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..the celestial sphere is a sphere by definition.  I don't see this as being 
any more or less true than treating the earth as being round.

We get away with calling it a sphere only because everything is so far away 
from us, that we can't perceive depth.  So it becomes a matter of how big is 
big enough to ignore the imperfections.

I'll argue that a 12nm error is no different in relevance at the center of a 
circle that has a radius over 3400nm than the width of a pencil mark on a 
plotting sheet.

Original Message:
-----------------
From- Herbert Prinz hprinz@ATTGLOBAL.NET
Date: Mon, 21 Jan 2002 16:18:12 +0000
To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
Subject: [NAV-L] On the Mischief of Geographical Position.


Nine out of ten popular books on celestial navigation define the
Geographical Position of a celestial body as  that point on the Earth�s
surface where the latter is intersected by a line from the body to the
center of the Earth. If this definition were correct, the body would not
be in the zenith of its Geographical Position on a non-spherical Earth.
The navigator would be in a worse situation than the proverbial man who
hunts his own shadow: the sub-stellar point of his zenith, i.e. his own
position, could be as far as 12 nm away from him.

To remedy this situation the author will (sometimes after admitting that
the Earth is in reality a spheroid) tacitly assume that the celestial
navigator uses a spherical Earth at any rate and will in particular
present the concept of latitude as if there were only geocentric
latitude. Hence the author has to make believe that it is the latter
that is related to the declination of the stars and therefore of
interest to the navigator.

Even the most reputable books such as Dutton�s engage in this kind of
deceptive oversimplification, leaving many readers wondering, why it all
works on an elliptical Earth. Indeed, it would not. But as we are, in
fact, knowingly or unknowingly, performing all sight reduction on the
CELESTIAL sphere, which is a sphere by definition, our sight reduction
methods based on spherical trigonometry are strictly rigorous. It is the
ZENITH that the navigator is attempting to locate in the celestial
sphere. Once that has been accomplished, he projects it down via the
local vertical, simply by renaming declination latitude, and GHA
longitude, and calls it his �position�. This works on an egg, a pear, a
lemon or an onion.

Herbert Prinz (from 1368950/-4603950/4182550 ECEF)

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