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    Re: Sun sights by 13 year-olds
    From: Charles Seitz
    Date: 2004 Sep 27, 10:28 -0400

    I was 13 years old 48 years ago but have always been intrigued with the
    mysteries of celestial navigation.  So I finally got on the web and
    searched for some pertinent links (including this list).  Surprise, it's
    very simple in concept.  A fix is obtained from the intersection of the
    circles of equal altitude obtained from sextant sightings to several
    heavenly bodies.
    
    Well it seems no one really does it that way because of plotting scale
    problems.  The solution requires a sight reduction procedure that
    refines a dead reckoning position.  OK, I can't argue against that time
    proven methodology.  With a computer, what's wrong with a direct
    calculation in the event that you don't have the 'foggiest' idea of
    where you are?
    
    Getting back to the intersection of circles of equal altitude, I had to
    convince myself of the validity of this concept with real world data.
    How accurate can a 'low tech' approach be?  Looking at the Dec and GHA
    table values to 0.1 minute precision (about 600 Ft) suggests nautical
    mile accuracy is possible if the sight timing and measuring process is
    under control.  That's not too bad.
    
    I found some useful equations for spherical earth calculations (Aviation
    Formulary by Ed Williams) and wrote a software program that calculates
    the locus of Lat-Lon points at 0.01 degree increments around the
    Geographical Position of a body.  I borrowed a plastic Davis sextant and
    took it on vacation to Myrtle Beach, SC.  On a clear morning, I trekked
    to the beach, checked sextant alignment per its instructions, measured a
    reference position with time by GPS and finally, took several sun sights
    timing them with an alarm chime from my watch.
    
    To my amazement, a point on a resulting equal altitude circle passes
    within 0.8 nm of the GPS position!  Close enough?
    
    Obviously, the next step would be to rewrite the software to accept data
    from additional sightings and calculate the circle intersections.
    That's easier said than done.  Many hours of web searching have failed
    to reveal any equations to do this.  I can't believe that during several
    thousand years of spherical geometry study, someone has not solved this
    problem.  It might be a horrendous problem but the solution is out there
    somewhere.  GPS is based on a similar concept.
    
    I'm not a mathematician and will not attempt to derive the equations.
    I'll look into solving this problem numerically.  But, that is a brute
    force approach that is not particularly satisfying from an aesthetic
    viewpoint.
    
    
                                                   ---  CHAS
    
    
    

       
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