4.57.2 equation_of_time.c

/*
 * (C)2012 Michael Duane Rice All rights reserved.
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/* $Id$ */

/*
    The so called Equation of Time.

    The eccentricity of Earths orbit contributes about 7.7 minutes of variation to the result. It
    has a period of 1 anomalous year, with zeroes at perihelion and aphelion.

    The tilt of Earths rotational axis (obliquity) contributes about 9.9 minutes of variation. It
    has a period of 1/2 tropical year, with zeroes at solstices and equinoxes. The time of Earths
    arrival at these events is influenced by the eccentricity, which causes it to progress along its
    orbital path faster as it approaches perihelion, imposing a 'modulation' on the tropical phase.

    The algorithm employed computes the orbital position with respect to perihelion, deriving
    from that a 'velocity correction factor'. The orbital position with respect to the winter solstice
    is then computed, as modulated by that factor. The individual contributions of the obliquity and the
    eccentricity components are then summed, and returned as an integer value in seconds.

*/

#include <time.h>
#include <math.h>
#include "ephemera_common.h"

int
equation_of_time(const time_t * timer)
{
    int32_t         s, p;
    double          pf, sf, dV;

    /* compute orbital position relative to perihelion */
    p = *timer % ANOM_YEAR;
    p += PERIHELION;
    pf = p;
    pf /= ANOM_CYCLE;
    pf = sin(pf);

    /* Derive a velocity correction factor from the perihelion angle */
    dV = pf * DELTA_V;

    /* compute approximate position relative to solstice */
    s = *timer % TROP_YEAR;
    s += SOLSTICE;
    s *= 2;
    sf = s;
    sf /= TROP_CYCLE;

    /* modulate to derive actual position */
    sf += dV;
    sf = sin(sf);

    /* compute contributions */
    sf *= 592.2;
    pf *= 459.6;
    s = pf + sf;
    return -s;

}