/*
 * sidereal_time.c -- Greenwich sidereal time (mean and apparent)
 *
 * Clean-room implementation from published standards:
 *
 * Mean sidereal time:
 *   Capitaine, Guinot & McCarthy (2000), A&A 355, 398-405.
 *   IERS Conventions (2010), IERS Technical Note 36, Ch. 5,
 *   Eq. 5.29 (GMST as polynomial in UT1).
 *
 * The polynomial form is:
 *   GMST(UT1) = theta_0 + theta_1*T + theta_2*T^2 + theta_3*T^3
 * where T is Julian centuries of UT1 from J2000.0, and the
 * result is in seconds of time.  Coefficients from Capitaine
 * et al. (2000), Eq. (42), which are the values adopted by
 * the IERS for consistency with IAU 2000/2006 precession.
 *
 * Apparent sidereal time:
 *   GAST = GMST + equation_of_equinoxes
 *   EqEq = delta_psi * cos(epsilon_A)
 * IERS Conventions (2010), Eq. 5.30.
 */

#include "sidereal_time.h"
#include "precession.h"
#include <math.h>

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

/* Arcseconds to radians */
#define ARCSEC_TO_RAD (M_PI / (180.0 * 3600.0))

/*
 * get_mean_sidereal_time
 *
 * GMST in radians from the classical polynomial expression.
 *
 * The polynomial (Capitaine et al. 2000, Eq. 42):
 *   GMST = 67310.54841
 *        + (876600h + 8640184.812866) * T
 *        + 0.093104 * T^2
 *        - 6.2e-6 * T^3
 *
 * where T = (JD_UT1 - 2451545.0) / 36525.0
 * and the result is in seconds of sidereal time.
 *
 * The constant 876600h = 876600 * 3600 = 3155760000 seconds
 * accounts for complete rotations.
 *
 * To convert seconds of time to radians:
 *   1 day = 86400 seconds of time = 2*pi radians
 *   1 second of time = 2*pi/86400 = pi/43200 radians
 *
 * JDE is accepted for interface consistency but unused here;
 * GMST is fundamentally a UT1 quantity.
 */
double
get_mean_sidereal_time(double JD, double JDE)
{
    double T, T2, T3;
    double gmst_sec;
    double gmst_rad;

    (void)JDE;  /* GMST depends on UT1, not TDB */

    T  = (JD - 2451545.0) / 36525.0;
    T2 = T * T;
    T3 = T2 * T;

    /*
     * Polynomial in seconds of sidereal time.
     * The large linear coefficient includes whole rotations
     * accumulated since J2000.0.
     */
    gmst_sec = 67310.54841
             + (876600.0 * 3600.0 + 8640184.812866) * T
             + 0.093104 * T2
             - 6.2e-6 * T3;

    /* Seconds of time -> radians, then normalize to [0, 2*pi) */
    gmst_rad = fmod(gmst_sec * (M_PI / 43200.0), 2.0 * M_PI);
    if (gmst_rad < 0.0)
        gmst_rad += 2.0 * M_PI;

    return gmst_rad;
}


/*
 * get_apparent_sidereal_time
 *
 * GAST = GMST + equation of the equinoxes.
 *
 * The equation of the equinoxes (IERS 2010, Eq. 5.30):
 *   EqEq = delta_psi * cos(epsilon_A)
 *
 * where delta_psi is nutation in longitude and epsilon_A is
 * the mean obliquity of the ecliptic, both in arcseconds.
 *
 * For the full IAU 2000A model, there is an additional
 * "complementary terms" correction to EqEq (Eq. 5.31),
 * but it is at the 0.1 mas level and negligible for our
 * accuracy requirements.
 */
double
get_apparent_sidereal_time(double JD, double JDE)
{
    double gmst;
    double epsilon_A, chi_A, omega_A, psi_A;
    double delta_psi, delta_epsilon;
    double eq_eq;
    double gast;

    gmst = get_mean_sidereal_time(JD, JDE);

    /* Get mean obliquity from precession (in arcseconds) */
    get_precession_angles_vondrak(JDE, &epsilon_A, &chi_A, &omega_A, &psi_A);

    /* Get nutation in longitude (in arcseconds) */
    get_nutation_angles_iau2000b(JDE, &delta_psi, &delta_epsilon);

    /*
     * Equation of the equinoxes:
     * delta_psi is in arcseconds, epsilon_A is in arcseconds.
     * Convert delta_psi to radians, multiply by cos(epsilon_A in radians),
     * result is in radians.
     */
    eq_eq = (delta_psi * ARCSEC_TO_RAD) * cos(epsilon_A * ARCSEC_TO_RAD);

    gast = gmst + eq_eq;

    /* Normalize to [0, 2*pi) */
    gast = fmod(gast, 2.0 * M_PI);
    if (gast < 0.0)
        gast += 2.0 * M_PI;

    return gast;
}