# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: A ramble on "new improved methods"**

**From:**Frank Reed

**Date:**2020 Jun 30, 14:35 -0700

You wrote:

"*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.

Frank Reed