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    Re: Latitude by law of cosines
    From: Robert Bernecky
    Date: 2018 Jan 14, 17:38 -0800

    I tested out the formulas, with the following data:

    2017 August 20 Sunday 17h 04m 31s UT   Aries 225d 21.0' LHA 255d 19.0'

     Position N 29d 11.4'   E 29º 58.0'

          Body        GHA        LHA        Dec        Hc         Zn

    -1.8  Jupiter    26º 27.1'  56º 25.1' S 6º 46.7'  24º 57.5' 245.9º

    -----------------------------------------------------------------------

    Using a calculator, and storing the values in variables:

    Hc   24º 57.5' = 24.9583333 in A

    dec S 6º 46.7' = -6.7783333 in B

    LHA  56º 25.1' = 56.4183333 in C

    Now, compute G:

      tan^-1( tan B / cos C) --> X  (store in variable X)

      X = -12.1276811

    Next, compute coL + G:

      sin^-1 ( sin A * sin X / sin d) --> Y (store in Y)

      Y = 48.68471841

    Y = coL + G  so by algebra

    coL = Y- G

    where G's value is stored in variable X.

    we do:  Y - X -> D (store in D)

    D = 60.81239952

    D is the coL, and the Latitude is 90 - D = 29.18760049

    or  L = 29º 11.3'

    which (almost) matches the position's latitude N 29º 11.4'

       
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