A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Hanno Ix
Date: 2015 Feb 23, 22:40 -0800
Hello Paul Bedel, Antoine Couette, and All of you,
I had a number of contacts with Georges Bodenez, when and after I have published my own method (Planar Vertices method, 1995).
I appreciated very much every dicussion I had with him. I did again a number of his original examples.
Often he said himself that the basis of the 3D methods have been set by Antoine Yvon-Villarceau in his famous book on 1877: "Nouvelle navigation astronomique : théorie et pratique". "New" means using chronometers but no longer Lunar Distances. This book -which is a classical one- gives a lot of justifications for Marcq Saint-Hilaire method but, in a preliminary part, Villarceau set a very clever formulation of the 3D problem. See my enclosed slide, from a conference given at Maritime Museum, in Paris.
I give hereafter some translation of the original text (1877!) :
"... so that the 2 first equations formulate 2 planes and the last equation formulates the (Earth) sphere itself. Then the solution is given by the intersection of 1 straight line and 1 sphere. But for practical reasons, we do not recommend to use these formulas, because of the length of the implied computations. We present a less DIRECT solution, but quicker to implement". Obviously, " less DIRECT" was LOP intersection method...
You can realise that, if you add a 3rd equation to the 2 first equations, you get a linear system: this has been the essential complement brought by Georges Bodenez in the seventies (one century later, indeed!).
I know that a lot of people were working about the same subject elsewhere, noticeably in the move of first receiver design for GPS (to begin with Ivan Getting team).
Notice that Villarceau has a street to his name in Paris, but Marcq Saint-Hilaire has not...
By the way, Villarceau has been a rival of Le Verrier, inside Paris Observatory.
(AAMM-14_Villarceau_yrj1.pdf: Open and save or View online)