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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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