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    Re: Reeds versine formulas
    From: Frank Reed
    Date: 2021 Nov 12, 11:18 -0800

    For reference, here are the earlier messages of this thread, from April 2019. And by the way, the "Reed" referenced here is neither me nor any relative. :) 

    David McN, first, welcome, and thank you for commenting on this topic. :)  One small note: the formula you provided has a little typo. It's missing a wrapped versine. The left should be ver(ZD) or the right side should be inside a ver-1[... ]:
      ver(ZD) = cos(L) · cos(δ) · ver(HA) + ver(L - δ),
    with L for latitude and δ for declination. And I'm assuming that lat and dec have the usual modern, algebraic signs (N positive, S negative) which means we don't need a separate rule for the argument of the final versine on the right -- it's always L-δ.

    For anyone interested, it's not hard to show that this versine formula is identical to the familiar, standard "law of cosines" or "fundamental formula" expression for cos(ZD). To see it, replace every ver(x) by 1-cos(x) and use the standard trig identity for the cosine of a difference of angles: cos(a-b) = cos(a)·cos(b)+sin(a)·sin(b). It all drops out...

    Frank Reed

       
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