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The Naval Observatory has an online calculator for sight reduction:

                     http://aa.usno.navy.mil/   (Data Services)

They specifically refer to geocentric altitude.

'Data are shown for the navigational stars and planets only if their
computed geocentric altitude, Hc, is equal to or greater than +1 degree at
the place and time specified. '

This, I assume means with respect to observations from a spherical earth.
But,
we all know the real earth is better  modeled as a geoid.  That means
observations
made with respect to the local horizon on the real earth will be slightly
different than
those made from a spherical earth.  It follows that circles of equal
altitude, the
basis of CN,  are not perfectly circular.

(I suspect observations of altitude would be nearly identical for both
reference systems at the poles, equator and near 45 deg lat.  At these
locations, the center of the earth will be directly under you)

Since there are numerous geodetic datams, your geographical position does
indeed depend on your assumed datum.  So, why wouldn't there also be
some inherent positional discrepancy between a geocentic and geoidal earth
model?

I suspect that sight reduction tables would be nearly impossible to prepare
if
all of the possible complications were considered.  We choose an earth shape
model that works best for a particular purpose.



                  --- CHAS

   

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