I've just finished a piece of college work on gravity in a hollow sphere and come to the conclusion... that there isn't any.

By way of explanation: the sphere is hollow (filled with a vacuum), has a thin (read: thickness=0) shell of mass M with radius and all the usual properties.

Anyway, I've come to the conclusion that a body inside the shell is subjected to zero external force. Which means if you hollow out, say, a planet and jump inside then, wherever you are - even next to the shell - you are not attracted to part of any side.

I posted because it's interesting that this goes against common intuition. I originally speculated that the body would accelerate towards a side of the shell.

I remember that Guv is quite into problems of this nature? If he's around could he comment how he'd go about this problem? I split the sphere into rings of mass m' and considered the force towards the centre of each ring and then went on from there.