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I recently learned about circumbinary planets ("recently" as in a few minutes ago) and I saw that there are cases in which a planet can orbit around one star, yet its orbit is close enough to the other star in the system that it is unstable, at risk of crashing into one of the stars or being yote out of the system altogether by intersecting gravity wells. This got me thinking: what if instead, the planet reached a sort of equilibrium with the two stars?

Here's what I'm imagining: two main sequence G-class stars of roughly equal mass orbit around eachother. However, right inbetween these two stars, there is a terrestrial planet roughly the size of Earth "held in place" relative to the two stars. Each star's gravity is pulling on the planet with basically equal strength (not enough difference to matter in the cosmic scheme of things), and the result is that the planet would orbit around neither star, instead trapped in the same place between the two stars. Would such a system be possible? And if so, in what scenario would such a setup come about?

Bonus question (only answer if you feel like it): Two stars at equal distance from the planet would surely heat it up more than one star would. If these two stars were the same mass as the sun, how many AU would they have to orbit away from eachother for the center of their orbits (where the planet is) to form a goldilocks zone where water would be liquid?

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    $\begingroup$ There is no such thing as not enough difference to matter in the cosmic scheme of things. In the cosmic scheme of things any difference is important because any little difference will only be amplified in time. In addition, even if the two forces are exquisitely balanced, any tiny little perturbation will result in the planet leaving its cosy position. Long story short, an unstable equilibrium is unstable. $\endgroup$
    – AlexP
    Commented Nov 25 at 0:53
  • $\begingroup$ see also: Three Body Problem Specifically "the Restricted three-body problem" $\endgroup$
    – JonSG
    Commented Nov 26 at 15:13

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Possible, but unstable

You're talking about having the planet be at the L1 Lagrange point of the binary star system. However L1 is unstable - any perturbations will over time amplify. In order to remain long-term at L1, you will need some active station keeping mechanism (straightforward for ships; rather less so for planets, but certainly within the scope of science fiction.)

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