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In a message dated 4/16/01 4:56:43 PM Eastern Daylight Time,
yves@REALNAMES.COM writes:


>

Here is how to calculate GHA Aries:

First determine the time in centuries of 36525 days from 1200 GMT 1 Jan 2000.
 Call that Tu.  There is a formula for doing it, but you may easily do it by
adding up the elapsed years, months, days, hours, minutes, and seconds since
1200 GMT 1 Jan 2000 (or negative if before).  You should get -.5 for 1200 1
Jan 1950, 0 for 1200 1 Jan 2000, and +.5 for 1200 1 Jan 2050.  Also,
calculate the ephemeris time (UT without the leap seconds):
Te = Tu+((63+60*Tu)/3,200,000,000)

Then calculate the longitude of the moon's ascending node;
N = 125.0 - (1934.1*Te)
and a number that is twice the sun's longitude:
L =  200.9 + (72001.7*Te)

With that in hand and a calculator with at least 12 significant digits,
calculate GHA Aries:
Aries = 360*(0.7790573 + (36625.0021390*Tu) + (0.0000011*Tu^2) -
(0.0000122*sin(N)) - (0.0000009*sin(L)))

Go to the library and copy the insert from the Nautical Almanac with the SHA
and Dec of the stars.  The numbers on the card are good for a few years until
the proper motions of a few of the stars move them over a bit.  With GHA
Aries, SHA star and Dec star, you are in business.

Caveats: (1) I am a miserable typist.  Watch out for my mistakes.  (2) The
last three terms of the formula above have precious little effect on GHA
Aries.  You can leave them off with little loss of accuracy.  There are far
more terms, I left them off too.   (3) The formula for converting Te to Tu is
an approximation I made a few years back.  There may be better estimates now,
but again, it makes little difference.

If you want do it for real, buy a copy of "Explanatory Supplement to the
Astronomical Almanac" and enjoy a year of night time reading.  "Astronomy on
the Personal Computer", and "Astronomical Algorithms" will also help.  With
these (and a Cambridge Catalogue), you can absolutely nail the positions of
the stars and reproduce all the other numbers in the Nautical Almanac.

Bill Murdoch

   

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