solar_declination.c

/*
 * (C)2012 Michael Duane Rice All rights reserved.
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 * modification, are permitted provided that the following conditions are
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 * form must reproduce the above copyright notice, this list of conditions
 * and the following disclaimer in the documentation and/or other materials
 * provided with the distribution. Neither the name of the copyright holders
 * nor the names of contributors may be used to endorse or promote products
 * derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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/* $Id$ */

/*
    Were it not for the eccentricity of Earths orbit, this would be a trivial function.

    We compute the Earths orbital position with respect to perihelion, from which we derive a
    'velocity correction factor'. We then compute the orbital angle with respect to the
    December solstice, as 'modulated' by that correction factor.

    Due to the accumulation of rounding errors, the computed December solstice of 2135 will lag
    the actual solstice by many hours. A fudge factor, 'LAG', distributes the error across
    the 136 year range of this library.
*/

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

#define LAG 38520

double
solar_declination(const time_t * timer)
{

    uint32_t        fT, oV;
    double          dV, dT;

    /* Determine orbital angle relative to perihelion of January 1999 */
    oV = *timer % ANOM_YEAR;
    oV += PERIHELION;
    dV = oV;
    dV /= ANOM_CYCLE;

    /* Derive velocity correction factor from the perihelion angle */
    dV = sin(dV);
    dV *= DELTA_V;

    /* Determine orbital angle relative to solstice of December 1999 */
    fT = *timer % TROP_YEAR;
    fT += SOLSTICE + LAG;
    dT = fT;
    dT /= TROP_CYCLE;
    dT += dV;

    /* Finally having the solstice angle, we can compute the declination */
    dT = cos(dT) * INCLINATION;

    return -dT;
}