NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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.