Let's say that I have an imaginary planet with the same mass as earth, and it's completely smooth. No indentations, no obtrusions, nothing, just a large rocky ball. And now let's say around this planet, for some reason I build a huge ring around it, and once I finish building it, I remove the supports that hold it up. The ring is equidistant at every point from the planet at exactly 1 kilometer above the surface. What does the ring do, then? Collapse, remain stable, start to turn, or just stay still?

If you made it out of tissue paper, it probably collapses. There would be some compression force.

 

I think the ring is in an unstable equilibrium, so at the first perturbation, some point will be closer to the center and it will fall to the surface.

Just my guess...

 

I would think if it is truly equidistant, gravity being uniform, and all things perfect, without outside interference, then it should remain stable.

 

However, at the first slight movement, one part will get closer and you better run.

 

Bettina