Shell theorem

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In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular application to astronomy. Isaac Newton proved the shell theorem and stated that: A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell. A corollary is that inside a solid sphere of constant density, the gravitational force within the object varies linearly with distance from the center, becoming zero by symmetry at the center of mass. This can be seen as follows: take a point within such a sphere, at a distance r {\displaystyle r} from the center of the sphere. Then you can ignore all of...

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