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    Re: Sextant Positions versus Map Datums?
    From: Lu Abel
    Date: 2002 Jan 19, 2:17 PM

    At 10:06 AM 1/18/2002 -0800, Hal Mueller wrote:
    
    >[Meeus] goes on (p. 83) to give a formula for the difference between
    >geocentric latitude (assuming a spherical earth) and geographic
    >latitude (using the local vertical; what is plotted on charts).  It
    >reaches a maximum of 11'32" at 45 degrees latitude.
    
    Wow, that's counter-intuitive!  I would have expected the difference
    between geocentric latitude and the geographic latitude (I assume this is
    the same as Bowditch's definition of astronomic latitude, ie, the angle
    between a plumb line through a point and the plane of the equator) would be
    greatest at the poles and the equator.
    
    For those who are completely lost:  although it may at first be
    counter-intuitive, the "radius" of an ellipse is greatest across its
    thinnest part (across the poles in the earth's case) and smallest across
    its widest part (around the equator).  The extreme case is an ellipse so
    flat it's almost a straight line.  A plumb line perpendicular to the
    surface of this ellipse starting from a point 60 nm from the pole would
    intersect the equatorial plane almost 60 nm from the axis.  Alternatively,
    a line drawn from the center of this ellipse through the point would be
    substantially off perpendicular at the point.  Similar arguments can be
    made for points near the equator.  I'd therefore assume the region near
    45deg would be of "average" radius and perpendiculars to points in that
    region would intersect the center of the ellipse.
    
    Any insight into why my reasoning is completely opposite the truth is
    welcome...
    
    Lu Abel
    

       
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