I recognize the first of these as the Greenwich Hour Angle, but do not recognize SHA. GHA is calculated by subtracting your Greenwich Sidereal Time (GST) from the Right Ascension of the object you are interested in. If the answer is positive, the object is to the east of the meridian, if negative it is to the west. To calculate local sidereal time from Universal Time, you use the formula:
LST = K + 1.0027379 x t + 0.06570982 x D - Longitude/15.
where, t, is the Universal Time in decimal hours, D ,is the number of days since December 31 of the previous year, and, Longitude, is the west longitude of your location. The constant, k, has to be looked up in the U.S. Nautical Almanac and is the Sidereal Time at 0h Universal Time for December 31. This quantity cannot be easily derived with any accuracy and requires a detailed dynamical model of the Earth-Moon-Sun system. The table below gives recent values in decimal hours:
Year.............K...... 1994 17.371435 1995 17.387349 1996 17.403263 1997 17.353468 1998 17.369382 1999 17.385297 2000 17.401211 ........................
UT is just the Greenwich Mean Time, so just use this as your local time. Then from the year, and day of the year, compute 0.0657098 times the number of days since January 0.0 and the date in question and subtract the constant. This gives GST. Example, on April 22, 1998 the constant is 17.369282, and April 22 is 113 days after January 0.0 so 113 x 0.0657098 = 7.425207. Then the GST = 7.425207 - 17.369282 = -9.944075. If the decimal UT is 12.35 then multiply this by 1.002738 to get 12.38381. Add this to -9.944075 to get 2.43974 or 2h 26m 23.06s as the GST. For an object with Right Ascension = 2h 26m 23.06, it will be exactly on the meridian at this time, with an hour angle 360 x ( RA - GST)/24 = 0 degrees.
Copyright 1997 Dr. Sten Odenwald
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