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A rigid ring or sphere surrounding a single massive body will not be stable, but in the “restricted 3-body problem” where the ring/sphere is infinitesimally light, and one massive body is orbiting another, there can be some stable configurations.

For example, if the lighter of the two bodies is less than 1/9 the mass of the heavier one, a rigid sphere enclosing the lighter body can be stable.

H/T Shubhendu Trivedi

https://academic.oup.com/mnras/article/537/2/1249/7989465