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    Re: Still on LOP's
    From: Bill Murdoch
    Date: 2002 May 6, 16:56 EDT
    In a message dated 5/4/02 6:24:07 PM Eastern Daylight Time, george{at}HUXTABLE.U-NET.COM writes:


    Bill Noyce made a perceptive contribution a few days ago, about systematic
    errors in celestial observations that can increase the probability of the
    true position lying within the cocked hat. This happens because those
    errors expand the cocked hats to surround the true position.


    I am not sure that is correct.  A three body fix using celestial navigation puts three small circles on the surface of the earth.  If all were perfect, the three would intercept at one point.  Because all is not perfect they intercept making a triangle.  Draw three circles intercepting to form a triangle in the middle.  If you are like me, you drew three circles of about the same size intercepting in a total of six places with a small triangle in the middle with all three sides bulging outward.  You pointed at the small triangle in the middle, the one with three convex sides, and said, "I am here."  That is true if all three LOPs are away from their bodies.  Surrounding that triangle are three more triangles with two convex sides and one convex side.  You would be in one of them if two of the LOPs were away and the third was toward.  To see the other two cases, you have to redraw the circles moving the centers around to l! eave triangles with either three concave sides or two concave sides and one convex side.

    If the usual systematic error is to tilt the sextant and record an erroneously large reading, the circles will be too large.  In some cases that will make the triangle larger.  In other cases it will make the triangle smaller.

    Bill Murdoch
       
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