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Cassis
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The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
This isn't difficult to do. A key ring is a circle of wire - have you ever noticed anything like infinite forces trying to take your keys put of your pocket?Cassis said:The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
The inverse square law applies to the exterior of spherically symmetrical sources.Cassis said:The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
Depending on the relative size and the orientation of the ring, the system could oscillate about the barycenter of the pair, or they would collide, to finally settle, looking like a miniature Saturn with one wire ring.Cassis said:What would happens if we put a marble and a wire into an empty space.
Hm. Larry Niven thought so too. He wrote an essay on it, then followed up with a novel. That is, until his fans (many of whom of whom are mathematicians) disagreed. Niven had to write an entire sequel to Ringworld just to ret-con the engineering.Baluncore said:Depending on the relative size and the orientation of the ring, the system could oscillate about the barycenter of the pair, or they would collide, to finally settle, looking like a miniature Saturn with one wire ring.
OK, but the OP did not specify a relative diameter, nor any nudge away from perfect stability.DaveC426913 said:A mass at the centre of a ring of mass is not stable. Given any nudge it will drift away from the centre until the centre and the ring touch.
Yes this is what unstable usually means. If you place the mass at rest inside the ring, off-center, in the plane of the ring, there should be no oscillation, just a crash into the inside of the ring.DaveC426913 said:Yeah, that was kind of what i was trying to point out. Unless I'm wrong, a ringed sphere is not only unstable, it is a positive feedback loop. Like a ball balancing on another ball. Even a miniscule deviation from exact centre is magnified and accelerated.