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    Re: Haversines with Logarithms
    From: Matthew Gianelloni
    Date: 2020 Oct 15, 03:31 -0700

    As promised: 

    Spherical Triangle Formula using only Haversines:

    hava = hav(b-c) +{[hav(b+c) - hav(b-c)]}havA

    A is Meridian Angle (LHA or 360°-LHA)

    a is Zenith Distance (90°-altitude, which is 90°-Ho)

    b is Polar Distance (90°-declination)

    c is CoLatitude (90°-latitude)

    Note: Meridian Angle is only the same as LHA if the target star, planet or Sun is WEST of your position. If the target is EAST of your position, 360° minus the Meridian Angle gives the LHA of the target.

    Transformation for solving for A (Meridian Angle) :

    hava - hav(b-c) = [hav(b+c)-hav(b-c)]havA

    then:

    [hava - hav(b-c)]/[hav(b+c)-hav(b-c)= havA

    Resulting Meridian Angle Formula:

    Same Name (dec and lat):

    havA=[hav(90°-Ho)]-hav[(90°-dec)-(90°-lat)]/[(hav(90°-dec)+(90°-lat)]-hav[(90°-dec)-(90°-lat)]

    Contrary Name (dec and lat):

    havA=[hav(90°-Ho)]-[(hav(90°-dec)+(90°-lat)]/[(90°-dec)-(90°-lat)]-[(hav(90°-dec)+(90°-lat)]

    So, with this, and logarithms, no more complicated math. LAZY.

       
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