1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
|
#!/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 sun(latitude, longitude, t = None, low = -6.0, high = 3.0):
'''
Get the visibility of the Sun
@param latitude:float The latitude component of your GPS coordinate
@param longitude:float The longitude component of your GPS coordinate
@param t:float? The time in Julian Centuries, `None` for current time
@param low:float The 100 % night limit elevation of the Sun (highest when not visible)
@param high:float The 100 % day limit elevation of the Sun (lowest while fully visible)
@return :float The visibilty of the sun, 0 during the night, 1 during the day,
between 0 and 1 during twilight. Other values will not occur.
'''
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)
# The following functions are used to calculate the result for `sun`
# (most of them) but could be used for anything else. There name is
# should tell you enough, `t` (and `noon`) is in Julian centuries
# except for in the convertion methods
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():
'''
Get current POSIX time
'''
return time.time()
def julian_day():
'''
Get current Julian Day time
'''
return epoch_to_julian_day(epoch())
def julian_centuries():
'''
Get current Julian Centuries time
'''
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)
|
