In a binary star system, what stability arrangement involves the planet orbiting only one of the two stars?

Answer

The planet orbits the primary star while the second star orbits much further away

One recognized, albeit more precarious, mechanism for orbital stability in a binary star environment involves the planet maintaining a dedicated orbit around just one of the two stars, designated as the primary star. For this to remain stable over billions of years, the secondary star must remain at a considerably greater distance from this planetary path. The gravitational influence exerted by this distant second star must be sufficiently mild so that it does not induce destructive perturbations that would destabilize the planet's path around its primary star. This contrasts with the wider orbit where the planet circles both stars simultaneously.

In a binary star system, what stability arrangement involves the planet orbiting only one of the two stars?
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