[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.