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Was wondering about Shell Theorem, specifically about the immediate results.

  • Force (on a point mass) inside a shell is 0.
  • Force (on a point mass) outside a shell is GmM/r^2

From what i know the force from a similar scenario but with a solid sphere (outisde) is the same right? What is the result of the Force inside for a solid sphere? Still 0?

thanks

Jesse
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1 Answers1

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Suppose you have a solid sphere of mass $M$ and radius $R$ and a smaller mass $m$ at a distance $r<R$ from the centre.

Note that a solid sphere is equal to a smaller solid sphere of radius $r$ plus an outer shell:

enter image description here

The force from the outer shell is zero, and the force from the inner sphere is $$ Gm\left(M\frac{r^3}{R^3}\right) \frac{1}{r^2}$$

lemon
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