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    Sunrise and Sunset Calculations
    From: Bill Murdoch
    Date: 1997 Feb 11, 10:25 EST

    From: W. S. Murdoch, Polymers D&C (Kpt. 1027)
    Subject: Sunrise and Sunset Calculations
    "Explanatory Supplement to the Astronomical Almanac" has a relatively short
    way of calculating the times of sunrise, sunset, and twilight on page 484ff.
    Guess the GMT time of the phenomena, UTp
    Find JD, the number of days after GMT 1200 1 Jan -4712
             for example noon 25 Jun 1990 is 2448068.000
             midnight JD will end in .500
    Change that to centuries after 1200 1 Jan 2000 T=(JD-2451545.0)/36525
     (Current dates are negative around -0.1.)
    Calculate the mean aberrated longitude of the sun in degrees
     L=280.460+36000.770T
    Calculate the mean anomaly of the sun in degrees
     G=357.528+35999.050T
    Calculate the ecliptic longitude of the sun in degrees
     Lambda=L+1.915sinG+0.020sin2G
    and the obliquity of the ecliptic in degrees
     epsilon=23.4393-0.01300T
    If UT is the current GMT time,
     GHA=15UT-180-1.915sinG-0.020sin2G+2.466sin2Lambda-0.053sin4Lambda
     Dec=arcsin(sinepsilonsinLambda)
    For civil twilight h=-6, for nautical twilight h=-12, for sunrise and
    sunset h=-0.83, calculate the hour angle of the sun.
     t=arccos((sinh-sinLat)/(cosLatcosDec))
    The time of the phenomenon is
     UTp=UT-(GHA+Lambda+-t)/15  (where + is rising and - is setting)
    If UTp and UT are not within 0.008 hours of each other, use UTp as a better
    guess of the time of the phenomenon and go through the calculations again.
    This should work for latitudes up to 45 degrees and is obviously better
    for a programmable calculator than for hand work.
    
                      Bill Murdoch
    
    
    

       
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