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    Sight reduction using a calculator's POL (arctan2) key
    From: Robert Bernecky
    Date: 2018 Apr 2, 06:37 -0700

    Now that calculators (in my opinion) are rapidly becoming "old technology" --

    I thought it would be good to highlight a formula for sight reduction that calculates the altitude and azimuth of a body, given its declination and local hour angle.

       < r, A> = POL( tan dec cos lat - sin lat cos lha, -sin lha)

       Hc = acos(r * cos dec)

       Zn = A  (add 360 if A is negative)

    After using this formula for some time, I think it should be more familiar, and possibly more popular, as it has some advantages:

       1) Only one complicated formula to memorize/type in

       2) The altitude Hc and azimuth Zn are (almost) found in one step

       3) No complicated sign rules to remember to find the azimuth

    I first became aware of this approach from a post by Robin Stuart.  After digging through the archives, I found that people have pieced together the idea, but never made much comment on it:

       http://fer3.com/arc/m2.aspx/Sight-Reduction-Formula-Question-Huxtable-jan-2005-w21338

       http://fer3.com/arc/m2.aspx/POL-arctan2-Bergman-nov-2005-w26304

       http://fer3.com/arc/m2.aspx/Which-calculator-use-for-arctantan269-Stuart-feb-2017-g38110

    Enclosed is:

    1) A short "how to use it" write-up, "Polar Reduction"

    2) A derivation, based on coordinate transformations (using rotation matrices)

    3) Some math background on rotation matrices that explain some of the details (for those who like such stuff).

    File:
    Polar-Reduction.pdf
    File:
    Derivation-Polar-Reduction.pdf
    File:
    Rotation-Matrices.pdf
       
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