# NavList:

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

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Re: Pear shaped Earth
From: Herbert Prinz
Date: 2002 Oct 2, 23:59 +0000

```Hello Peter,

I am glad to see that I am not the only one who gets these terrible attacks. I never
go into the bath tub without a sheet of paper and a pencil for that reason.

Of course, you are right, and your reasoning is perfectly logical. Except that it
only applies to geocentric latitude. A degree of geocentric latitude measured on the
surface of the Earth is shorter at the poles (must be so, as the section of the
perimeter that is cut off by the rays from the center of the Earth is closer to the
center there than at the equator).

But never forget that you must forget geocentric latitude when going sailing!
Sailors always use geodetic latitude. This relates to the curvature of the Earth,
which  is, because of the bulge at the equator, smallest there and largest at the
pole. One degree on a large circle, is wider than one on a small circle. Hence,  a
mile (defined as 1' of arc) is shorter on the equator than on the pole.

A corollary to this is that geocentric latitude is always smaller than geocentric
latitude, absolutely anywhere, except for L= 0d or L=90d,  where both are identical.
The biggest difference between the two occurs near latitude 45d, where the geodetic
mile equals the geocentric one.

Herbert

Peter Fogg wrote:

> Woke up in the middle of the night, an attack of logic: if the earth bulges out
> at the equator and is flattened at the poles, then shouldn't a degree, expressed
> as nm, be longer at the equator and shorter at the pole?

```
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