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What is the connection between Newton's Shell Theorem and Bertrand's Theorem?
The most general force that can fulfil the first part of Newton's Shell theorem (any spherically symmetric body affects external bodies as if its mass were concentrated at its centre) is an inverse ...
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The converse of Newton's shell theorem
The shell theorem states that a spherically symmetric body $S$ of mass $m$ has a gravitational field identical to that of a point particle $P$ of mass $m$ located at the center of $S$.
We can ask the ...