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    Re: LOP's without DR (so-called "Douwes's problem")
    From: Yves Robin-Jouan
    Date: 2015 Feb 23, 02:42 -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.

    Yves Robin-Jouan




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