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/* marstime.cpp: convert Martian "standard" time to/from TT
(Temps Terrestienne, Earth-based atomic time)
Copyright (C) 2016, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* Underlying algorithms copied from : */
/* http://www.giss.nasa.gov/tools/mars24/help/algorithm.html */
/* Routines to compute "Mars Coordinated Time" (MCT), the Martian */
/* equivalent of UTC, and "Mars True Solar Time (MTST) at Airy" (Airy is */
/* the Martian equivalent of the Greenwich meridian), for a given JDT. */
/* The "reverse" code to convert MTST to TT was added by me (Bill Gray). */
/* A test case, from the above URL: if run with JDT=2451549.50074, */
/* one should get: */
/* */
/* pbs = 0.001418; a_fms = 272.744861; v_minus_m = 4.441908 */
/* MTC = 44795.999760 (23:59:39.281); eot = -0.014410 */
/* LTST at Airy: 23:38:54.247 */
/* */
/* The "recovered JD" should be equal to the input JDT of 2451549.50074; */
/* i.e., the time transformations should all be correctly reversed. */
#include <math.h>
#include <stdlib.h>
#ifdef TEST_PROGRAM
#include <stdio.h>
#endif
const double days_per_sol = 1.0274912517;
const double zero_sol_point = 44796.0 - 0.0009626;
const double zero_jd_point = 2451549.5;
double tt_to_mtc( const double jd);
double mtc_to_tt( const double mtc);
double mars_true_solar_minus_mean_solar_time( const double jd);
double mtst_at_airy_to_tt( const double mtst);
double tt_to_mtc( const double jd)
{
/* eqn C-2: */
return( (jd - zero_jd_point) / days_per_sol + zero_sol_point);
}
double mtc_to_tt( const double mtc)
{
/* C-2 equation reversed: */
return( (mtc - zero_sol_point) * days_per_sol + zero_jd_point);
}
/* "longitude_sun" = 0 degrees at the northern hemisphere vernal equinox;
= 90 degrees at summer solstice, = 180 at autumnal equinox, = 270 at
winter solstice. */
double mars_true_solar_minus_mean_solar_time( const double jd)
{
const double jd_2000 = 2451545.0; /* JD 2451545.0 = 1.5 Jan 2000 */
const double t = jd - jd_2000;
const double pi =
3.1415926535897932384626433832795028841971693993751058209749445923;
const double D2R = pi / 180.;
/* equations B-1 & B-2: */
const double mars_mean_anom = 19.3871 * D2R + .52402073 * D2R * t;
/* 'a_fms' = 'angle of fictitious mean sun' */
const double a_fms = 270.3871 * D2R + .524038496 * D2R * t;
#ifndef IGNORE_PERTURBERS
const double tconst = 2. * pi / 365.25;
static const double amplit[7] = { .0071 * D2R, .0057 * D2R,
.0039 * D2R, .0037 * D2R, .0021 * D2R,
.0020 * D2R, .0018 * D2R};
static const double freq[7] = { tconst / 2.2353, tconst / 2.7543,
tconst / 1.1177, tconst / 15.7866, tconst / 2.1354,
tconst / 2.4694, tconst / 32.8493 };
static const double phase[7] = { 49.409 * D2R, 168.173 * D2R,
191.837 * D2R, 21.736 * D2R, 15.704 * D2R,
95.528 * D2R, 49.095 * D2R };
#endif
/* v_minus_m = true minus mean anomaly, a.k.a. the */
/* equation of the center: */
double v_minus_m = (10.691 * D2R + 3e-7 * D2R * t)
* sin( mars_mean_anom)
+ 0.623 * D2R * sin( 2. * mars_mean_anom)
+ 0.050 * D2R * sin( 3. * mars_mean_anom)
+ 0.005 * D2R * sin( 4. * mars_mean_anom)
+ 0.0005 * D2R * sin( 5. * mars_mean_anom);
double longitude_sun, eqn_of_time;
#ifndef IGNORE_PERTURBERS
double pbs = 0.;
int i;
for( i = 0; i < 7; i++) /* eqn B-3 */
pbs += amplit[i] * cos( freq[i] * t + phase[i]);
v_minus_m += pbs;
#endif
longitude_sun = a_fms + v_minus_m; /* eqn B-5 */
#ifdef TEST_PROGRAM
printf( "a_fms = %f; v_minus_m = %f; longitude of sun = %f\n",
a_fms / D2R, v_minus_m / D2R, longitude_sun / D2R);
#endif
eqn_of_time = (2.861 / 360.) * sin( 2. * longitude_sun) /* eqn C-1 */
- (0.071 / 360.) * sin( 4. * longitude_sun)
+ (0.002 / 360.) * sin( 6. * longitude_sun)
- v_minus_m / (2. * pi);
/* Above equation of time = true - mean time, in sols. */
return( eqn_of_time);
}
/* Reversing MTST (Mars True Solar Time) to other systems is made */
/* slightly tricky by the fact that the first step involves computing */
/* the equation of time, which takes TT as an input. So we pretend */
/* the input MTST is actually an MTC, and compute a TT from it using */
/* mtc_to_tt. This gives us an "approx_tt" which may be up to an hour */
/* off (it basically is ignoring the Martian equation of time). */
/* However, if we compute the Martian EOT using approx_tt, we'll */
/* get a passably correct EOT and can use it to compute a better TT. */
/* And we can then compute the EOT using this better TT to get a still */
/* better TT. These two iterations of computing the EOT are enough to */
/* get a "real" TT that's good to machine precision. */
double mtst_at_airy_to_tt( const double mtst)
{
const double approx_tt = mtc_to_tt( mtst);
double rval = approx_tt;
int iter;
for( iter = 2; iter; iter--)
{
const double eqn_of_time =
mars_true_solar_minus_mean_solar_time( rval);
rval = approx_tt - eqn_of_time * days_per_sol;
}
return( rval);
}
#ifdef TEST_PROGRAM
static void format_time( const double day, char *buff)
{
const double time_of_day = day - floor( day);
const int n_millisec = (int)( time_of_day * 24. * 60. * 60. * 1000. + .5);
sprintf( buff, "%02d:%02d:%02d.%03d",
n_millisec / (60 * 60 * 1000), /* hour */
(n_millisec / (60 * 1000)) % 60, /* minutes */
(n_millisec / 1000) % 60, /* seconds */
n_millisec % 1000); /* millisec */
}
int main( const int argc, const char **argv)
{
const double jd = (argc > 1 ? atof( argv[1]) : 2451549.50074);
const double mtc = tt_to_mtc( jd);
const double eot = mars_true_solar_minus_mean_solar_time( jd);
const double ltst_at_airy = mtc + eot;
char buff[80];
/* Above equation of time = true - mean time. */
format_time( mtc, buff);
printf( "MTC = %f (%s); eot = %f\n", mtc, buff, eot);
format_time( ltst_at_airy, buff);
printf( "LTST at Airy: %s\n", buff);
printf( "Recovered JD: %.8f\n", mtst_at_airy_to_tt( ltst_at_airy));
if( argc > 2)
{
const double lon = atof( argv[2]);
double ltst = ltst_at_airy - lon / 360.;
double lmst = mtc - lon / 360.;
format_time( ltst, buff);
printf( "LTST at loc: %s\n", buff);
format_time( lmst, buff);
printf( "LMST at loc: %s\n", buff);
}
return( 0);
}
#endif
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