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In my world-building project, a decades long orbital conflict has resulted in the trashing of Earth's orbit with massive amounts of debris, shipwrecks, and space junk. However, after an anomalous terraforming event, all this space junk magically consolidated into one large ring that circled the earth around the equator.

Is it possible to create a ring out of space debris that is visible from the surface? I am aware that the mass required to create a ring with the likes of Saturn would be practically unfeasible, and that the ring would likely prevent space exploration and result in space debris showers, but would such a ring be able to last for longer than, say, 100 years? Is there a way to calculate/derive how long such a ring may last until it is eventually destroyed by gravitational forces of both the moon and sun?

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Very Likely to Be Highly Unstable

The length of time that the ring stays in orbit would depend on a large amount of factors, for instance, the general type of space debris and the distance between the rings and the Earth, not to mention that the amount of space junk makes Kessler Syndrome very likely so the ring will be self destructive.

But beyond that, this paper on Saturn's seems to indicate that there's a threshold that the ratio of m/M needs to be under that is required for ring stabilization, where m is the average mass of the objects within the ring and M is the mass of the planet its orbiting. Saturn has a mass close to 2 magnitudes higher than Earth and the particles of its ring are mostly small crystals, which have a mass several magnitudes smaller than your average piece of space junk. Saturn's m/M ratio would be far, far smaller than Earth's in this scenario, so while Saturn can have it's rings, this space junk ring would be highly unstable and unlikely to last for any significant period of time. Admittedly, the paper does not indicate an upper limit of the ratio, but given the difference, it's a fair guess to say that the ring is unstable.

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