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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Spherical earth model vs. ellipsoid
From: Lu Abel
Date: 1999 Mar 13, 10:43 AM

```As my mother used to say, "you're in the right church, but sitting in the
wrong pew."

Latitude and longitude are defined as angles with respect to the earth's
center.  But Mike is definitely right that our horizon will not be
perfectly perpendicular to the line of L/Lo eminating from the earth's
center.  I would correct his diagram by labelling the line perpendicular to
the local horizon "altitude" and not "latitude."

Let's clearly understand that with celestial observations, we're trying to
use observations made at the earth's surface and almanac data to deduce our
L/Lo.  But L/Lo have to be defined with respect to the earth's center, or
else how do we end up with the situation where one may move slightly more
or slightly less than a nautical mile when one makes a one minute change in
latitude near the equator or north pole?

When I made my earlier comment on this thread, I did recognize that the
oblateness of the earth causes the local horizon to be not precisely
perpendicular to a line drawn from the center of the earth, but I chose not
to cloud a discussion of whether elipsoidal models affect celestial fixes
with that relatively minor point.

Unfortunately, my trig and calculus are sufficiently rusty that I can't
dash off an estimate of the error induced by the earth's oblateness.
Anybody??

Lu Abel

At 02:03 PM 3/12/99 EST, Mike Wescott wrote:
>We have, I think, a misconception being promulgated in this thread, or
>at least some difficulty in the definitions in being used (or maybe
>it's just me).
>
>See the attached diagram.
>
>The measured or actual latitude is with reference to the vertical, as
>GRAVITY would have it. This corresponds to a line normal
>(perpendicular) to the plane of the horizon when at sea. This is the
>Latitude that we measure with a sextant or theodolite. The geocentric
>("spherical model" ?) latitude is not easily measured. As the diagram
>shows, if the Earth isn't a perfect sphere, the two do not coincide.
>
>But neither is the Earth a perfect ellipsoid. And the measured
>latitude will be affected by regional variations in the shape of the
>Earth and by regional variations in gravity.
>
>The standard ellipsoids are attempts to model the actual earth with a
>standard, smooth shape. Each standard ellipsoid is an attempt to
>specify an ellipsoid that will minimize some given set of discrepancies
>between the model and actual measurements. That minimization is either
>for the whole earth (i.e. WGS84 ellipsoid) or just for some region
>(e.g. the country standards).
>
>
>
>
>Attachment Converted: "c:\program files\eudora\attach\fig1.gif"
>	-Mike Wescott
>	 mike.wescott{at}ColumbiaSC.NCR.COM
>
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