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    Almanac for Computers
    From: Gordon Talge
    Date: 1996 Aug 28, 04:09 EDT

    Since I found out that the "Almanac for Computers" is no longer available
    from the USNO since 1991, I decided to try and duplicate some of their
    results. I would like a little bit of feed back on my efforts.
    Power Series for the Sun
    Dates : Sep. 1 to Oct. 1 1996
             A = 16.0  W = 1
                   Sun                  Sun           S.D.
                   GHA                  Dec.
      0          6301.3640             2.2319         0.2652
      1          5761.4229            -6.1853         0.0012
      2             0.0052            -0.0954         0.0001
      3            -0.0506             0.0697         0.0000
      4            -0.0067             0.0045         0.0000
      5            -0.0023            -0.0063         0.0000
    sums        12062.7325            -3.9809         0.2665
    They way to use these series is first convert UT into decimal then
       t = d + 24 /UT,     where d is the day of the month.
      Next, get x where x in between -1 and +1. ie [-1,+1] using the formula
        x =  ( (t - W ) / A ) -1, use x as the argument to evaluate the polynomial.
    f(x) = a0 + a1*x + a2 * x^2 + a3 * x^3 + a4 * x^4 + a5 *x^5 .
     This can be better evaluated as
     f(x) = a0 + x*(a1+x*(a2+x*(a3+x*(a4+x*a5)))).
    Once the GHA, Dec. or S.D. is obtained, remove any multiples of 360 degrees
    and convert to degrees and mins. or in the case of the S.D. mins, round off
    to the nearest .1 min
    Example:  GHA for Sept 18th  7h 28m 19s  UT
     7h 28m 19s = 7.471944444 hours or  7.471944444 / 24 = 0.311331019 parts of
     a day.
    Since d= 18 we have for t, t= 18.311331019 days
     x = (( 18.311331019  - 1 )/ 16 ) -1   or x = 0.081958189
    This is what we use for the argument of the polynomial.
    Evaluating the GHA polynomial at 0.081958189 we get
    GHA = 6773.559794 .  Removing multiples of 360 degrees we get
               293.5597932d or  ** 293d 33.6 mins  **
    So the GHA for Sept 18th 7h 28m 19s is 293d 33.6min
      By the 1996 Air Almanac I get for Sept 18th 7h 20mins
               291d  28.8 min
               The correction for 8min 19s is 2d 4.8min
               so the   **  GHA is 293d 33.6 min   **
    Using the same argument for the Dec. Series I get
                1.7244 or  **  N 1d 43.5   **
      (Note: N is + and S is - )
        The Air Almanac give  N 1d 43.6 for 7h 20min and
                              N 1d 43.4 for 7h 30min
      Since 28min 19sec is between 20 and 30mins and is closer to 30 but
        still less and the dec is going down, N 1d 43.5 seems resonable.
        I don't know what the Nautical Almanac says with it's d correction.
    I have tried to fit the polynomial to give the proper value with an
    error of not more then 0.1 min
    The series is ONLY valid for Sept 1996, NOT before and NOT after.
    The sums at the bottom are NOT used in calculations, they are used to
    check that you entered the coefficients correctly.
    What I did was use a programable calculator to evaluate the polynomial
    by loading in the coefficients into the storage registers and then
    running it through.
    The reference ephemeris used is JPL's DE200 which is the background basis for
    the Astronomial Almanac and Nautical Almanacs.
    -- Gordon
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