Ryan Malloy
0544a78276
Phase 1 — Stars, comets, Keplerian propagation: - star_observe() / star_observe_safe(): fixed star alt/az via IAU 1976 precession, equatorial-to-horizontal transform - kepler_propagate(): two-body Keplerian orbit propagation for elliptic, parabolic, and hyperbolic orbits - comet_observe(): observe comets/asteroids from orbital elements - heliocentric type: ecliptic J2000 position (x, y, z in AU) Phase 2 — VSOP87 planets, ELP82B Moon, Sun: - planet_heliocentric(): VSOP87 heliocentric ecliptic J2000 positions for Mercury through Neptune (Bretagnon & Francou, MIT) - planet_observe(): full observation pipeline for any planet - sun_observe(): Sun position from negated Earth VSOP87 - moon_observe(): ELP2000-82B lunar position (Chapront-Touzé, MIT) - Clean-room precession (IAU 2006) and sidereal time (IERS 2010) - elliptic_to_rectangular utility (Stellarium, MIT) All Stellarium extractions are MIT-licensed, thread-safe (static caching removed for PARALLEL SAFE), zero external data files. All 9 regression tests pass (90ms total).
141 lines
3.8 KiB
C
141 lines
3.8 KiB
C
/*
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* sidereal_time.c -- Greenwich sidereal time (mean and apparent)
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*
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* Clean-room implementation from published standards:
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*
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* Mean sidereal time:
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* Capitaine, Guinot & McCarthy (2000), A&A 355, 398-405.
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* IERS Conventions (2010), IERS Technical Note 36, Ch. 5,
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* Eq. 5.29 (GMST as polynomial in UT1).
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*
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* The polynomial form is:
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* GMST(UT1) = theta_0 + theta_1*T + theta_2*T^2 + theta_3*T^3
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* where T is Julian centuries of UT1 from J2000.0, and the
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* result is in seconds of time. Coefficients from Capitaine
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* et al. (2000), Eq. (42), which are the values adopted by
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* the IERS for consistency with IAU 2000/2006 precession.
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*
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* Apparent sidereal time:
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* GAST = GMST + equation_of_equinoxes
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* EqEq = delta_psi * cos(epsilon_A)
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* IERS Conventions (2010), Eq. 5.30.
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*/
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#include "sidereal_time.h"
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#include "precession.h"
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#include <math.h>
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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/* Arcseconds to radians */
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#define ARCSEC_TO_RAD (M_PI / (180.0 * 3600.0))
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/*
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* get_mean_sidereal_time
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*
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* GMST in radians from the classical polynomial expression.
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*
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* The polynomial (Capitaine et al. 2000, Eq. 42):
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* GMST = 67310.54841
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* + (876600h + 8640184.812866) * T
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* + 0.093104 * T^2
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* - 6.2e-6 * T^3
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*
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* where T = (JD_UT1 - 2451545.0) / 36525.0
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* and the result is in seconds of sidereal time.
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*
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* The constant 876600h = 876600 * 3600 = 3155760000 seconds
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* accounts for complete rotations.
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*
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* To convert seconds of time to radians:
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* 1 day = 86400 seconds of time = 2*pi radians
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* 1 second of time = 2*pi/86400 = pi/43200 radians
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*
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* JDE is accepted for interface consistency but unused here;
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* GMST is fundamentally a UT1 quantity.
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*/
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double
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get_mean_sidereal_time(double JD, double JDE)
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{
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double T, T2, T3;
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double gmst_sec;
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double gmst_rad;
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(void)JDE; /* GMST depends on UT1, not TDB */
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T = (JD - 2451545.0) / 36525.0;
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T2 = T * T;
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T3 = T2 * T;
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/*
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* Polynomial in seconds of sidereal time.
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* The large linear coefficient includes whole rotations
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* accumulated since J2000.0.
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*/
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gmst_sec = 67310.54841
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+ (876600.0 * 3600.0 + 8640184.812866) * T
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+ 0.093104 * T2
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- 6.2e-6 * T3;
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/* Seconds of time -> radians, then normalize to [0, 2*pi) */
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gmst_rad = fmod(gmst_sec * (M_PI / 43200.0), 2.0 * M_PI);
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if (gmst_rad < 0.0)
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gmst_rad += 2.0 * M_PI;
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return gmst_rad;
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}
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/*
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* get_apparent_sidereal_time
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*
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* GAST = GMST + equation of the equinoxes.
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*
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* The equation of the equinoxes (IERS 2010, Eq. 5.30):
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* EqEq = delta_psi * cos(epsilon_A)
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*
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* where delta_psi is nutation in longitude and epsilon_A is
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* the mean obliquity of the ecliptic, both in arcseconds.
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*
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* For the full IAU 2000A model, there is an additional
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* "complementary terms" correction to EqEq (Eq. 5.31),
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* but it is at the 0.1 mas level and negligible for our
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* accuracy requirements.
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*/
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double
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get_apparent_sidereal_time(double JD, double JDE)
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{
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double gmst;
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double epsilon_A, chi_A, omega_A, psi_A;
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double delta_psi, delta_epsilon;
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double eq_eq;
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double gast;
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gmst = get_mean_sidereal_time(JD, JDE);
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/* Get mean obliquity from precession (in arcseconds) */
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get_precession_angles_vondrak(JDE, &epsilon_A, &chi_A, &omega_A, &psi_A);
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/* Get nutation in longitude (in arcseconds) */
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get_nutation_angles_iau2000b(JDE, &delta_psi, &delta_epsilon);
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/*
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* Equation of the equinoxes:
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* delta_psi is in arcseconds, epsilon_A is in arcseconds.
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* Convert delta_psi to radians, multiply by cos(epsilon_A in radians),
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* result is in radians.
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*/
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eq_eq = (delta_psi * ARCSEC_TO_RAD) * cos(epsilon_A * ARCSEC_TO_RAD);
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gast = gmst + eq_eq;
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/* Normalize to [0, 2*pi) */
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gast = fmod(gast, 2.0 * M_PI);
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if (gast < 0.0)
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gast += 2.0 * M_PI;
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return gast;
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}
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