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    Re: Interesting challenge
    From: Peter Hakel
    Date: 2012 Aug 5, 19:08 -0700
    Lu,

    This page from my website:

    http://www.navigation-spreadsheets.com/lops.html

    refers to three methods relevant to your friend's question.  Here are the references:

    1a. lops.xls: (3-D flat geometry)
    James A. Van Allen, An Analytical Solution Of The Two Star Sight Problem Of Celestial Navigation, Navigation 28 (1), (1981).

    1b. two_body_fix.xls: (2-D spherical geometry)
    John Karl, Celestial Navigation in the GPS Age, pp. 78-79

    2. many_body_fix.xls: (a least-squares-based technique with the intercept method under the hood)
    Nautical Almanac, 2010 Commercial Edition, pp. 282-283

    Methods 1a and 1b are equivalent.  Usually they yield two distinct mathematical solutions.  No "assumed position" is needed in either case.

    Method 2 gives one location.  Assumed position is one of the inputs.  Two, three, or more sights can be entered on input.


    Peter Hakel


    From: Lu Abel <luabel@ymail.com>
    To: Navigation <NavList@fer3.com>
    Sent: Sunday, August 5, 2012 11:41 AM
    Subject: [NavList] Interesting challenge

    When celestial navigators draw a LOP, it's usually by the altitude-intercept method, ie, "here's where I think I am, but where would I have to be to see get this Ho?"

    A friend asked me the following:   "If I know my [great circle] distance from three points on earth, can I determine my location?"   Of course one can.   But beyond getting a globe and using dividers or a string to draw arcs of the proper distance on it, is there a mathematical/paper-and-pencil way of determining latitude and longitude?   I guess the celnav equivalent would be determining location from three sights (or each of the two possible positions from two sights) with no assumed position.

    Lu


       
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