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Sunrise/Sunset Algorithm
Source:
Almanac for Computers, 1990
published by Nautical Almanac Office
United States Naval Observatory
Washington, DC 20392
Inputs:
day, month, year: date of sunrise/sunset
latitude, longitude: location for sunrise/sunset
zenith: Sun's zenith for sunrise/sunset
offical = 90 degrees 50'
civil = 96 degrees
nautical = 102 degrees
astronomical = 108 degrees
NOTE: longitude is positive for East and negative for West
1. first calculate the day of the year
N1 = floor(275 * month / 9)
N2 = floor((month + 9) / 12)
N3 = (1 + floor((year - 4 * floor(year / 4) + 2) / 3))
N = N1 - (N2 * N3) + day - 30
2. convert the longitude to hour value and calculate an approximate time
lngHour = longitude / 15
if rising time is desired:
t = N + ((6 - lngHour) / 24)
if setting time is desired:
t = N + ((18 - lngHour) / 24)
3. calculate the Sun's mean anomaly
M = (0.9856 * t) - 3.289
4. calculate the Sun's true longitude
L = M + (1.916 * sin(M)) + (0.020 * sin(2 * M)) + 282.634
NOTE: L potentially needs to be adjusted into the range [0,360) by adding/subtracting 360
5a. calculate the Sun's right ascension
RA = atan(0.91764 * tan(L))
NOTE: RA potentially needs to be adjusted into the range [0,360) by adding/subtracting 360
5b. right ascension value needs to be in the same quadrant as L
Lquadrant = (floor( L/90)) * 90
RAquadrant = (floor(RA/90)) * 90
RA = RA + (Lquadrant - RAquadrant)
5c. right ascension value needs to be converted into hours
RA = RA / 15
6. calculate the Sun's declination
sinDec = 0.39782 * sin(L)
cosDec = cos(asin(sinDec))
7a. calculate the Sun's local hour angle
cosH = (cos(zenith) - (sinDec * sin(latitude))) / (cosDec * cos(latitude))
if (cosH > 1)
the sun never rises on this location (on the specified date)
if (cosH < -1)
the sun never sets on this location (on the specified date)
7b. finish calculating H and convert into hours
if if rising time is desired:
H = 360 - acos(cosH)
if setting time is desired:
H = acos(cosH)
H = H / 15
8. calculate local mean time of rising/setting
T = H + RA - (0.06571 * t) - 6.622
9. adjust back to UTC
UT = T - lngHour
NOTE: UT potentially needs to be adjusted into the range [0,24) by adding/subtracting 24
10. convert UT value to local time zone of latitude/longitude
localT = UT + localOffset