/**
* Copyright © 2016 Mattias Andrée <maandree@member.fsf.org>
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*/
#include <math.h>
#include <time.h>
#include <errno.h>
/**
* Get current Julian Centuries time (100 Julian days since J2000.)
*
* @return The current Julian Centuries time.
*
* @throws 0 On success.
* @throws Any error specified for clock_gettime(3) on error.
*/
static double
julian_centuries()
{
struct timespec now;
double tm;
#if defined(CLOCK_REALTIME_COARSE)
if (clock_gettime(CLOCK_REALTIME_COARSE, &now))
#else
if (clock_gettime(CLOCK_REALTIME, &now))
#endif
return 0.0;
tm = (double)(now.tv_nsec);
tm /= 1000000000.0;
tm += (double)(now.tv_sec);
tm = (tm / 86400.0 + 2440587.5 - 2451545.0) / 36525.0;
return errno = 0, tm;
}
/**
* Convert a Julian Centuries timestamp to a Julian Day timestamp.
*
* @param tm The time in Julian Centuries
* @return The time in Julian Days
*/
static inline double
julian_centuries_to_julian_day(double tm)
{
return tm * 36525.0 + 2451545.0;
}
/**
* Convert an angle (or otherwise) from degrees to radians.
*
* @param deg The angle in degrees.
* @param The angle in radians.
*/
static inline double
radians(double deg)
{
return deg * (double)M_PI / 180.0;
}
/**
* Convert an angle (or otherwise) from radians to degrees.
*
* @param rad The angle in radians.
* @param The angle in degrees.
*/
static inline double
degrees(double rad)
{
return rad * 180.0 / (double)M_PI;
}
/**
* Calculates the Sun's elevation from the solar hour angle
*
* @param longitude The longitude in degrees eastwards.
* from Greenwich, negative for westwards.
* @param declination The declination, in radians.
* @param hour_angle The solar hour angle, in radians.
* @return The Sun's elevation, in radians.
*/
static inline double
elevation_from_hour_angle(double latitude, double declination, double hour_angle)
{
double rc = cos(radians(latitude));
rc *= cos(hour_angle) * cos(declination);
rc += sin(radians(latitude)) * sin(declination);
return asin(rc);
}
/**
* Calculates the Sun's geometric mean longitude.
*
* @param tm The time in Julian Centuries.
* @return The Sun's geometric mean longitude in radians.
*/
static inline double
sun_geometric_mean_longitude(double tm)
{
double rc = pow(0.0003032 * tm, 2.0) + 36000.76983 * tm + 280.46646;
return radians(fmod(rc, 360.0));
/*
CANNIBALISERS:
The result of this function should always be positive, this
means that after division modulo 360 but before `radians`,
you will need to add 360 if the value is negative. This can
only happen if `tm` is negative, which can only happen for date
times before 2000-(01)Jan-01 12:00:00 UTC par division modulo
implementations with the signess of at least the left operand.
More precively, it happens between circa 1970-(01)Jan-11
16:09:02 UTC and circa 374702470660351740 seconds before
January 1, 1970 00:00 UTC, which is so far back in time
it cannot be reliable pinned down to the right year, but it
is without a shadow of a doubt looooong before the Earth
was formed, is right up there with the age of the Milky Way
and the universe itself.
*/
}
/**
* Calculates the Sun's geometric mean anomaly.
*
* @param tm The time in Julian Centuries.
* @return The Sun's geometric mean anomaly in radians.
*/
static inline double
sun_geometric_mean_anomaly(double tm)
{
return radians(pow(-0.0001537 * tm, 2.0) + 35999.05029 * tm + 357.52911);
}
/**
* Calculates the Earth's orbit eccentricity.
*
* @param tm The time in Julian Centuries.
* @return The Earth's orbit eccentricity.
*/
static inline double
earth_orbit_eccentricity(double tm)
{
return pow(-0.0000001267 * tm, 2.0) - 0.000042037 * tm + 0.016708634;
}
/**
* Calculates the Sun's equation of the centre, the difference
* between the true anomaly and the mean anomaly.
*
* @param tm The time in Julian Centuries.
* @return The Sun's equation of the centre, in radians.
*/
static inline double
sun_equation_of_centre(double tm)
{
double a = sun_geometric_mean_anomaly(tm), rc;
rc = sin(1.0 * a) * (pow(-0.000014 * tm, 2.0) - 0.004817 * tm + 1.914602);
rc += sin(2.0 * a) * (-0.000101 * tm + 0.019993);
rc += sin(3.0 * a) * 0.000289;
return radians(rc);
}
/**
* Calculates the Sun's real longitudinal position.
*
* @param tm The time in Julian Centuries.
* @return The longitude, in radians.
*/
static inline double
sun_real_longitude(double tm)
{
double rc = sun_geometric_mean_longitude(tm);
return rc + sun_equation_of_centre(tm);
}
/**
* Calculates the Sun's apparent longitudinal position.
*
* @param tm The time in Julian Centuries.
* @return The longitude, in radians.
*/
static inline double
sun_apparent_longitude(double tm)
{
double rc = degrees(sun_real_longitude(tm)) - 0.00569;
rc -= 0.00478 * sin(radians(-1934.136 * tm + 125.04));
return radians(rc);
}
/**
* Calculates the mean ecliptic obliquity of the Sun's
* apparent motion without variation correction.
*
* @param tm The time in Julian Centuries.
* @return The uncorrected mean obliquity, in radians.
*/
static double
mean_ecliptic_obliquity(double tm)
{
double rc = pow(0.001813 * tm, 3.0) - pow(0.00059 * tm, 2.0) - 46.815 * tm + 21.448;
rc = 26 + rc / 60;
rc = 23 + rc / 60;
return radians(rc);
}
/**
* Calculates the mean ecliptic obliquity of the Sun's
* parent motion with variation correction.
*
* @param tm The time in Julian Centuries.
* @return The mean obliquity, in radians.
*/
static double
corrected_mean_ecliptic_obliquity(double tm)
{
double rc = -1934.136 * tm + 125.04;
rc = 0.00256 * cos(radians(rc));
rc += degrees(mean_ecliptic_obliquity(tm));
return radians(rc);
}
/**
* Calculates the Sun's declination.
*
* @param tm The time in Julian Centuries.
* @return The Sun's declination, in radian.
*/
static inline double
solar_declination(double tm)
{
double rc = sin(corrected_mean_ecliptic_obliquity(tm));
rc *= sin(sun_apparent_longitude(tm));
return asin(rc);
}
/**
* Calculates the equation of time, the discrepancy
* between apparent and mean solar time.
*
* @param tm The time in Julian Centuries.
* @return The equation of time, in degrees.
*/
static inline double
equation_of_time(double tm)
{
double l, e, m, y, rc;
l = sun_geometric_mean_longitude(tm);
e = earth_orbit_eccentricity(tm);
m = sun_geometric_mean_anomaly(tm);
y = corrected_mean_ecliptic_obliquity(tm);
y = pow(tan(y / 2.0), 2.0);
rc = y * sin(2.0 * l);
rc += (4.0 * y * cos(2.0 * l) - 2.0) * e * sin(m);
rc -= pow(0.5 * y, 2.0) * sin(4.0 * l);
rc -= pow(1.25 * e, 2.0) * sin(2.0 * m);
return 4.0 * degrees(rc);
}
/**
* Calculates the Sun's elevation as apparent.
* from a geographical position.
*
* @param tm The time in Julian Centuries.
* @param latitude The latitude in degrees northwards from
* the equator, negative for southwards.
* @param longitude The longitude in degrees eastwards from
* Greenwich, negative for westwards.
* @return The Sun's apparent elevation at the specified time as seen
* from the specified position, measured in radians.
*/
static inline double
solar_elevation_from_time(double tm, double latitude, double longitude)
{
double rc = julian_centuries_to_julian_day(tm);
rc = (rc - round(rc) - 0.5) * 1440;
rc = 720.0 - rc - equation_of_time(tm);
rc = radians(rc / 4.0 - longitude);
return elevation_from_hour_angle(latitude, solar_declination(tm), rc);
}
/**
* Calculates the Sun's elevation as apparent.
* from a geographical position.
*
* @param latitude The latitude in degrees northwards from
* the equator, negative for southwards.
* @param longitude The longitude in degrees eastwards from
* Greenwich, negative for westwards.
* @return The Sun's apparent elevation as seen, right now,
* from the specified position, measured in degrees.
*
* @throws 0 On success.
* @throws Any error specified for clock_gettime(3) on error.
*/
double
solar_elevation(double latitude, double longitude)
{
double tm = julian_centuries();
return errno ? -1 : degrees(solar_elevation_from_time(rm, latitude, longitude));
}
