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From: George Huxtable (no email)
Date: Sun Aug 17 2003 - 08:37:27 EDT
George Istok wrote->
Mr. Huxtable,
>
>Though I am now in agreement with you, I came to that position by a slightly
>different argument (that may or may not be valid).
I'm delighted that we now agree, though I fear that George Istok's argument
is indeed invalid, even though it gives what I believe to be correct
answer!
To digress slightly beforehand, when discussing gravity, one has to
distinguish carefully between upper-case G, and lower-case g, which by
convention mean very different things. G is the Universal Constant of
Gravitation, defining the force between any two masses at a distance apart,
and takes the same value anywhere in the Universe (or so our observations
indicate). On the other hand, g is the acceleration due to gravity, a local
matter that defines the force on a certain mass, caused by the pull of the
Earth with all its irregularities, and varying with position and height or
depth. It's an unfortunate choice of symbols which causes much confusion.
Where George refers to changes in G, I think we should take it that he
really means changes in g.
George goes on to say-
>I assumed a completely
>isolated sphere of a light matter covered with water, a distance from the
>center of the sphere to the surface of the water, a value (G) for the
>gravitational attraction at the surface of the water, and that the surface
>of the water at any point must always be at a distance from the center of
>the sphere such that the value of G is constant.
And there's the problem. The water surface (or a spirit-level) adjusts
itself so that it's everywhere at a right-angle to the local direction of
gravity, but that does NOT imply that over the sea surface the value of g
is constant. There's no reason why it should be. Indeed, in an earlier
mailing, I pointed out that g varied (at sea-level) between 978 and 983 cm
per square second, between the equator and the poles. So, the basic
assumption being wrong, that argument fails.
He goes on to say-
>I do not claim that the argument above is whole or that it is valid, but it
>did convince me that there will be a mound over an anomaly where the
>attraction is stronger and a dip where it is weaker. Your argument is much
>simpler and even more convincing.
Thank you. We are in accord. Sorry I didn't get it right first time round;
it would hace saved some trouble.
George Huxtable.
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