A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Geoffrey Kolbe
Date: 2020 May 12, 02:55 -0700
What's with all this iteration...?
I presented equations for finding LAT and LONG from the measured altitude Ho and measured azimuth Zo of a celestial body back in 2008 at the Mystic navigation conference when I gave a talk about navigating with a theodolite... I am shocked nobody remembers!
In this case, we have Ho = 54° 56', Zo = 120° 28' . The DEC for the sun was 16° 46.9' and the GHA was 45° 51'
Let MA = Sin-1(Sin Zo · Cos Ho / Cos DEC) = 31° 09'
Since Zo is < 180, LHA = 360 - MA = 328° 51', from which we get a longitude of 77° West in the usual way
We can find the latitude from:
LAT = Sin-1[(Sin Ho·Sin DEC - Cos Ho·Cos DEC·Cos MA·Cos Zo)/(1 - (Cos DEC·Sin MA)2)] = 39° North