NavList:

David Pike... Thanks for posting your written notes on this. Interesting. But let me back up...

It's two stars, and you have given us their altitudes. That's a two-star fix. And we know many, many ways to solve a two-star fix. Agreed? The only thing missing, as far as I can tell, is an estimated position at some known time such as I might use to pick an AP for a normal H.O. 249 fix. 

In actual marine navigation I would ALWAYS have an estimated position. By whatever means even a hundred years ago my estimated position would never be wrong by more than a degree at the outside. Your problem that you posted here is really a textbook story... An imaginary situation that I might get on an exam but not in real navigation. The only exception I can think of is a case like the photo Frank Reed posted that's similar, but that's the only case I can think of that wouldn't be a "trick question" on an exam. It's still not navigation, but it's similar.

Okay. Moving on! With the inputs you gave, my next step should be to get a crude estimated position from the altitudes as given. Then I can use that as an "AP". Then from there it's just another NO-FRILLS two-star fix. No tricky math. No spherical trigonometry (at least not directly). No Van Allen Belts needed either! Does anyone have a good way to get an initial position estimate? 

Josh