if we were to build a ring five feet from the ground, encircling the earth at the equator....?

Question

which way would it fall? or would it just float there?

Answer 1

It would be unstable, in much the way that no arrangement of magnets can stabily levitate an object (wikipedia "Earnshaw's Theorem"), but not require much force to stabilize it, as in the force required would probably be only a small fraction of the weight of the ring . Of course, we're assumming perfection everywhere in this experiment, such as the ring is say 100% over level surface such as water, is stiff enough to support its own weight without flexing, blahblahblah.

It would tend to be unstable because gravity is inversely proportionalto the square of distance, so if one point on the ring moved slightly toward Earth, the slightly stronger gravity at that lower altitude, as well as the resulting slightly-weaker gravity on the opposite side of the planet will tend to draw it even more strongly to the ground. It's much like trying to balance one ball on top of another - if it's close to perfectly balanced, it takes practically no force to keep it there. But the further away from balance that it is, the more force required to restore it.

Answer 2

The ring would experience tidal forces and bend in an oval shape. In addition, gravity from the Earth would bend all of it inward. If you assume that the ring is sufficiently rigid such that it won't bend under these forces, then it would always crash into the dark side of the Earth. If we assume the Earth is always pulling it equally in all directions, the sun still pulls it and thus the people on the light side of the planet see it shift away.

Answer 3

Well, if you didn't take external forces (such as the sun and moon's gravity) into account, it would just float there.

Answer 4

In a perfect World, it would just float there (assuming it could support its own weight).

Doug