#!/usr/bin/env python3 # Copyright © 2014 Mattias Andrée (maandree@member.fsf.org) # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU Affero General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # # This program 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 Affero General Public License for more details. # # You should have received a copy of the GNU Affero General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import math import time def julian_day_to_epoch(t): return (jd - 2440587.5) * 86400.0 def epoch_to_julian_day(t): return t / 86400.0 + 2440587.5 def julian_day_to_julian_centuries(t): return (t - 2451545.0) / 36525.0 def julian_centuries_to_julian_day(t): return t * 36525.0 + 2451545.0 def epoch_to_julian_centuries(t): return julian_day_to_julian_centuries(epoch_to_julian_day(t)) def julian_centuries_to_epoch(t): return julian_day_to_epoch(julian_centuries_to_julian_day(t)) def epoch(): return time.time() def julian_day(): return epoch_to_julian_day(epoch()) def julian_centuries(): return epoch_to_julian_centuries(epoch()) def radians(deg): return deg * math.pi / 180 def degrees(rad): return rad * 180 / math.pi def sun_geometric_mean_longitude(t): return radians((0.0003032 * t ** 2 + 36000.76983 * t + 280.46646) % 360) def sun_geometric_mean_anomaly(t): return radians(-0.0001537 * t ** 2 + 35999.05029 * t + 357.52911) def earth_orbit_eccentricity(t): return -0.0000001267 * t ** 2 - 0.000042037 * t + 0.016708634 def sun_equation_of_centre(t): a = sun_geometric_mean_anomaly(t) rc = math.sin(1 * a) * (-0.000014 * t ** 2 - 0.004817 * t + 1.914602) rc += math.sin(2 * a) * (-0.000101 * t + 0.019993) rc += math.sin(3 * a) * 0.000289 return radians(rc) def sun_real_longitude(t): rc = sun_geometric_mean_longitude(t) return rc + sun_equation_of_centre(t) def sun_apparent_longitude(t): rc = degrees(sun_real_longitude(t)) - 0.00569 rc -= 0.00478 * math.sin(radians(-1934.136 * t + 125.04)) return radians(rc) def mean_ecliptic_obliquity(t): rc = 0.001813 * t ** 3 - 0.00059 * t ** 2 - 46.815 * t + 21.448 rc = 26 + rc / 60 rc = 23 + rc / 60 return radians(rc) def corrected_mean_ecliptic_obliquity(t): rc = -1934.136 * t + 125.04 rc = 0.00256 * math.cos(radians(rc)) rc += degrees(mean_ecliptic_obliquity(t)) return radians(rc) def solar_declination(t): rc = math.sin(corrected_mean_ecliptic_obliquity(t)) rc *= math.sin(sun_apparent_longitude(t)) return math.asin(rc) def equation_of_time(t): l = sun_geometric_mean_longitude(t) e = earth_orbit_eccentricity(t) m = sun_geometric_mean_anomaly(t) y = corrected_mean_ecliptic_obliquity(t) y = math.tan(y / 2) ** 2 rc = y * math.sin(2 * l) rc += (4 * y * math.cos(2 * l) - 2) * e * math.sin(m) rc -= 0.5 * y ** 2 * math.sin(4 * l) rc -= 1.25 * e ** 2 * math.sin(2 * m) return 4 * degrees(rc) def hour_angle_from_elevation(latitude, declinaton, elevation): if elevation == 0: return 0 rc = math.cos(abs(elevation)) rc -= math.sin(radians(latitude)) * math.sin(declinaton) rc /= math.cos(radians(latitude)) * math.cos(declinaton) rc = math.acos(rc) return -rc if (rc < 0) == (elevation < 0) else rc; def elevation_from_hour_angle(latitude, declinaton, hour_angle): rc = math.cos(radians(latitude)) rc *= math.cos(hour_angle) * math.cos(declinaton) rc += math.sin(radians(latitude)) * math.sin(declinaton) return math.asin(rc) def time_of_solar_noon(t, longitude): t, rc = julian_centuries_to_julian_day(t), longitude for (k, m) in ((-360, 0), (1440, -0.5)): rc = julian_day_to_julian_centuries(t + m + rc / k) rc = 720 - 4 * longitude - equation_of_time(rc) return rc def time_of_solar_elevation(t, noon, latitude, longitude, elevation): rc = noon rc, et = solar_declination(rc), equation_of_time(rc) rc = hour_angle_from_elevation(latitude, rc, elevation) rc = 720 - 4 * (longitude + degrees(rc)) - et rc = julian_day_to_julian_centuries(julian_centuries_to_julian_day(t) + rc / 1440) rc, et = solar_declination(rc), equation_of_time(rc) rc = hour_angle_from_elevation(latitude, rc, elevation) rc = 720 - 4 * (longitude + degrees(rc)) - et return rc def solar_elevation_from_time(t, latitude, longitude): rc = julian_centuries_to_julian_day(t) rc = (rc - float(int(rc + 0.5)) - 0.5) * 1440 rc = 720 - rc - equation_of_time(t) rc = radians(rc / 4 - longitude) return elevation_from_hour_angle(latitude, solar_declination(t), rc) def solar_elevation(latitude, longitude, t = None): rc = julian_centuries() if t is None else t rc = solar_elevation_from_time(rc, latitude, longitude) return degrees(rc) def sun(latitude, longitude, t = None, low = -6.0, high = 3.0): t = julian_centuries() if t is None else t e = solar_elevation(latitude, longitude, t) e = (e - low) / (high - low) return min(max(0, e), 1)