# NavList:

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

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Re: Plumb-line horizon vs. geocentric horizon
From: Trevor Kenchington
Date: 2005 Feb 10, 10:16 -0400

```Charles Seitz wrote:

> I must have a basic misunderstanding about how
> a plumb line (the suspended weight) works.
>
> My concept of gravity is that it is a force that orginates
> from the center of mass of a body. On earth, that place
> would be earth center regardless of the earth shape
> model.  If this is what happens, the plumb line should
> extend to earth center.

I can still vividly recall having that error corrected for me by a
physics teacher back in my high-school days! (Must have been an
impressive teacher.)

Assuming that gravity operates through the centre of mass is a
convenient approximation which works quite well when you are a long way
from the object in question (e.g. Earth orbiting the Sun). However,
gravity actually acts through each piece of mass -- each proton and
neutron in the nucleus of each atom, if you wish to think of it that
way. The effect of each proton or neutron drops off, of course, with the
square of distance. If you have a whole lot of heavy atoms close aboard
on one beam (as in a mountain) and a lack of them on the other beam (as
in deep ocean filled only with water), the summed effect of all the
gravitational attraction of all the atomic nuclei in the planet will be
a force in a direction slightly deflected from the perpendicular to the
near-ellipsoid shape of the Earth. (Hence Pierre's situation on Reunion.)

Then there is the difference between that perpendicular and a line from
your position to the centre of mass of the Earth, which has already been
explained on this thread.

Trevor Kenchington

--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

Science Serving the Fisheries

```
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