Re: Question on the medium gravitational force through a body
From: Uncle Al (UncleAl0_at_hate.spam.net)
Date: 12/22/04
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Date: Wed, 22 Dec 2004 11:55:38 +0000 (UTC)
Markus wrote:
>
> Perhaps an absolutely trivial exercise, but for some reason I don't
> come up with this simple problem when I have to prove it analytically.
>
> Immagine a an extended (regular or irregular) body immersed in a
> gravitational force field (not necessarily that produced by a
> pointmass, but more generally of any kind). I have to show that the
> medium gravitational force exerted on the body turns out to be the
> same force we find at its center of mass. That's quite intuitive, but
> I have no certainty, and I read that somewhere those people working
> with tidal forces have shown this. "It has been shown", they tell, but
> then don't furnish any reference, and I couldn't find any.
>
> Has somebody a reference or a link that proves this? Otherwise can
> someone outline briefly the proof?
One imagines summing the gravitational interaction with each point
within the extended mass will give you an overall total identical to
the classical expectation that (less tidal forces) all the mass could
have been cocentrated at the center of mass to give identical results.
Sounds like job for Green's function.
-- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf
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