A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Jun 30, 14:35 -0700
"The formula for h is easy to remember and if I make the effort I could probably remember the formula for t."
Yes. Same thing!
sin(Alt) = sin(Lat) sin(Dec) + cos(Lat) cos(Dec) cos(HA).
Or turn it around:
cos(HA) = [sin(Alt) - sin(Lat) sin(Dec)] / [cos(Lat) cos(Dec)].
Or with fewer keystrokes:
cos(HA) = sin(Alt) / cos(Lat) / cos(Dec) - tan(Lat) tan(Dec).
I prefer ZD instead of Alt, primarily for pedagogic reasons. From a conceptual point of view, zenith distance is the key to celestial navigation. It's an easy change in the math: replace sin(Alt) with cos(ZD) because Alt is co-ZD and v.v.
I use this as the basis for "Modern Celestial Navigation" calculations with an "ABC" setup:
A = cos(ZD / cos(Lat) / cos(Dec)
B = tan(Lat) tan(Dec)
C = A - B
HA = acos(C)
and finally of course
Lon = GHA +/- HA.