sunrise_sunset

Calculate sun rise and sun set times.

Sunrise/Sunset Algorithm

There are many implementations of this algorithm but most can be traced back to the Almanac for Computers, 1990 published by Nautical Almanac Office, United States Naval Observatory, Washington, DC 20392

See also https://en.m.wikipedia.org/wiki/Sunrise_equation

Inputs: day, month, year: date of sunrise/sunset latitude, longitude: location for sunrise/sunset zenith: Sun's zenith for sunrise/sunset official = 90 degrees 50 minutes civil = 96 degrees nautical = 102 degrees astronomical = 108 degrees

NOTE: longitude is positive for East and negative for West

The algorithm assumes the use of trig functions in "degree" mode, 
rather than "radian" mode. 

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

5. Right ascension

   1. 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

   2. 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)

   3. 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))

7. Local hour angle

   1. 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)

   2. 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