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    Re: Algorithm for star ephemerides?
    From: Bill Murdoch
    Date: 2001 Apr 16, 8:29 PM

    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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