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Imagine a planet with two moons that have an orbital pattern similar to that of Janus and Epimetheus of Saturn...

Is there a way for one of these moons to keep a stable pair of Trojan sub moons? I'm hoping to make this all happen within the habitable zone around a star, but not sure if it's possible.

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    $\begingroup$ I'm too lazy to do the maths on this, but Hill spheres being what they are, you're unlikely to be able to get a sub-moon much bigger than a potato (or altenatively the co-orbital body might be a hell of a long way away, or relatively small, or both, Cruithne style). $\endgroup$ – Starfish Prime Jul 9 at 14:18
  • $\begingroup$ Have you considered asking this over on physics.stackexchange.com ? $\endgroup$ – CaM Jul 9 at 16:10
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    $\begingroup$ Answering this question completely should be rather complicated. You should search for questions about the possibility of moons of moons. The short answer about moons of moons should be that they are possible under restricted conditions, thus making them rare. $\endgroup$ – M. A. Golding Jul 9 at 16:46
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That depends on what exactly you mean by "Trojan sub moons"

If you mean one of the co-orbital bodies has an additional smaller body trapped in each of its leading and trailing Trojan points with respect to the primary, then no. The other co-orbital body will make close passes by each of them twice during each orbit-swap cycle, making those points unstable.

If, however, you mean that you want one of the co-orbital bodies to itself have moons orbiting it, one of which is in a Trojan orbit with respect to the other, then it may be possible--but only on a very large scale. I.e., this might work with co-orbiting planets and a pair of very small, close-in moons--or planet-sized co-orbiting moons of a gas giant and a pair of still-very-small, close-in sub-moons. The co-orbiting bodies would need to have their orbits tuned to maximize their separation at closest approach during a swap, and the sub-moons would need to be well within to the Hill sphere of their primary during said closest approach.

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