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    Sample Polynomials
    From: Gordon Talge
    Date: 2002 Oct 23, 22:39 -0700

    Hi,
    
    Here are some Sample polynomials calculated by me from DE200/LE200
    for Nov. 2002.
    
    
    They are evaluated as follows:
    
    f(x) = a0+a1x+a2x^2+a3x^3+a4^x4+a5x^5
    
    Evaluate with Horner's Method:
    
    
    b5=xa5
    
    b4 = x(a4+b5)
    b3 = x(a3+b4)
    b2 = x(a2+b3)
    b1 = x(a1+b2)
    f(x) = a0 + b1
    
    
    
    d = day of month
    UT = Univ Time ( GMT ) in hours
    
    t = d + UT/24
    
    x = ((t-W)/A)-1
    
    W = weight for Sun.
    
    A = 16 .0  1/2 way mark
    
    
    Example:
    
    GHA and Dec Sun Nov 11, 2002 at 11h 11min 11 sec UT
    
    t = 11.4661
    
    x = -0.3459
    
    GHA Sun = 3951.17852 degs
    Remove multiples of 360 degs
    
    --> GHA Sun = 351.7902 or 351 degs 47.4 min
    
    --> Dec Sun = -17.4393 degs or S 17 degs 26.4 mins
    
    --> SD = .2695 and .2695 x 60 = 16.1725 or 16.2 mins.
    
    Nautical Almanac gives:
    
    Nov 11 at 11h
    
    348 degs 59.6 mins     Dec S 17 degs 26.2 mins  SD 16.2 mins
    
    d correction  +0.7
    
    Correction 11 min 11 sec 2 degs 47.8 min for GHA and +0.1 for Dec
    
    --> GHA is 351 degs 47.4 mins and Dec S 17 degs 26.3 mins SD 16.2 min
    
    I tried to get the polynomials to match the Almanac to 0.1 min of Arc.
    
    The NA does say that "The tabulated hourly values of the Sun's GHA have
    been adjusted to reduce to a minimum the error caused by treating v as
    negligible".
    
    I have generally found that the polynomials match better to the "Air
    Almanac"
    then the "Nautical Almanac". I do not have a 2002 copy of the "Air
    Almanac"
    to Check however.
    
    
    The Polynomials are valid for 32 days, starting at Nov 1, 2002 0h 00m
    00s UT.
    
    The Polynomials for the Navigation Planets are all valid for 1 month
    each,
    For the Moon, 8 days with 8 terms. Includes polynomial for H.P.
    
    -- Gordon
    
    
    
    
    
    
    
    
                             Dates:  Nov.  1 - Nov. 32
    
                              A = 16.0   W = 1
    
                     Aries        Sun          Sun           Sun
                     GHA          GHA          Dec.          S.D.
    Term              �            �            �            �
      0           5815.8788    5943.7870     -18.8849        .2699
      1           5775.7703    5759.2473      -3.9398        .0010
      2               .0001       -.4415        .7179       -.0001
      3               .0008        .0066        .0687        .0000
      4               .0000        .0090       -.0040        .0000
      5              -.0006        .0034        .0008        .0000
    
    Sums         11591.6494   11702.6118     -22.0413        .2708
    
    
    

       
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