/* solar.c -- Solar position source
This file is part of redshift-ng.
redshift-ng 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 3 of the License, or
(at your option) any later version.
redshift-ng 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 redshift-ng. If not, see .
Copyright (c) 2010 Jon Lund Steffensen
*/
/* Ported from javascript code by U.S. Department of Commerce,
National Oceanic & Atmospheric Administration:
http://www.srrb.noaa.gov/highlights/sunrise/calcdetails.html
It is based on equations from "Astronomical Algorithms" by
Jean Meeus. */
#include "common.h"
#include "solar.h"
#define RAD(x) ((x)*(M_PI/180))
#define DEG(x) ((x)*(180/M_PI))
/* Angels of various times of day. */
static const double time_angle[] = {
[SOLAR_TIME_ASTRO_DAWN] = RAD(-90.0 + SOLAR_ASTRO_TWILIGHT_ELEV),
[SOLAR_TIME_NAUT_DAWN] = RAD(-90.0 + SOLAR_NAUT_TWILIGHT_ELEV),
[SOLAR_TIME_CIVIL_DAWN] = RAD(-90.0 + SOLAR_CIVIL_TWILIGHT_ELEV),
[SOLAR_TIME_SUNRISE] = RAD(-90.0 + SOLAR_DAYTIME_ELEV),
[SOLAR_TIME_NOON] = RAD(0.0),
[SOLAR_TIME_SUNSET] = RAD(90.0 - SOLAR_DAYTIME_ELEV),
[SOLAR_TIME_CIVIL_DUSK] = RAD(90.0 - SOLAR_CIVIL_TWILIGHT_ELEV),
[SOLAR_TIME_NAUT_DUSK] = RAD(90.0 - SOLAR_NAUT_TWILIGHT_ELEV),
[SOLAR_TIME_ASTRO_DUSK] = RAD(90.0 - SOLAR_ASTRO_TWILIGHT_ELEV)
};
/* Unix epoch from Julian day */
static double
epoch_from_jd(double jd)
{
return 86400.0*(jd - 2440587.5);
}
/* Julian day from unix epoch */
static double
jd_from_epoch(double t)
{
return (t / 86400.0) + 2440587.5;
}
/* Julian centuries since J2000.0 from Julian day */
static double
jcent_from_jd(double jd)
{
return (jd - 2451545.0) / 36525.0;
}
/* Julian day from Julian centuries since J2000.0 */
static double
jd_from_jcent(double t)
{
return 36525.0*t + 2451545.0;
}
/* Geometric mean longitude of the sun.
t: Julian centuries since J2000.0
Return: Geometric mean logitude in radians. */
static double
sun_geom_mean_lon(double t)
{
/* FIXME returned value should always be positive */
return RAD(fmod(280.46646 + t*(36000.76983 + t*0.0003032), 360));
}
/* Geometric mean anomaly of the sun.
t: Julian centuries since J2000.0
Return: Geometric mean anomaly in radians. */
static double
sun_geom_mean_anomaly(double t)
{
return RAD(357.52911 + t*(35999.05029 - t*0.0001537));
}
/* Eccentricity of earth orbit.
t: Julian centuries since J2000.0
Return: Eccentricity (unitless). */
static double
earth_orbit_eccentricity(double t)
{
return 0.016708634 - t*(0.000042037 + t*0.0000001267);
}
/* Equation of center of the sun.
t: Julian centuries since J2000.0
Return: Center(?) in radians */
static double
sun_equation_of_center(double t)
{
/* Use the first three terms of the equation. */
double m = sun_geom_mean_anomaly(t);
double c = sin(m)*(1.914602 - t*(0.004817 + 0.000014*t)) +
sin(2*m)*(0.019993 - 0.000101*t) +
sin(3*m)*0.000289;
return RAD(c);
}
/* True longitude of the sun.
t: Julian centuries since J2000.0
Return: True longitude in radians */
static double
sun_true_lon(double t)
{
double l_0 = sun_geom_mean_lon(t);
double c = sun_equation_of_center(t);
return l_0 + c;
}
/* Apparent longitude of the sun. (Right ascension).
t: Julian centuries since J2000.0
Return: Apparent longitude in radians */
static double
sun_apparent_lon(double t)
{
double o = sun_true_lon(t);
return RAD(DEG(o) - 0.00569 - 0.00478*sin(RAD(125.04 - 1934.136*t)));
}
/* Mean obliquity of the ecliptic
t: Julian centuries since J2000.0
Return: Mean obliquity in radians */
static double
mean_ecliptic_obliquity(double t)
{
double sec = 21.448 - t*(46.815 + t*(0.00059 - t*0.001813));
return RAD(23.0 + (26.0 + (sec/60.0))/60.0);
}
/* Corrected obliquity of the ecliptic.
t: Julian centuries since J2000.0
Return: Currected obliquity in radians */
static double
obliquity_corr(double t)
{
double e_0 = mean_ecliptic_obliquity(t);
double omega = 125.04 - t*1934.136;
return RAD(DEG(e_0) + 0.00256*cos(RAD(omega)));
}
/* Declination of the sun.
t: Julian centuries since J2000.0
Return: Declination in radians */
static double
solar_declination(double t)
{
double e = obliquity_corr(t);
double lambda = sun_apparent_lon(t);
return asin(sin(e)*sin(lambda));
}
/* Difference between true solar time and mean solar time.
t: Julian centuries since J2000.0
Return: Difference in minutes */
static double
equation_of_time(double t)
{
double epsilon = obliquity_corr(t);
double l_0 = sun_geom_mean_lon(t);
double e = earth_orbit_eccentricity(t);
double m = sun_geom_mean_anomaly(t);
double y = pow(tan(epsilon/2.0), 2.0);
double eq_time = y*sin(2*l_0) - 2*e*sin(m) +
4*e*y*sin(m)*cos(2*l_0) -
0.5*y*y*sin(4*l_0) -
1.25*e*e*sin(2*m);
return 4*DEG(eq_time);
}
/* Hour angle at the location for the given angular elevation.
lat: Latitude of location in degrees
decl: Declination in radians
elev: Angular elevation angle in radians
Return: Hour angle in radians */
static double
hour_angle_from_elevation(double lat, double decl, double elev)
{
double omega = acos((cos(fabs(elev)) - sin(RAD(lat))*sin(decl))/
(cos(RAD(lat))*cos(decl)));
return copysign(omega, -elev);
}
/* Angular elevation at the location for the given hour angle.
lat: Latitude of location in degrees
decl: Declination in radians
ha: Hour angle in radians
Return: Angular elevation in radians */
static double
elevation_from_hour_angle(double lat, double decl, double ha)
{
return asin(cos(ha)*cos(RAD(lat))*cos(decl) +
sin(RAD(lat))*sin(decl));
}
/* Time of apparent solar noon of location on earth.
t: Julian centuries since J2000.0
lon: Longitude of location in degrees
Return: Time difference from mean solar midnigth in minutes */
static double
time_of_solar_noon(double t, double lon)
{
/* First pass uses approximate solar noon to
calculate equation of time. */
double t_noon = jcent_from_jd(jd_from_jcent(t) - lon/360.0);
double eq_time = equation_of_time(t_noon);
double sol_noon = 720 - 4*lon - eq_time;
/* Recalculate using new solar noon. */
t_noon = jcent_from_jd(jd_from_jcent(t) - 0.5 + sol_noon/1440.0);
eq_time = equation_of_time(t_noon);
sol_noon = 720 - 4*lon - eq_time;
/* No need to do more iterations */
return sol_noon;
}
/* Time of given apparent solar angular elevation of location on earth.
t: Julian centuries since J2000.0
t_noon: Apparent solar noon in Julian centuries since J2000.0
lat: Latitude of location in degrees
lon: Longtitude of location in degrees
elev: Solar angular elevation in radians
Return: Time difference from mean solar midnight in minutes */
static double
time_of_solar_elevation(double t, double t_noon,
double lat, double lon, double elev)
{
/* First pass uses approximate sunrise to
calculate equation of time. */
double eq_time = equation_of_time(t_noon);
double sol_decl = solar_declination(t_noon);
double ha = hour_angle_from_elevation(lat, sol_decl, elev);
double sol_offset = 720 - 4*(lon + DEG(ha)) - eq_time;
/* Recalculate using new sunrise. */
double t_rise = jcent_from_jd(jd_from_jcent(t) + sol_offset/1440.0);
eq_time = equation_of_time(t_rise);
sol_decl = solar_declination(t_rise);
ha = hour_angle_from_elevation(lat, sol_decl, elev);
sol_offset = 720 - 4*(lon + DEG(ha)) - eq_time;
/* No need to do more iterations */
return sol_offset;
}
/* Solar angular elevation at the given location and time.
t: Julian centuries since J2000.0
lat: Latitude of location
lon: Longitude of location
Return: Solar angular elevation in radians */
static double
solar_elevation_from_time(double t, double lat, double lon)
{
/* Minutes from midnight */
double jd = jd_from_jcent(t);
double offset = (jd - round(jd) - 0.5)*1440.0;
double eq_time = equation_of_time(t);
double ha = RAD((720 - offset - eq_time)/4 - lon);
double decl = solar_declination(t);
return elevation_from_hour_angle(lat, decl, ha);
}
/* Solar angular elevation at the given location and time.
date: Seconds since unix epoch
lat: Latitude of location
lon: Longitude of location
Return: Solar angular elevation in degrees */
double
solar_elevation(double date, double lat, double lon)
{
double jd = jd_from_epoch(date);
return DEG(solar_elevation_from_time(jcent_from_jd(jd), lat, lon));
}
void
solar_table_fill(double date, double lat, double lon, double *table)
{
/* Calculate Julian day */
double jd = jd_from_epoch(date);
/* Calculate Julian day number */
double jdn = round(jd);
double t = jcent_from_jd(jdn);
/* Calculate apparent solar noon */
double sol_noon = time_of_solar_noon(t, lon);
double j_noon = jdn - 0.5 + sol_noon/1440.0;
double t_noon = jcent_from_jd(j_noon);
table[SOLAR_TIME_NOON] = epoch_from_jd(j_noon);
/* Calculate solar midnight */
table[SOLAR_TIME_MIDNIGHT] = epoch_from_jd(j_noon + 0.5);
/* Calulate absoute time of other phenomena */
for (int i = 2; i < SOLAR_TIME_MAX; i++) {
double angle = time_angle[i];
double offset = time_of_solar_elevation(t, t_noon, lat, lon, angle);
table[i] = epoch_from_jd(jdn - 0.5 + offset/1440.0);
}
}