NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bill Lionheart
Date: 2024 Mar 16, 14:57 +0000
Re: Spherical Trig
From: Frank Reed
Date: 2024 Mar 16, 04:56 -0700Chris L., you asked:
"can you suggest a good book to self teach spherical trigonometry. I've taken plane trigonometry."I wouldn't recommend a book. Learning spherical trigonometry abstracted from its navigational context is not that useful. The only thing you need for almost everything is the spherical "law of cosines" (which also goes by other names). It's very little more than the great circle distance equation:
cos(dist) = sin(Lat1)·sin(Lat2) + cos(Lat1)·cos(Lat2)·cos(dLon).
You might imagine that it would be useful to know the derivation of this equation. I occasionally teach a derivation in classes when students insist, but I find there's almost no benefit. This equation "is what it is". You might be surprised how completely this one equation solves almost every problem that arises in celestial navigation!If you want more anyway, I can recommend the Wikipedia article on spherical trigonometry. It's extensive and detailed, and despite the reputation of some Wikipedia articles, this one is well-written and has no obvious flaws that I could find (with a cursory reading). It includes things like half-angle formulae and Napier's rules that have are important historically in navigation.
Frank Reed
