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## Main Question or Discussion Point

I was looking at some interesting resonant orbits in our solar system and was wondering if someone who knows a lot more about planetary orbits than I might be able to answer if a certain scenario would actually lead to stable orbits or not. The scenario I have in mind is four planets tightly packed around their primary so that the first, second, and fourth planets are in a 4:2:1 orbital resonance like Io, Europa, and Ganymede are. Then the third planet from the primary (probably smaller than the others) is placed in a slightly eccentric orbit (I'm thinking eccentricity between .15 and .2) between the second and fourth so that it is in a 3:2 orbital resonance with the fourth planet, and therefore a 3:4 orbital resonance with the second. This could put it in an orbit similar to how the Hilda family of asteroids are to Jupiter, so that whenever it approaches the orbit of the second planet or the fourth planet, the other planet is well ahead, behind, or on the far side of their orbit.

I know all the pieces are stable as we have real life examples, but put together I don't know what would happen. Over all, they would be in a 8:4:3:2 orbital resonance.

I know all the pieces are stable as we have real life examples, but put together I don't know what would happen. Over all, they would be in a 8:4:3:2 orbital resonance.