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