All of the planets in the TRAPPIST-1 system are all orbiting very closely and are somewhat large. Would it be possible for at least one of the planets to have a stable moon in orbit around it? Or would the gravitational interactions between the seven planets and the TRAPPIST system's star make it too unstable for any moons? Would it be possible for any planets orbiting red dwarfs closely to have moons?

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    $\begingroup$ Wikipedia has a rather good section on this; have you seen it? $\endgroup$ – HDE 226868 Jan 13 '18 at 14:53
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    $\begingroup$ @HDE226868 that's a good recommendation, (references are this and ArXiv). The inner Roche limit applies to a body held together by self gravitation, and so formation certainly is no likely below it. But would that limit apply to a small, previously formed solid rocky body that somehow ended up there? (leftover from some hypothetical breakup, collision, capture) I can ask this separately if it warrants more than a comment $\endgroup$ – uhoh Jan 14 '18 at 9:38

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