[rascalpenguin]

This is very true, and is the case with many 'laws'. Another example is with centre of masses: Take a hollow sphere, clearly the c.o.m. should be in the very middle, yet an object placed inside has not force whatsoever on it so it isn't attracted to the c.o.m. and the idea breaks down (NB objects outside are attracted predictably).

This is because this idea is purely a tool to make calculations of large groups of particles as easy as one, but it does break down occasionally.

[dahart]

Which law are you thinking of? There isn't a physical law I'm aware of that claims gravitational attraction toward a center of mass, you might be conflating several laws or thinking of an approximation rule that was never intended to cover one object inside or even near another.

Newton's law of gravitation is stated in terms of a particle to particle relationship.

Center of Mass is the balance point of an object, and objects will always rotate around their center of mass unless constrained, but this doesn't relate to gravity.

You can approximate gravity at a distance from any object by using the object's center of mass, but that approximation breaks down when you're close to it.

[xenadu02]

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]

It's absolutely true, and it's known as the shell theorem. It's an old result actually.

https://en.wikipedia.org/wiki/Shell_theorem

[acchow]

An 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]

The best way is to use symmetry. Ask yourself, which way would the net force be directed?

[acchow]

I 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]

At the center of a uniform hollow sphere the force will be precisely 0.

[SticksAndBreaks]

Every pyhsics problem with a uniform sphere reaches the escape velocity necessary to escape the complex calculus problem well.

[pdonis]

Not just at the center; everywhere inside it.

[maverick_iceman]

Of course, Gauss's law. :)