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Precession formulae from 2000 Astro. Almanac
Closes #45 by merging in its changes; thank you, Francois Meyer!
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francois.meyer
Brandon Rhodes
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266ef93744
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5522e1039b
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@ -4,12 +4,18 @@
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#include <stdio.h>
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#ifndef PI
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#define PI 3.141592653589793
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#define PI 3.141592653589793238
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#endif
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#ifndef TWOPI
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#define TWOPI 6.283185307179586477
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#endif
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/* conversions among hours (of ra), degrees and radians. */
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#define degrad(x) ((x)*PI/180.)
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#define raddeg(x) ((x)*180./PI)
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#define radarcsec(x) ((x)*2.06264806247096355e5)
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#define arcsecrad(x) ((x)*4.84813681109535993e-6)
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#define hrdeg(x) ((x)*15.)
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#define deghr(x) ((x)/15.)
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#define hrrad(x) degrad(hrdeg(x))
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@ -1,144 +1,69 @@
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#include <stdio.h>
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#include <math.h>
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#include "astro.h"
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static void precess_hiprec (double mjd1, double mjd2, double *ra, double *dec);
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/* Precession computation to or from J2000
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* If dir < 0 go from equinox to J2000
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* If dir > 0 go from J2000 to equinox
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*/
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static void
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do_precess (
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double equinox, double *alpha, double *delta, int dir
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)
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{
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double T;
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double zeta_A, z_A, theta_A;
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double A, B, C;
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/* Precession progresses about 1 arc second in .047 years = 17 days
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* Threshold must be at most 1.7 days for 0.1 arcsec accuracy */
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double threshhold=1;
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#define DCOS(x) cos(degrad(x))
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#define DSIN(x) sin(degrad(x))
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#define DASIN(x) raddeg(asin(x))
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#define DATAN2(y,x) raddeg(atan2((y),(x)))
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if (fabs (equinox - J2000) < threshhold)
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return;
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/* corrects ra and dec, both in radians, for precession from epoch 1 to epoch 2.
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* the epochs are given by their modified JDs, mjd1 and mjd2, respectively.
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* N.B. ra and dec are modifed IN PLACE.
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T = (equinox - J2000)/36525.0;
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/* Compute coefficients in arcseconds from the Naval
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* Observatory, Her Majesty's Nautical Amanac Office;
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* Rutherford Appleton Laboratory, ISSN 0737-6421. */
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zeta_A = arcsecrad(2.650545 + T*(2306.083227+T*(0.2988499 + T*(0.01801828 +T*(-5.971e-6-3.173e-7*T)))));
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z_A = arcsecrad(-2.650545+T*(2306.077181+T*(1.0927348+T*(0.01826837 +T*(-28.596e-6-2.904e-7*T)))));
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theta_A = arcsecrad(T*(2004.191903-T*(0.4294934+T*(0.04182264+T*(7.089e-6+1.274e-7*T)))));
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if (dir<0){
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/* If dir is negative, go from equinox to 2000.0 */
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A = sin(*alpha - z_A) * cos(*delta);
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B = cos(*alpha - z_A) * cos(theta_A) * cos(*delta)
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+ sin(theta_A) * sin(*delta);
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C = -cos(*alpha - z_A) * sin(theta_A) * cos(*delta)
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+ cos(theta_A) * sin(*delta);
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*alpha = atan2(A,B) - zeta_A;
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} else {
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/* If dir is positive, go from 2000.0 to equinox */
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A = sin(*alpha + zeta_A) * cos(*delta);
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B = cos(*alpha + zeta_A) * cos(theta_A) * cos(*delta)
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- sin(theta_A) * sin(*delta);
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C = cos(*alpha + zeta_A) * sin(theta_A) * cos(*delta)
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+ cos(theta_A) * sin(*delta);
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*alpha = atan2(A,B) + z_A;
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}
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range (alpha, TWOPI);
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*delta = asin(C);
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}
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/* Corrects ra and dec, both in radians, for precession from epoch 1 to
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* epoch 2. The epochs are given by their modified JDs, from_mjd and
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* to_mjd, respectively. N.B. ra and dec are modifed IN PLACE.
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*/
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void
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precess (
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double mjd1, double mjd2, /* initial and final epoch modified JDs */
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double *ra, double *dec) /* ra/dec for mjd1 in, for mjd2 out */
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double from_mjd, double to_mjd, /* initial and final epoch modified JDs */
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double *ra, double *dec) /* ra/dec for from_mjd in, for to_mjd out */
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{
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precess_hiprec (mjd1, mjd2, ra, dec);
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/* From mjd1 to J2000, "backwards" inplace transformation : */
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do_precess(from_mjd, ra, dec, -1);
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/* From J2000 to mjd2, "forward" inplace transformation : */
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do_precess(to_mjd, ra, dec, 1);
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}
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/*
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* Copyright (c) 1990 by Craig Counterman. All rights reserved.
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*
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* This software may be redistributed freely, not sold.
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* This copyright notice and disclaimer of warranty must remain
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* unchanged.
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*
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* No representation is made about the suitability of this
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* software for any purpose. It is provided "as is" without express or
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* implied warranty, to the extent permitted by applicable law.
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*
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* Rigorous precession. From Astronomical Ephemeris 1989, p. B18
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*
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* 96-06-20 Hayo Hase <hase@wettzell.ifag.de>: theta_a corrected
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*/
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static void
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precess_hiprec (
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double mjd1, double mjd2, /* initial and final epoch modified JDs */
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double *ra, double *dec) /* ra/dec for mjd1 in, for mjd2 out */
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{
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static double last_mjd1 = -213.432, last_from;
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static double last_mjd2 = -213.432, last_to;
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double zeta_A, z_A, theta_A;
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double T;
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double A, B, C;
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double alpha, delta;
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double alpha_in, delta_in;
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double from_equinox, to_equinox;
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double alpha2000, delta2000;
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/* convert mjds to years;
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* avoid the remarkably expensive calls to mjd_year()
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*/
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if (last_mjd1 == mjd1)
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from_equinox = last_from;
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else {
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mjd_year (mjd1, &from_equinox);
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last_mjd1 = mjd1;
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last_from = from_equinox;
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}
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if (last_mjd2 == mjd2)
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to_equinox = last_to;
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else {
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mjd_year (mjd2, &to_equinox);
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last_mjd2 = mjd2;
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last_to = to_equinox;
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}
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/* convert coords in rads to degs */
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alpha_in = raddeg(*ra);
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delta_in = raddeg(*dec);
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/* precession progresses about 1 arc second in .047 years */
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/* From from_equinox to 2000.0 */
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if (fabs (from_equinox-2000.0) > .02) {
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T = (from_equinox - 2000.0)/100.0;
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zeta_A = 0.6406161* T + 0.0000839* T*T + 0.0000050* T*T*T;
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z_A = 0.6406161* T + 0.0003041* T*T + 0.0000051* T*T*T;
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theta_A = 0.5567530* T - 0.0001185* T*T - 0.0000116* T*T*T;
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A = DSIN(alpha_in - z_A) * DCOS(delta_in);
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B = DCOS(alpha_in - z_A) * DCOS(theta_A) * DCOS(delta_in)
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+ DSIN(theta_A) * DSIN(delta_in);
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C = -DCOS(alpha_in - z_A) * DSIN(theta_A) * DCOS(delta_in)
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+ DCOS(theta_A) * DSIN(delta_in);
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alpha2000 = DATAN2(A,B) - zeta_A;
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range (&alpha2000, 360.0);
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delta2000 = DASIN(C);
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} else {
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/* should get the same answer, but this could improve accruacy */
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alpha2000 = alpha_in;
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delta2000 = delta_in;
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};
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/* From 2000.0 to to_equinox */
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if (fabs (to_equinox - 2000.0) > .02) {
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T = (to_equinox - 2000.0)/100.0;
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zeta_A = 0.6406161* T + 0.0000839* T*T + 0.0000050* T*T*T;
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z_A = 0.6406161* T + 0.0003041* T*T + 0.0000051* T*T*T;
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theta_A = 0.5567530* T - 0.0001185* T*T - 0.0000116* T*T*T;
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A = DSIN(alpha2000 + zeta_A) * DCOS(delta2000);
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B = DCOS(alpha2000 + zeta_A) * DCOS(theta_A) * DCOS(delta2000)
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- DSIN(theta_A) * DSIN(delta2000);
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C = DCOS(alpha2000 + zeta_A) * DSIN(theta_A) * DCOS(delta2000)
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+ DCOS(theta_A) * DSIN(delta2000);
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alpha = DATAN2(A,B) + z_A;
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range(&alpha, 360.0);
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delta = DASIN(C);
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} else {
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/* should get the same answer, but this could improve accruacy */
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alpha = alpha2000;
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delta = delta2000;
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};
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*ra = degrad(alpha);
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*dec = degrad(delta);
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}
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#if 0
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static void
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precess_fast (
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double mjd1, double mjd2, /* initial and final epoch modified JDs */
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double *ra, double *dec) /* ra/dec for mjd1 in, for mjd2 out */
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{
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#define N degrad (20.0468/3600.0)
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#define M hrrad (3.07234/3600.0)
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double nyrs;
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nyrs = (mjd2 - mjd1)/365.2425;
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*dec += N * cos(*ra) * nyrs;
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*ra += (M + (N * sin(*ra) * tan(*dec))) * nyrs;
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range (ra, 2.0*PI);
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}
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#endif
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