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Would it be possible for two planets orbiting around each other to share a moon that orbits both separately? Would the moon in question would do something akin to a large figure 8 as it orbited both or would this be possible in the first place?

Also, what effects might we see on the planets because of this?

(Side note: This stems from a Worldbuilding question, but I figured I would ask the astronomy question on the Astronomy StackExchange)

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    $\begingroup$ A figure-8 orbit is possible, but it's only stable if the 3 bodies have almost identical masses. See tuvalu.santafe.edu/~moore/gallery.html and the linked articles there for details. $\endgroup$ – PM 2Ring Jul 25 '17 at 22:52
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    $\begingroup$ Despite the comment above saying it's possible, it's really not, not long term. 3 body systems are chaotic. Objects can orbit a single object or more distantly orbit a binary system - like Pluto/Charon's moons. But a figure 8 orbit, while it can be worked out mathematically to almost work if conditions are just right, it's really not possible for any lasting period of time. $\endgroup$ – userLTK Jul 26 '17 at 3:05
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    $\begingroup$ Also keep in mind you're really dealing with at least a four body system when you add a star for the planets to orbit. That's going to increase instability of the moon's orbit as would any other bodies in the system. $\endgroup$ – StephenG Jul 26 '17 at 7:27

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