * sinlon;
xx[2] = l[2] * sinlat;
/* speed; explanation s. swi_cartpol_sp(), same method the other way round*/
rxyz = l[2];
rxy = sqrt(xx[0] * xx[0] + xx[1] * xx[1]);
xx[5] = l[5];
xx[4] = l[4] * rxyz;
x[5] = sinlat * xx[5] + coslat * xx[4]; /* speed z */
xx[3] = coslat * xx[5] - sinlat * xx[4];
xx[4] = l[3] * rxy;
x[3] = coslon * xx[3] - sinlon * xx[4]; /* speed x */
x[4] = sinlon * xx[3] + coslon * xx[4]; /* speed y */
x[0] = xx[0]; /* return position */
x[1] = xx[1];
x[2] = xx[2];
}
double swi_dot_prod_unit(double *x, double *y)
{
double dop = x[0]*y[0]+x[1]*y[1]+x[2]*y[2];
double e1 = sqrt(x[0]*x[0]+x[1]*x[1]+x[2]*x[2]);
double e2 = sqrt(y[0]*y[0]+y[1]*y[1]+y[2]*y[2]);
dop /= e1;
dop /= e2;
if (dop > 1)
dop = 1;
if (dop < -1)
dop = -1;
return dop;
}
/* functions for precession and ecliptic obliquity according to Vondrak et alii, 2011 */
#define AS2R (DEGTORAD / 3600.0)
#define D2PI TWOPI
#define EPS0 (84381.406 * AS2R)
#define NPOL_PEPS 4
#define NPER_PEPS 10
#define NPOL_PECL 4
#define NPER_PECL 8
#define NPOL_PEQU 4
#define NPER_PEQU 14
/* for pre_peps(): */
/* polynomials */
static const double pepol[NPOL_PEPS][2] = {
{+8134.017132, +84028.206305},
{+5043.0520035, +0.3624445},
{-0.00710733, -0.00004039},
{+0.000000271, -0.000000110}
};
/* periodics */
static const double peper[5][NPER_PEPS] = {
{+409.90, +396.15, +537.22, +402.90, +417.15, +288.92, +4043.00, +306.00, +277.00, +203.00},
{-6908.287473, -3198.706291, +1453.674527, -857.748557, +1173.231614, -156.981465, +371.836550, -216.619040, +193.691479, +11.891524},
{+753.872780, -247.805823, +379.471484, -53.880558, -90.109153, -353.600190, -63.115353, -28.248187, +17.703387, +38.911307},
{-2845.175469, +449.844989, -1255.915323, +886.736783, +418.887514, +997.912441, -240.979710, +76.541307, -36.788069, -170.964086},
{-1704.720302, -862.308358, +447.832178, -889.571909, +190.402846, -56.564991, -296.222622, -75.859952, +67.473503, +3.014055}
};
/* for pre_pecl(): */
/* polynomials */
static const double pqpol[NPOL_PECL][2] = {
{+5851.607687, -1600.886300},
{-0.1189000, +1.1689818},
{-0.00028913, -0.00000020},
{+0.000000101, -0.000000437}
};
/* periodics */
static const double pqper[5][NPER_PECL] = {
{708.15, 2309, 1620, 492.2, 1183, 622, 882, 547},
{-5486.751211, -17.127623, -617.517403, 413.44294, 78.614193, -180.732815, -87.676083, 46.140315},
// original publication A&A 534, A22 (2011):
//{-684.66156, 2446.28388, 399.671049, -356.652376, -186.387003, -316.80007, 198.296071, 101.135679},
// typo fixed according to A&A 541, C1 (2012)
{-684.66156, 2446.28388, 399.671049, -356.652376, -186.387003, -316.80007, 198.296701, 101.135679},
{667.66673, -2354.886252, -428.152441, 376.202861, 184.778874, 335.321713, -185.138669, -120.97283},
{-5523.863691, -549.74745, -310.998056, 421.535876, -36.776172, -145.278396, -34.74445, 22.885731}
};
/* for pre_pequ(): */
/* polynomials */
static const double xypol[NPOL_PEQU][2] = {
{+5453.282155, -73750.930350},
{+0.4252841, -0.7675452},
{-0.00037173, -0.00018725},
{-0.000000152, +0.000000231}
};
/* periodics */
static const double xyper[5][NPER_PEQU] = {
{256.75, 708.15, 274.2, 241.45, 2309, 492.2, 396.1, 288.9, 231.1, 1610, 620, 157.87, 220.3, 1200},
{-819.940624, -8444.676815, 2600.009459, 2755.17563, -167.659835, 871.855056, 44.769698, -512.313065, -819.415595, -538.071099, -189.793622, -402.922932, 179.516345, -9.814756},
{75004.344875, 624.033993, 1251.136893, -1102.212834, -2660.66498, 699.291817, 153.16722, -950.865637, 499.754645, -145.18821, 558.116553, -23.923029, -165.405086, 9.344131},
{81491.287984, 787.163481, 1251.296102, -1257.950837, -2966.79973, 639.744522, 131.600209, -445.040117, 584.522874, -89.756563, 524.42963, -13.549067, -210.157124, -44.919798},
{1558.515853, 7774.939698, -2219.534038, -2523.969396, 247.850422, -846.485643, -1393.124055, 368.526116, 749.045012, 444.704518, 235.934465, 374.049623, -171.33018, -22.899655}
};
void swi_ldp_peps(double tjd, double *dpre, double *deps)
{
int i;
int npol = NPOL_PEPS;
int nper = NPER_PEPS;
double t, p, q, w, a, s, c;
t = (tjd - J2000) / 36525.0;
p = 0;
q = 0;
/* periodic terms */
for (i = 0; i < nper; i++) {
w = D2PI * t;
a = w / peper[0][i];
s = sin(a);
c = cos(a);
p += c * peper[1][i] + s * peper[3][i];
q += c * peper[2][i] + s * peper[4][i];
}
/* polynomial terms */
w = 1;
for (i = 0; i < npol; i++) {
p += pepol[i][0] * w;
q += pepol[i][1] * w;
w *= t;
}
/* both to radians */
p *= AS2R;
q *= AS2R;
/* return */
if (dpre != NULL)
*dpre = p;
if (deps != NULL)
*deps = q;
//fprintf(stderr, "%.17f\n", *deps / DEGTORAD);
}
/*
* Long term high precision precession,
* according to Vondrak/Capitaine/Wallace, "New precession expressions, valid
* for long time intervals", in A&A 534, A22(2011).
*/
/* precession of the ecliptic */
static void pre_pecl(double tjd, double *vec)
{
int i;
int npol = NPOL_PECL;
int nper = NPER_PECL;
double t, p, q, w, a, s, c, z;
t = (tjd - J2000) / 36525.0;
p = 0;
q = 0;
/* periodic terms */
for (i = 0; i < nper; i++) {
w = D2PI * t;
a = w / pqper[0][i];
s = sin(a);
c = cos(a);
p += c * pqper[1][i] + s * pqper[3][i];
q += c * pqper[2][i] + s * pqper[4][i];
}
/* polynomial terms */
w = 1;
for (i = 0; i < npol; i++) {
p += pqpol[i][0] * w;
q += pqpol[i][1] * w;
w *= t;
}
/* both to radians */
p *= AS2R;
q *= AS2R;
/* ecliptic pole vector */
z = 1 - p * p - q * q;
if (z < 0)
z = 0;
else
z = sqrt(z);
s = sin(EPS0);
c = cos(EPS0);
vec[0] = p;
vec[1] = - q * c - z * s;
vec[2] = - q * s + z * c;
}
/* precession of the equator */
static void pre_pequ(double tjd, double *veq)
{
int i;
int npol = NPOL_PEQU;
int nper = NPER_PEQU;
double t, x, y, w, a, s, c;
t = (tjd - J2000) / 36525.0;
x = 0;
y = 0;
for (i = 0; i < nper; i++) {
w = D2PI * t;
a = w / xyper[0][i];
s = sin(a);
c = cos(a);
x += c * xyper[1][i] + s * xyper[3][i];
y += c * xyper[2][i] + s * xyper[4][i];
}
/* polynomial terms */
w = 1;
for (i = 0; i < npol; i++) {
x += xypol[i][0] * w;
y += xypol[i][1] * w;
w *= t;
}
x *= AS2R;
y *= AS2R;
/* equator pole vector */
veq[0] = x;
veq[1] = y;
w = x * x + y * y;
if (w < 1)
veq[2] = sqrt(1 - w);
else
veq[2] = 0;
}
#if 0
static void swi_cross_prod(double *a, double *b, double *x)
{
x[0] = a[1] * b[2] - a[2] * b[1];
x[1] = a[2] * b[0] - a[0] * b[2];
x[2] = a[0] * b[1] - a[1] * b[0];
}
#endif
/* precession matrix */
static void pre_pmat(double tjd, double *rp)
{
double peqr[3], pecl[3], v[3], w, eqx[3];
//tjd = 1219339.078000;
/*equator pole */
pre_pequ(tjd, peqr);
/* ecliptic pole */
pre_pecl(tjd, pecl);
// fprintf(stderr, "%.17f %.17f %.17f\n", peqr[0], peqr[1], peqr[2]);
// fprintf(stderr, "%.17f %.17f %.17f\n", pecl[0], pecl[1], pecl[2]);
/* equinox */
swi_cross_prod(peqr, pecl, v);
w = sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
eqx[0] = v[0] / w;
eqx[1] = v[1] / w;
eqx[2] = v[2] / w;
swi_cross_prod(peqr, eqx, v);
rp[0] = eqx[0];
rp[1] = eqx[1];
rp[2] = eqx[2];
rp[3] = v[0];
rp[4] = v[1];
rp[5] = v[2];
rp[6] = peqr[0];
rp[7] = peqr[1];
rp[8] = peqr[2];
// int i;
// for (i = 0; i < 3; i++) {
// fprintf(stderr, "(%.17f %.17f %.17f)\n", rp[i*3], rp[i*3+1],rp[i*3+2]);
// } /**/
}
/* precession according to Owen 1990:
* Owen, William M., Jr., (JPL) "A Theory of the Earth's Precession
* Relative to the Invariable Plane of the Solar System", Ph.D.
* Dissertation, University of Florida, 1990.
* Implemented for time range -18000 to 14000.
*/
/*
* p. 177: central time Tc = -160, covering time span -200 <= T <= -120
* i.e. -14000 +- 40 centuries
* p. 178: central time Tc = -80, covering time span -120 <= T <= -40
* i.e. -6000 +- 40 centuries
* p. 179: central time Tc = 0, covering time span -40 <= T <= +40
* i.e. 2000 +- 40 centuries
* p. 180: central time Tc = 80, covering time span 40 <= T <= 120
* i.e. 10000 +- 40 centuries
* p. 181: central time Tc = 160, covering time span 120 <= T <= 200
* i.e. 10000 +- 40 centuries
*/
static const double owen_eps0_coef[5][10] = {
{23.699391439256386, 5.2330816033981775e-1, -5.6259493384864815e-2, -8.2033318431602032e-3, 6.6774163554156385e-4, 2.4931584012812606e-5, -3.1313623302407878e-6, 2.0343814827951515e-7, 2.9182026615852936e-8, -4.1118760893281951e-9,},
{24.124759551704588, -1.2094875596566286e-1, -8.3914869653015218e-2, 3.5357075322387405e-3, 6.4557467824807032e-4, -2.5092064378707704e-5, -1.7631607274450848e-6, 1.3363622791424094e-7, 1.5577817511054047e-8, -2.4613907093017122e-9,},
{23.439103144206208, -4.9386077073143590e-1, -2.3965445283267805e-4, 8.6637485629656489e-3, -5.2828151901367600e-5, -4.3951004595359217e-5, -1.1058785949914705e-6, 6.2431490022621172e-8, 3.4725376218710764e-8, 1.3658853127005757e-9,},
{22.724671295125046, -1.6041813558650337e-1, 7.0646783888132504e-2, 1.4967806745062837e-3, -6.6857270989190734e-4, 5.7578378071604775e-6, 3.3738508454638728e-6, -2.2917813537654764e-7, -2.1019907929218137e-8, 4.3139832091694682e-9,},
{22.914636050333696, 3.2123508304962416e-1, 3.6633220173792710e-2, -5.9228324767696043e-3, -1.882379107379328e-4, 3.2274552870236244e-5, 4.9052463646336507e-7, -5.9064298731578425e-8, -2.0485712675098837e-8, -6.2163304813908160e-10,},
};
static const double owen_psia_coef[5][10] = {
{-218.57864954903122, 51.752257487741612, 1.3304715765661958e-1, 9.2048123521890745e-2, -6.0877528127241278e-3, -7.0013893644531700e-5, -4.9217728385458495e-5, -1.8578234189053723e-6, 7.4396426162029877e-7, -5.9157528981843864e-9,},
{-111.94350527506128, 55.175558131675861, 4.7366115762797613e-1, -4.7701750975398538e-2, -9.2445765329325809e-3, 7.0962838707454917e-4, 1.5140455277814658e-4, -7.7813159018954928e-7, -2.4729402281953378e-6, -1.0898887008726418e-7,},
{-2.041452011529441e-1, 55.969995858494106, -1.9295093699770936e-1, -5.6819574830421158e-3, 1.1073687302518981e-2, -9.0868489896815619e-5, -1.1999773777895820e-4, 9.9748697306154409e-6, 5.7911493603430550e-7, -2.3647526839778175e-7,},
{111.61366860604471, 56.404525305162447, 4.4403302410703782e-1, 7.1490030578883907e-2, -4.9184559079790816e-3, -1.3912698949042046e-3, -6.8490613661884005e-5, 1.2394328562905297e-6, 1.7719847841480384e-6, 2.4889095220628068e-7,},
{228.40683531269390, 60.056143904919826, 2.9583200718478960e-2, -1.5710838319490748e-1, -7.0017356811600801e-3, 3.3009615142224537e-3, 2.0318123852537664e-4, -6.5840216067828310e-5, -5.9077673352976155e-6, 1.3983942185303064e-6,},
};
static const double owen_oma_coef[5][10] = {
{25.541291140949806, 2.377889511272162e-1, -3.7337334723142133e-1, 2.4579295485161534e-2, 4.3840999514263623e-3, -3.1126873333599556e-4, -9.8443045771748915e-6, -7.9403103080496923e-7, 1.0840116743893556e-9, 9.2865105216887919e-9,},
{24.429357654237926, -9.5205745947740161e-1, 8.6738296270534816e-2, 3.0061543426062955e-2, -4.1532480523019988e-3, -3.7920928393860939e-4, 3.5117012399609737e-5, 4.6811877283079217e-6, -8.1836046585546861e-8, -6.1803706664211173e-8,},
{23.450465062489337, -9.7259278279739817e-2, 1.1082286925130981e-2, -3.1469883339372219e-2, -1.0041906996819648e-4, 5.6455168475133958e-4, -8.4403910211030209e-6, -3.8269157371098435e-6, 3.1422585261198437e-7, 9.3481729116773404e-9,},
{22.581778052947806, -8.7069701538602037e-1, -9.8140710050197307e-2, 2.6025931340678079e-2, 4.8165322168786755e-3, -1.906558772193363e-4, -4.6838759635421777e-5, -1.6608525315998471e-6, -3.2347811293516124e-8, 2.8104728109642000e-9,},
{21.518861835737142, 2.0494789509441385e-1, 3.5193604846503161e-1, 1.5305977982348925e-2, -7.5015367726336455e-3, -4.0322553186065610e-4, 1.0655320434844041e-4, 7.1792339586935752e-6, -1.603874697543020e-6, -1.613563462813512e-7,},
};
static const double owen_chia_coef[5][10] = {
{8.2378850337329404e-1, -3.7443109739678667, 4.0143936898854026e-1, 8.1822830214590811e-2, -8.5978790792656293e-3, -2.8350488448426132e-5, -4.2474671728156727e-5, -1.6214840884656678e-6, 7.8560442001953050e-7, -1.032016641696707e-8,},
{-2.1726062070318606, 7.8470515033132925e-1, 4.4044931004195718e-1, -8.0671247169971653e-2, -8.9672662444325007e-3, 9.2248978383109719e-4, 1.5143472266372874e-4, -1.6387009056475679e-6, -2.4405558979328144e-6, -1.0148113464009015e-7,},
{-4.8518673570735556e-1, 1.0016737299946743e-1, -4.7074888613099918e-1, -5.8604054305076092e-3, 1.4300208240553435e-2, -6.7127991650300028e-5, -1.3703764889645475e-4, 9.0505213684444634e-6, 6.0368690647808607e-7, -2.2135404747652171e-7,},
{-2.0950740076326087, -9.4447359463206877e-1, 4.0940512860493755e-1, 1.0261699700263508e-1, -5.3133241571955160e-3, -1.6634631550720911e-3, -5.9477519536647907e-5, 2.9651387319208926e-6, 1.6434499452070584e-6, 2.3720647656961084e-7,},
{6.3315163285678715e-1, 3.5241082918420464, 2.1223076605364606e-1, -1.5648122502767368e-1, -9.1964075390801980e-3, 3.3896161239812411e-3, 2.1485178626085787e-4, -6.6261759864793735e-5, -5.9257969712852667e-6, 1.3918759086160525e-6,},
};
static void get_owen_t0_icof(double tjd, double *t0, int *icof)
{
int i, j = 0;
double t0s[5] = {-3392455.5, -470455.5, 2451544.5, 5373544.5, 8295544.5, };
*t0 = t0s[0];
for (i = 1; i < 5; i++) {
if (tjd < (t0s[i-1] + t0s[i]) / 2) {
;
} else {
*t0 = t0s[i];
j++;
}
}
*icof = j;
}
/* precession matrix Owen 1990 */
static void owen_pre_matrix(double tjd, double *rp, int iflag)
{
int i, icof = 0;
double eps0 = 0, chia = 0, psia = 0, oma = 0;
double coseps0, sineps0, coschia, sinchia, cospsia, sinpsia, cosoma, sinoma;
double k[10], tau[10];
double t0;
get_owen_t0_icof(tjd, &t0, &icof);
// fprintf(stderr, "%d, %.17f\n", icof, t0);
tau[0] = 0;
tau[1] = (tjd - t0) / 36525.0 / 40.0;
for (i = 2; i <= 9; i++) {
tau[i] = tau[1] * tau[i-1];
}
k[0] = 1;
k[1] = tau[1];
k[2] = 2 * tau[2] - 1;
k[3] = 4 * tau[3] - 3 * tau[1];
k[4] = 8 * tau[4] - 8 * tau[2] + 1;
k[5] = 16 * tau[5] - 20 * tau[3] + 5 * tau[1];
k[6] = 32 * tau[6] - 48 * tau[4] + 18 * tau[2] - 1;
k[7] = 64 * tau[7] - 112 * tau[5] + 56 * tau[3] - 7 * tau[1];
k[8] = 128 * tau[8] - 256 * tau[6] + 160 * tau[4] - 32 * tau[2] + 1;
k[9] = 256 * tau[9] - 576 * tau[7] + 432 * tau[5] - 120 * tau[3] + 9 * tau[1];
for (i = 0; i < 10; i++) {
//eps += (k[i] * owen_eps0_coef[icof][i]);
psia += (k[i] * owen_psia_coef[icof][i]);
oma += (k[i] * owen_oma_coef[icof][i]);
chia += (k[i] * owen_chia_coef[icof][i]);
}
if (iflag & (SEFLG_JPLHOR | SEFLG_JPLHOR_APPROX)) {
/*
* In comparison with JPL Horizons we have an almost constant offset
* almost constant offset in ecl. longitude of about -0.000019 deg.
* We fix this as follows: */
psia += -0.000018560;
}
eps0 = 84381.448 / 3600.0;
//fprintf(stderr, "e=%.17f, ps=%.17f, om=%.17f, ch=%.17f\n", eps0, psia, oma, chia);
eps0 *= DEGTORAD;
psia *= DEGTORAD;
chia *= DEGTORAD;
oma *= DEGTORAD;
coseps0 = cos(eps0);
sineps0 = sin(eps0);
coschia = cos(chia);
sinchia = sin(chia);
cospsia = cos(psia);
sinpsia = sin(psia);
cosoma = cos(oma);
sinoma = sin(oma);
rp[0] = coschia * cospsia + sinchia * cosoma * sinpsia;
rp[1] = (-coschia * sinpsia + sinchia * cosoma * cospsia) * coseps0 + sinchia * sinoma * sineps0;
rp[2] = (-coschia * sinpsia + sinchia * cosoma * cospsia) * sineps0 - sinchia * sinoma * coseps0;
rp[3] = -sinchia * cospsia + coschia * cosoma * sinpsia;
rp[4] = (sinchia * sinpsia + coschia * cosoma * cospsia) * coseps0 + coschia * sinoma * sineps0;
rp[5] = (sinchia * sinpsia + coschia * cosoma * cospsia) * sineps0 - coschia * sinoma * coseps0;
rp[6] = sinoma * sinpsia;
rp[7] = sinoma * cospsia * coseps0 - cosoma * sineps0;
rp[8] = sinoma * cospsia * sineps0 + cosoma * coseps0;
/*for (i = 0; i < 3; i++) {
fprintf(stderr, "(%.17f %.17f %.17f)\n", rp[i*3], rp[i*3+1],rp[i*3+2]);
} */
}
static void epsiln_owen_1986(double tjd, double *eps)
{
int i, icof = 0;
double k[10], tau[10];
double t0;
get_owen_t0_icof(tjd, &t0, &icof);
*eps = 0;
tau[0] = 0;
tau[1] = (tjd - t0) / 36525.0 / 40.0;
for (i = 2; i <= 9; i++) {
tau[i] = tau[1] * tau[i-1];
}
k[0] = 1;
k[1] = tau[1];
k[2] = 2 * tau[2] - 1;
k[3] = 4 * tau[3] - 3 * tau[1];
k[4] = 8 * tau[4] - 8 * tau[2] + 1;
k[5] = 16 * tau[5] - 20 * tau[3] + 5 * tau[1];
k[6] = 32 * tau[6] - 48 * tau[4] + 18 * tau[2] - 1;
k[7] = 64 * tau[7] - 112 * tau[5] + 56 * tau[3] - 7 * tau[1];
k[8] = 128 * tau[8] - 256 * tau[6] + 160 * tau[4] - 32 * tau[2] + 1;
k[9] = 256 * tau[9] - 576 * tau[7] + 432 * tau[5] - 120 * tau[3] + 9 * tau[1];
for (i = 0; i < 10; i++) {
*eps += (k[i] * owen_eps0_coef[icof][i]);
}
//fprintf(stderr, "eps=%.17f\n", *eps);
}
/* Obliquity of the ecliptic at Julian date J
*
* IAU Coefficients are from:
* J. H. Lieske, T. Lederle, W. Fricke, and B. Morando,
* "Expressions for the Precession Quantities Based upon the IAU
* (1976) System of Astronomical Constants," Astronomy and Astrophysics
* 58, 1-16 (1977).
*
* Before or after 200 years from J2000, the formula used is from:
* J. Laskar, "Secular terms of classical planetary theories
* using the results of general theory," Astronomy and Astrophysics
* 157, 59070 (1986).
*
* Bretagnon, P. et al.: 2003, "Expressions for Precession Consistent with
* the IAU 2000A Model". A&A 400,785
*B03 84381.4088 -46.836051*t -1667*10-7*t2 +199911*10-8*t3 -523*10-9*t4 -248*10-10*t5 -3*10-11*t6
*C03 84381.406 -46.836769*t -1831*10-7*t2 +20034*10-7*t3 -576*10-9*t4 -434*10-10*t5
*
* See precess and page B18 of the Astronomical Almanac.
*/
#define OFFSET_EPS_JPLHORIZONS (35.95)
#define DCOR_EPS_JPL_TJD0 2437846.5
#define NDCOR_EPS_JPL 51
double dcor_eps_jpl[] = {
36.726, 36.627, 36.595, 36.578, 36.640, 36.659, 36.731, 36.765,
36.662, 36.555, 36.335, 36.321, 36.354, 36.227, 36.289, 36.348, 36.257, 36.163,
35.979, 35.896, 35.842, 35.825, 35.912, 35.950, 36.093, 36.191, 36.009, 35.943,
35.875, 35.771, 35.788, 35.753, 35.822, 35.866, 35.771, 35.732, 35.543, 35.498,
35.449, 35.409, 35.497, 35.556, 35.672, 35.760, 35.596, 35.565, 35.510, 35.394,
35.385, 35.375, 35.415,
};
double swi_epsiln(double J, int32 iflag)
{
double T, eps;
double tofs, dofs, t0, t1;
int prec_model = swed.astro_models[SE_MODEL_PREC_LONGTERM];
int prec_model_short = swed.astro_models[SE_MODEL_PREC_SHORTTERM];
int jplhora_model = swed.astro_models[SE_MODEL_JPLHORA_MODE];
AS_BOOL is_jplhor = FALSE;
if (prec_model == 0) prec_model = SEMOD_PREC_DEFAULT;
if (prec_model_short == 0) prec_model_short = SEMOD_PREC_DEFAULT_SHORT;
if (jplhora_model == 0) jplhora_model = SEMOD_JPLHORA_DEFAULT;
if (iflag & SEFLG_JPLHOR)
is_jplhor = TRUE;
if ((iflag & SEFLG_JPLHOR_APPROX)
&& jplhora_model == SEMOD_JPLHORA_3
&& J <= HORIZONS_TJD0_DPSI_DEPS_IAU1980)
is_jplhor = TRUE;
T = (J - 2451545.0)/36525.0;
if (is_jplhor) {
if (J > 2378131.5 && J < 2525323.5) { // between 1.1.1799 and 1.1.2202
eps = (((1.813e-3*T-5.9e-4)*T-46.8150)*T+84381.448)*DEGTORAD/3600;
} else {
epsiln_owen_1986(J, &eps);
eps *= DEGTORAD;
}
} else if ((iflag & SEFLG_JPLHOR_APPROX) && jplhora_model == SEMOD_JPLHORA_2) {
eps = (((1.813e-3*T-5.9e-4)*T-46.8150)*T+84381.448)*DEGTORAD/3600;
} else if (prec_model_short == SEMOD_PREC_IAU_1976 && fabs(T) <= PREC_IAU_1976_CTIES ) {
eps = (((1.813e-3*T-5.9e-4)*T-46.8150)*T+84381.448)*DEGTORAD/3600;
} else if (prec_model == SEMOD_PREC_IAU_1976) {
eps = (((1.813e-3*T-5.9e-4)*T-46.8150)*T+84381.448)*DEGTORAD/3600;
} else if (prec_model_short == SEMOD_PREC_IAU_2000 && fabs(T) <= PREC_IAU_2000_CTIES ) {
eps = (((1.813e-3*T-5.9e-4)*T-46.84024)*T+84381.406)*DEGTORAD/3600;
} else if (prec_model == SEMOD_PREC_IAU_2000) {
eps = (((1.813e-3*T-5.9e-4)*T-46.84024)*T+84381.406)*DEGTORAD/3600;
} else if (prec_model_short == SEMOD_PREC_IAU_2006 && fabs(T) <= PREC_IAU_2006_CTIES) {
eps = (((((-4.34e-8 * T -5.76e-7) * T +2.0034e-3) * T -1.831e-4) * T -46.836769) * T + 84381.406) * DEGTORAD / 3600.0;
} else if (prec_model == SEMOD_PREC_NEWCOMB) {
double Tn = (J - 2396758.0)/36525.0;
eps = (0.0017 * Tn * Tn * Tn - 0.0085 * Tn * Tn - 46.837 * Tn + 84451.68) * DEGTORAD / 3600.0;
} else if (prec_model == SEMOD_PREC_IAU_2006) {
eps = (((((-4.34e-8 * T -5.76e-7) * T +2.0034e-3) * T -1.831e-4) * T -46.836769) * T + 84381.406) * DEGTORAD / 3600.0;
} else if (prec_model == SEMOD_PREC_BRETAGNON_2003) {
eps = ((((((-3e-11 * T - 2.48e-8) * T -5.23e-7) * T +1.99911e-3) * T -1.667e-4) * T -46.836051) * T + 84381.40880) * DEGTORAD / 3600.0;/* */
} else if (prec_model == SEMOD_PREC_SIMON_1994) {
eps = (((((2.5e-8 * T -5.1e-7) * T +1.9989e-3) * T -1.52e-4) * T -46.80927) * T + 84381.412) * DEGTORAD / 3600.0;/* */
} else if (prec_model == SEMOD_PREC_WILLIAMS_1994) {
eps = ((((-1.0e-6 * T +2.0e-3) * T -1.74e-4) * T -46.833960) * T + 84381.409) * DEGTORAD / 3600.0;/* */
} else if (prec_model == SEMOD_PREC_LASKAR_1986 || prec_model == SEMOD_PREC_WILL_EPS_LASK) {
T /= 10.0;
eps = ((((((((( 2.45e-10*T + 5.79e-9)*T + 2.787e-7)*T
+ 7.12e-7)*T - 3.905e-5)*T - 2.4967e-3)*T
- 5.138e-3)*T + 1.99925)*T - 0.0155)*T - 468.093)*T
+ 84381.448;
eps *= DEGTORAD/3600.0;
} else if (prec_model == SEMOD_PREC_OWEN_1990) {
epsiln_owen_1986(J, &eps);
eps *= DEGTORAD;
//fprintf(stderr, "epso=%.17f\n", eps);
} else { /* SEMOD_PREC_VONDRAK_2011 */
swi_ldp_peps(J, NULL, &eps);
if ((iflag & SEFLG_JPLHOR_APPROX) && jplhora_model != SEMOD_JPLHORA_2) {
tofs = (J - DCOR_EPS_JPL_TJD0) / 365.25;
dofs = OFFSET_EPS_JPLHORIZONS;
if (tofs < 0) {
tofs = 0;
dofs = dcor_eps_jpl[0];
} else if (tofs >= NDCOR_EPS_JPL - 1) {
tofs = NDCOR_EPS_JPL;
dofs = dcor_eps_jpl[NDCOR_EPS_JPL - 1];
} else {
t0 = (int) tofs;
t1 = t0 + 1;
dofs = dcor_eps_jpl[(int)t0];
dofs = (tofs - t0) * (dcor_eps_jpl[(int)t0] - dcor_eps_jpl[(int)t1]) + dcor_eps_jpl[(int)t0];
}
dofs /= (1000.0 * 3600.0);
eps += dofs * DEGTORAD;
}
//fprintf(stderr, "epsv=%.17f\n", eps);
}
return(eps);
}
/* Precession of the equinox and ecliptic
* from epoch Julian date J to or from J2000.0
*
* Original program by Steve Moshier.
* Changes in program structure and implementation of IAU 2003 (P03) and
* Vondrak 2011 by Dieter Koch.
*
* SEMOD_PREC_VONDRAK_2011
* J. Vondrak, N. Capitaine, and P. Wallace, "New precession expressions,
* valid for long time intervals", A&A 534, A22 (2011)
*
* SEMOD_PREC_IAU_2006
* N. Capitaine, P.T. Wallace, and J. Chapront, "Expressions for IAU 2000
* precession quantities", 2003, A&A 412, 567-586 (2003).
* This is a "short" term model, that can be combined with other models
*
* SEMOD_PREC_WILLIAMS_1994
* James G. Williams, "Contributions to the Earth's obliquity rate,
* precession, and nutation," Astron. J. 108, 711-724 (1994).
*
* SEMOD_PREC_SIMON_1994
* 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).