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#!/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)
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