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    Re: Direct methods
    From: George Huxtable
    Date: 2007 Nov 3, 17:56 -0000

    Here's a rum thing. On 1 Nov  I posted a Navlist message "Re: [Navlist
    3728] Re: Direct methods." with a .rtf attachment. This attachment was
    exactly the same that I had sent on 12 June 06, in the days of Nav-l, and
    then it was successfully copied back to me as a .rtf file. No problems.
    
    But today I took a look at the same attachment, reflected back to me
    as Navlist 3731, from the message I sent on 1 Nov. It was still a .rtf
    file with the same name "intersecting circles.rtf". But now, it's badly
    corrupted, lots of spurious characters having been inserted, to make
    nonsense of the thing. If your copy is larded all over with "=" signs, where
    they clearly shouldn't be, as mine is, please don't try to make sense of it.
    You won't. The basic text of the email itself was unaffected; just the
    attachment.
    
    To check whether it was just a one-off glitch, I will send it again attached
    to this message; the text of my 1 Nov message is copied again below.
    
    ======================
    
    d walden's first posting with its attachment came over successfully to me.
    It may present problems to anyone that doesn't have Excel aboard as his
    spreadsheet.
    
    
    He wrote-
    
    |    It is of course possible, as has been pointed out, to calculate the
    latitude and longitude of the points of intersection of two circles of
    position directly with neither an estimated nor an assumed position.  Nor in
    fact are altitudes and intercepts or any plotting needed.  The intersection
    of cones method, described by Frank in the discussion of latitude by lunars,
    and shown in a previously posted FORTRAN and Maxima example can be used.  A
    few minor changes to the programs posted are needed.
    |
    |  The problem is, in fact, slightly easier.  It can be done with
    intersecting planes.  The attached little spread sheet is an example of how.
    One enters with the altitude, declination, and GHA of two bodies.  Out come
    the latitudes and longitudes of the two intersection points.  If you have
    three bodies, pick a different pair, and two of the points should wind up
    quite close.  There you are.
    |
    |  Seems to be working for me, but no guarantees.
    
    ===================
    
    For completeness, if nothing else, I resend an attachment which originally
    went out to the old Nav-L list on 12 June 06, under the threadname
    "positions from crossing two circles". That provided a routine, written in
    Bastard-Basic for a Casio pocket-calculator, to determine the two possible
    positions that result from crossing two observations. It also explains how
    the thing works.
    
    I remember that Andres followed it up with a posting in which he had
    converted it to a program written in C.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
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    File: 103754.intersecting-circles.rtf
       
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