# NavList:

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

**Re: Basic celestial naviagtion using a scientific calculator**

**From:**John Karl

**Date:**2010 Aug 14, 18:52 -0700

Gary,

You remind me of another reason why I like the book "CN in the GPS Age".

The azimuth angle A calculated with your equation, sin A = cos d sin LHA/cos H, requires the arc-sine which has two solutions for A between 0 and 180, leading to a complicated ambiguity.

But the above book uses Cos A = (sin d - sin L sin H)/(cos L cos H), employing arc-cosine for A which has a unique solution for A between 0 and 180. Then the rule to get Zn from A is simple:

if LHA is greater than 180, Zn = A

If LHA is less than 180, Zn = 360 - A.

Since the LHA is known exactly, there is no ambiguity -- just simplicity.

It's true that the cosine equation is a bit more complicated than the sine equation, but since d, L , and H are stored in the three calculator memories, punching in two more trig functions is an excellent trade off for avoiding ambiguity (and for keeping the discussion simple for beginners). Also this lack of ambiguity is even more valuable for higher level programming.

BTW, it's useful to distinguish between the azimuth and called "Z" in tables, and the azimuth angle called "A" used in the above equations. These are different angles as explained in the above book.

--JK

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