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 NOTE: the algorithm assumes the use of a calculator with the trig functions in "degree" (rather than "radian") mode. Most programming languages assume radian arguments, requiring back and forth convertions. The factor is 180/pi. So, for instance, the equation RA = atan(0.91764 * tan(L)) would be coded as RA = (180/pi)*atan(0.91764 * tan((pi/180)*L)) to give a degree answer with a degree input for L. 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