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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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