There is no net gravity in a hollow sphere. You can get this result using calculus but that's not really understanding it. There must be some special property of the hollow sphere which is unlike most, or all, other objects, because most or all other objects do not have zero net gravity in their interiors. Is there any other object which has no net gravity in its interior? Or even in regions of its interior? I was thinking about the intuitive reason and you can think of it like this: in the middle of the sphere there is clearly no net gravity. If you move towards one side of the sphere then that side pulls on you more strongly and the other side pulls on you more weakly, but also the side you move towards gets smaller. This can be understood in terms of the circle on the sphere's surface formed by the intersection of the sphere surface and the plane perpendicular to the sphere's radius at your location. All of the sphere's surface in front of this circle pulls you forward, and all of the sphere's surface behind this circle pulls you back, and as you move forward the surface in front of the circle shrinks and the surface behind the circle increases. So you have two influences as you move to the edge--the increasing closeness tends to pull you towards the edge of the sphere and the changing mass ratio tends to pull you back towards the middle. What is still not intuitive to me is why these must cancel each other exactly. Any ideas?