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I was wondering about a planet who orbits two stars. Could it be that it moves as in the image?

Planet orbit with stars

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    $\begingroup$ I think this is a duplicate of a Physics SE question : Might a planet perform figure-8 orbits around two stars?. $\endgroup$ – StephenG Oct 13 '17 at 17:34
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    $\begingroup$ As mentioned in an answer & comment on the Physics.SE question linked by StephenG, there's a stable figure-8 orbit found by Cris Moore. That configuration is stable to small perturbations of position or velocity, but it is rather sensitive to perturbations of mass: the 3 bodies must have almost identical mass. So you can't do it with 2 stars & a planet. You can read a paper (coauthored by Cris) about the stability of such orbits here: arxiv.org/abs/math/0511219 $\endgroup$ – PM 2Ring Aug 15 '20 at 13:58
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While such orbits can be proven to exist mathematically, they are unstable, and so no real planet has such an orbit. Such an orbit is analogous to balancing a pencil on its point. Mathematically there is a point of balance, but it is still impossible to do.

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  • $\begingroup$ I wonder if such an orbit could develop at all and if so for how long it would be able to exist in a pseudo stable form ? $\endgroup$ – StephenG Oct 13 '17 at 18:59
  • $\begingroup$ Might not be all that different than a horse-shoe orbit, which can be stable for a few hundred orbits. (kinda guessing though). $\endgroup$ – userLTK Oct 14 '17 at 3:24
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    $\begingroup$ remember that the two stars are also orbiting. No this kind of orbit highly unstable, unlike horseshoe orbits. $\endgroup$ – James K Oct 14 '17 at 6:18
  • $\begingroup$ almost always unstable $\endgroup$ – uhoh Aug 16 '20 at 22:24
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In this hypothetical theoretical situation, if the two stars are of the same size (they have the same mass) then the orbit of a planet passing through the center of mass of the two stars could traverse both binary stars as an 8 because the center of mass is an unstable point in which the attractive forces of the two stars are equal. If, for example, the planet has orbited the star S1, the inertia of the planet that adds to the force of attraction of the star S2 may also intervene in the center of mass and the planet may fall into the sphere of attraction of the star S2,following an orbit around it. Then the cycle resumes. In addition, if the planet's orbit is elliptical, in the center of mass of the two binary stars could intervene in addition to the force of inertia and the effect of gravitational slingshot.

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