Habitable planet at L4/L5 of binary gas giants?

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Malapine
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Would it be plausible to have two gas giants orbiting each other, a few million km apart, with a terrestrial planet at their mutual L4 or L5 point so that they both appear as visible disks fixed in the sky? Or would the terrestrial planet not be stable there and end up ejected?
 
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The two giants would have to have a mass ratio above approximately 25 (i.e. one of the giants has to be 25 times more massive than the other) for their L4 and L5 points to be stable (for a particle there).
 
Vanadium 50 said:
A possibly better question is "for how long"? A year? Easy. A hundred billion? Not so easy. In between is, well, in between.
And for a "Habitable planet" you probably need billions.
 
IIRC, even in 'halo' orbit around those nominally stable 'points', the unfortunate planet is not safe. Rather than perturbation causing ejection, it is more likely to become an impactor...

Which, IMHO, would be something to watch. By comparison, the SL_9 fragments' was almost trivial.
( FWIW, when I wondered if Jupiter's Great Red Spot was spawned by a mega-impact, it went badly... )

Ahead or behind at 'trojan' points of the two giants' combined mass-centre, your planet may stay around for a lot longer. Long enough for life to evolve beyond single-cells ??? I doubt it...