/** * Copyright © 2016 Mattias Andrée * * 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 #include #include /** * 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)); }