What is this quotient space of the torus?

There is a torus shaped ring around a planet which gradually condenses to a planar ring (cont)?

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There are two boundaries at work in planar ring systems. One, the outside edge of the rings, is the point where a large moon will break apart due to tidal forces and provide more debris for the rings. The second is the inside edge where the planet's atmosphere is thick enough to cause particles from the rings to slow down and de-orbit. Ring-rocks will fall out of the ring and into the planet at that point. Guess what? Saturn's ring system completely fills the space between these two boundaries. No ring system can move outside these boundaries. So C is the correct answer. So while any individual piece of ring rock is slowly jostling its way to the planet, the ring system itself can not move outside the two boundaries outlined above.

Owl Eye

Hello Frst Grader! Nice question. d, you should post in the physics section and get more responses, I guess. Anyhoo, if the "torus shaped ring gradually condenses to a planar ring", then it would flatten out, right? If it flattens out, then it, err, hmmm, well, I guess it would be stretched towards the planet, because of gravity, no?

Koshka

In an ideal Euclidean geometry, it would be C. In reality, it's A, for the reason phoenixshade said.

Alexis

that depends entirely upon the debris in question. If the debris is moving too fast, or the planet somehow loses mass, then the debris will slowly move out into space. If it is moving too slowly or the planet gains enough mass, the debris will move towards the planet. Often both cases occur in any ring, as bits of the stuff, due to collisions and the like, leave geostationary orbit above the planet and move either in or out.

Five Knot

a

Matt

stays in same spot

snea l

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