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    Re: Longhand Sight Reduction
    From: Greg Rudzinski
    Date: 2014 Nov 13, 07:53 -0800

    Gary,

    To get you introduced see this link to my blog on the Doniol sight reduction method using sin, cosine, and haversine tables.

    http://gregrudzinski.blogspot.com/2014/06/longhand-sight-reduction.html

    Hanno Ix has modified the original formula so that just haversines are used thus only a single table is needed to derive the zenith distance. My contribution is the formating of the modified haversine Doniol formula into a 2 column reduction for practical use. There are three natural haversine look-ups for L+d,L-d,LHA and a natural arc haversine look-up for zenith distance. No logs are used. There is a single multiplication step done longhand. There are five summing steps.

    L           

    d                             (A)                           (B)

    L+d            Hv                         Hv

    L-d           +Hv                         +P                 

                   1-sum                      Arc Hv sum

                   sum                          ZD

    LHA        * Hv                           Hc

                    P                            

    L=latitude, d=declination, Hv=haversine, LHA= local hour angle (converted to meridian angle for LHA>180°), P=product, ZD=zenith distance, Hc=calculated altitude

     

    Greg Rudzinski



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