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    The elegant 2 body fix
    From: Peter Fogg
    Date: 2005 Jun 5, 00:52 +1000

    > From: Fred Hebard
    > Without knowing GMT, one could not determine longitude from an altitude
    > of the Sun when it is due East or West.  I also wonder how much the
    > altitude of the sun varies with azimuth at various locations when it is
    > due East or West; it's azimuth can only be measured to perhaps 0.1
    > degrees, how much would that limit the precision of the measurement?
    
    The difference between 'modern' position finding techniques and those that
    perforce preceded them is that now we assume knowledge of the correct time
    as the necessary starting point.
    
    Its true that a noon sight relies little on precise time as the body
    obligingly hangs in the sky with little altitude change over a few minutes.
    Its a different story with a longitude sight. No hanging about, yet the
    sight must be calculated using the precise moment when the body (usually the
    sun) is due east or west. This presents practical problems. How to ensure
    that the moment of 'now!' is the desired one?
    
    LINEAR REGRESSION IN REVERSE
    The moment is calculated using the DR (assumed position, and the accuracy is
    dependent on this). Then as many sights as possible are made over about five
    minutes, a few minutes on either side of the desired moment. These are then
    plotted on a simple graph; time on one axis, altitude on the other. The
    slope of apparent rise or fall is compared with the pattern of sights to
    find the same slope that best fits this pattern. Then the desired moment is
    used to intersect with the slope to indicate the altitude to be used for
    sight reduction. The azimuth is then 90 or 270 degrees, the LOP runs due
    north/south, thus a line of longitude.
    
    At the risk of belabouring my earlier point:
    
    Good is good, VERY BAD is something else entirely that sounds deliciously
    naughty, and perfection, alas, eludes us all.
    
    
    

       
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