quote:
Just a few questions, let's say that all of the earth's mass was collected into 5 miles of crust so that on the surface, no change in vector or strength of gravity could be felt. If you dug down 5 miles and broke though, wouldn't you fall?
Yes, you would fall toward the point at the centre of the ring/sphere, and then oscillate around it.
But if you threw a ring onto a foam mattress and dropped a marble in the center, wouldn't it run towards the depression close to the ring?[/quote]
I would so yes and no, as Dormammu notes the anlogy can be pushed to far.
Yes the actual ring material is what is exerting gravity, and if you were very close to one side of the ring you would be attracted to that ring material gravitationally. But that attraction will be much smaller than the attraction exerted by the whole ring/sphere as if at its centre of mass. So you will still be attracted more toward the centre than toward the edge.
Where the analogy breaks down is that a ring exerts local pressure on a sheet that accords with the topology of a ring, while gravity always acts on the body as a whole and at a point of fulcrum at the centre of its mass/density distribution. The ring scenario should properly be imagined as making a dent in the rubber sheet that keeps sloping inward toward the centre of the ring, while having a lesser dent forming a shelf at the ring itself. At least, this is how I understand things.
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