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    Re: A ramble on "new improved methods"
    From: Frank Reed
    Date: 2020 Jun 30, 14:35 -0700

    You wrote:
    "The formula for h is easy to remember and if I make the effort I could probably remember the formula for t."

    Yes. Same thing!

       sin(Alt) = sin(Lat) sin(Dec) + cos(Lat) cos(Dec) cos(HA).

    Or turn it around:
       cos(HA) = [sin(Alt) - sin(Lat) sin(Dec)] / [cos(Lat) cos(Dec)].

    Or with fewer keystrokes:
       cos(HA) = sin(Alt) / cos(Lat) / cos(Dec) - tan(Lat) tan(Dec).

    I prefer ZD instead of Alt, primarily for pedagogic reasons. From a conceptual point of view, zenith distance is the key to celestial navigation. It's an easy change in the math: replace sin(Alt) with cos(ZD) because Alt is co-ZD and v.v.

    I use this as the basis for "Modern Celestial Navigation" calculations with an "ABC" setup:
       A = cos(ZD / cos(Lat) / cos(Dec)
       B = tan(Lat) tan(Dec)
       C = A - B
       HA = acos(C)
    and finally of course
       Lon = GHA +/- HA. 

    Frank Reed

       
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