Title says it all but I would also like to know if we could use earths gravity to keep it stable like saturns rings? (I'm trying to research other possibilities for getting to space without using brute force or space elevator)
closed as unclear what you're asking by Erik, Xandar The Zenon, The Anathema, Frostfyre, fi12 Mar 23 '16 at 20:45
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No, a Niven ring is inherently unstable regardless of the mass of the body in the center.
Any perturbation that makes the gravitational body off center will cause a stronger gravitational attraction between the closer part of the ringworld and the body at the center. As the ring gets more off-center, the force on the close portion increases (while the far portion decreases) until the ring inevitably collides with the central body.
On the other hand, rings (like the rings around Saturn) are not rigid. Each particle of rock or dust orbits independently of the others and will be subject to normal orbital dynamics. There is no instability because the rings are not rigid.
Interestingly, a rigid Dyson sphere is gravitationally stable. This is because the gravitational force is in three dimensions rather than the (basically) two dimensions of a ring.
I'd propose, if you're looking to make a stable ringworld-type object, going with a variation of a Dyson Swarm - something I'd like to call a 'Niven Swarm'. A series of habitats orbiting a planet / star independently. You could then connect them to one another via a flexible conduit, so each would be in an independent and stable orbit, but the occupants of the 'ringworld' could travel between segments. I believe this would give you a stable ringworld that doesn't require unobtanium or some other material with a unrealistic tensile strength. In fact, there isn't really anything that would prevent us from building this today with our level of technology beyond the massive amount of material needed in orbit, and each segment could be occupied and used before the full 'ringworld' was complete.
On the other hand, if you have the technology to build a ringworld, you also have the technology to make adjustments and cancel out any perturbations.