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    Mathematical Advancement of a celestial COP
    From: Buck Godwin
    Date: 1998 Oct 23, 10:24 PM

    On Fri, 23 Oct 1998 14:39:07 -0700, you wrote:
    
    >
    >The COP from the earlier of the two observations must be advanced
    >along the DR course.  In terms of the center of the circle, I propose ...
    
    strange you should mention this just hours after i was reading an
    article in Navigation, The Journal of the Institute of Navigation.
    according to the article, the problem of obtaining a direct fix from 2
    observatinos with an advanced (or retired) COP has not been solved
    analytically.  in a nutshell, assuming the observer moves along a
    rhumb line,  you have to advance each point on the COP along a
    loxidromic spiral to its new locus.  the new loci no longer lie on a
    circle, so the algorithm is not strictly valid.  the 1997 article by
    Stanley W. Gery  references 4 other articles between 1977 and 1981 in
    the same publication on the same subject.
    
    as a practical suggestion, take a run of sights on body 1 and a run on
    body 2.  pick a time between the two runs.  extrapolate the first set
    forward and second set backward to the chosen time.
    
    
    Buck Godwin
    
    
    
    
    
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