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    Re: A simple three-body fix puzzle
    From: Frank Reed
    Date: 2010 Dec 8, 22:23 -0800

    George Brandenburg, you wrote:
    "This is a simple case of a common problem in particle physics (my field) where you want to find the most probable "event vertex" when you have measured the tracks made by particles radiating from the event."

    Hmm! It's amazing where we find our analogies. I love that one!

    You wrote:
    "This turned out as Frank suggested to be a fairly messy algebraic undertaking"

    I was actually referring to something shorter. You've done a very thorough analysis from basic principles of this special case. Very nice, too! The general solution is available in a little section in the back of any modern Nautical Almanac. If you haven't acquired one yet, you can get used ones from a few years back for small change on ebay.

    Of course, any recent editions of the Nautical Almanac are protected under a (debatable) UK copyright so they are not available online --except when someone makes a mistake. There is a book on Google Books with an exciting title: "Youth and young adult conservation programs: oversight hearing before the Subcommittee on National Parks, Forests, and Public Lands of the Committee on Natural Resources, House of Representatives, One Hundred Third Congress (etc.)" And what do we find under that title? It's the official Nautical Almanac for 1994 (as Henry recently noted, sometimes things turn up in very strange places on Google Books). Does anyone know of any other modern, post-1958, Nautical Almanac available online? This is the first one I've found. Naturally the ephemeris data is widely available, but it's the other material that's nice to have for students to read over.

    There's plenty of interesting info in the explanatory section at the back of the modern Nautical Almanac. The general least squares solution for a bunch of LOPs is on page 282. Here's a direct link to that page:
    I'm also attaching the scan of the relevant paragraph. Note that in the last line, L and B with subscripts refer to longitude and latitude, but all we need here is the difference in these in miles which is given by (AE-BD)/G and (CD-BE)/G.


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