NavList:

Geoffrey,

This initial problem has raised some definite attention since it exceeds 30 contributions in just 5 days to date.

Why ?

Most probably because the [vast] majority of us is [much] more familiar with maritime CelNav - where such problems most frequently never arise for lack of any solid azimuth reference - than with land-based CelNav specific environment.

Hence could it not be expected from Sea Navigators that getting to grips with this new problem might involve some imagination to tackle such unfamiliar land based environment, yes ?

Nonetheless, some of us - the good students - did already know how to directly solve this problem, including through the method you are mentioning and they readily published their own results.

One of us even knows about 5 different methods including 2 iterative ones. Isn't that great ?

Well ... having probably ignored about the existence of direct methods on my side, and then lacking any solid Reference Book, I came up with a different iterative method (which works !). Isn't that great also ?

Direct methods are preferable, no doubt about that.

I have meanwhile studied 3 different such direct methods - and there are probably more - all published over 100 years ago.

All three are 2 step methods :

(1) Two of them start solving for an Inverse Sine as their 1 st Step to solve for LHA, hence yiedling Observer's Longitude

And as regards their 2nd step to solve for Observer's Latitude :

(2.1) One first and more immediate method (no variable change) uses the Napier's formulae, and

(2.1) A second method, namely the one you are mentioning, is based on the cosine formula after a variable change,

(3) And a third method uses a different variable change based on a tangent formula. It solves for Latitude first, then for Longitude.

As a Happy End to this story, I rather see that such thrilling information exchanges once again keep showing that :

All Roads Lead to Rome

Is this not re-assuring ? :-)

Best Navigational Regards,

Antoine M. Couëtte