EXAMPLE SUNSET CALCULATION
Sunset
January 13, 1888
Washington, D.C., USA
(38°50'N 77°00'W = +38.833333...° -77.000...°)
mean ecliptic longitude of the sun = 292.662°-000.107°-000.064°-000.358°+000.278° = 292.411°
ecliptic longitude of perigee of the sun = +000.86°+279.49°-000.03°+000.69° = 281.01°
mean anomaly of the sun = 292.411°-281.01° = 011.401°
ecliptic longitude of the sun = 292.411°+1.915°×(sin(011.401°))+0.020°×(sin(2×011.401°)) = 292.797297526...°
declination of the sun = asin(sin(292.797297526...°)×0.39777) = -21.5120425524...°
right ascension of the sun = 292.797297526...°-atan(sin(2×292.797297526...°)÷(23.2377+cos(2×292.797297526...°))) = 294.612846478...°
equation of time = 294.612846478...°-292.411° = +2.201846478...°
mean time of sunset = 270°-(-77.000...°) = 347.000...°
time of sunset = 347.000...°+asin(tan(+38.833333...°)×tan(-21.5120425524...°)+0.01454÷cos(+38.833333...°)÷cos(-21.5120425524...°))+(+2.201846478...°) = 331.91102521...° = 22h07m38s UT = 16h59m38s in Washington = 17h07m38s in the Eastern Standard Time Zone (which I don't think existed in the year 1888)
Now you should really interpolate the ecliptic longitude of the sun and do the whole calculation again. This will likely bring the rounded to the minute answer in agreement with the following.
U.S. Naval Observatory
Astronomical Applications Department
Sun and Moon Data for One Day
The following information is provided for Washington, DC, USA (longitude W77.0, latitude N38.8):
Friday
13 January 1888 Universal Time - 5h
SUN
Begin civil twilight 06:57
Sunrise 07:26
Sun transit 12:17
Sunset 17:09
End civil twilight 17:38
MOON
Moonset 16:41 on preceding day
Moonrise 07:33
Moon transit 12:36
Moonset 17:41
Moonrise 08:20 on following day
Please forgive me if I have made a typo or miscalculation on this page. -Author
copyright (c) 2001.SEP.05 Sean Barton, all rights reserved