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Gravitational force inside a "Pac-Man" shell
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I remember Newton's shell theorem, where inside a hollow sphere with uniform density the mass integration cancels out into a net zero force. One thing I've always wondered is: what would happen if we removed a section (let's say one fourth)?
If a small point mass was placed outside the opening, where would it settle into equilibrium once inside (if at all)? On the shell's interior opposite the missing section? At the center of gravity offset from what would otherwise be the sphere's center?
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