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It’s my understanding that most 3-body orbits are unstable; minor random perturbations will set them adrift.

Are there any 3-body orbits with a natural resonance that maintains the shape of the orbits?

If so, how large of a disturbance can the most-stable 3-body orbit withstand?

A few that I looked at are annotated, "It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble." Doesn't define "small nudge", alas...

further research indicates some do exist:

- equilateral triangle is the simple case

- some figure eight configurations

- some configurations that act like two nested binary systems

there might be others. fascinating stuff.

One interesting scenario is where the Sun, Jupiter, and another object are the three bodies in question. I think we could put an object at the L4 or L5 point of Jupiter's orbit (see the Trojans) and have it be stable. How large could this object be? Would an Earth-sized object be stable there? If so, how close would a passing star have to be to disturb that stability?

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