4 ms·
I don't think that's true. An object would be attracted to the inner surface of the sphere because that's where the mass actually is. The shape you're describin
by xenadu02 10y ago
I don't think that's true. An object would be attracted to the inner surface of the sphere because that's where the mass actually is. The shape you're describing doesn't have a center of mass the way we traditionally think of it.
- Florin_Andrei 10y agoIt's absolutely true, and it's known as the shell theorem. It's an old result actually. https://en.wikipedia.org/wiki/Shell_theorem https://en.wikipedia.org/wiki/Shell_theorem
- acchow 10y agoAn object inside the hollow sphere would in fact be attracted to each individual mass-ful particle on the surface of the hollow sphere. But (assuming uniform density on the sphere) the net effect is 0 (it feels no gravitational attraction whatsoever). The best way to prove this is to compute the gravitational force between your object and any arbitrary particle on the surface, then do the integration over all the particles (across the 3 dimensions).
- maverick_iceman 10y agoThe best way is to use symmetry. Ask yourself, which way would the net force be directed?
- acchow 10y agoI don't find this satisfactory - someone could just answer with "towards the center of the sphere", as if the center were some equilibrium.
- maverick_iceman 10y agoAt the center of a uniform hollow sphere the force will be precisely 0.
- pdonis 10y agoNot just at the center; everywhere inside it.
- maverick_iceman 10y agoOf course, Gauss's law. :)
- SticksAndBreaks 10y agoEvery pyhsics problem with a uniform sphere reaches the escape velocity necessary to escape the complex calculus problem well.