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Frank wrote:

>  Learning spherical trigonometry abstracted from its navigational context is not that useful.

I agree: one can practice cel nav without any knowledge of spherical trigonometry, just using tables
or computer programs.

But the question itself suggests that the purpose is not purely utilitarian 
but rather intellectual curiosity.
By far best book on spherical trigonometry that I know is

William Chauvenet, A treatise on plane and spherical geometry, Philadelphia, 1887.

Available online:  https://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABN6229

> 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).

There are few other formulas used in navigation:

For the azimuth sin(A)=sec(h)cos(declinatin)sin(hour angle)

And an alternative formula for the altitude:

sin^2(z/2)=sin^2(((lat-decl)/2)+cos(lat)cos(decl)sin^2(t/2),

where z is the zenith distance and t is the hour angle.
And the alternative formula for the azimuth sin(A)=cos(decl)sin(t)cosec(z).

Also spherical trigonometry gives you understanding of many other formulas used in navigation,
like the formulas for the lunar distances method.

Alex.

   

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