Habitable planet at L4/L5 of binary gas giants?

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The discussion centers on the feasibility of two gas giants orbiting each other with a terrestrial planet positioned at their L4 or L5 points. For stability at these points, the mass ratio of the gas giants must exceed 25, with one giant being significantly more massive than the other. While a terrestrial planet could remain stable at these points for short durations, such as a year, long-term stability over billions of years is highly questionable. Even in stable orbits, the planet may face risks from perturbations, leading to potential ejection or becoming an impactor. The stability of a planet at the L4 or L5 points is less reliable compared to positions ahead or behind the gas giants, which may allow for longer-term survival. However, the likelihood of life evolving on such a planet remains doubtful, particularly beyond single-celled organisms.
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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).
 
A possibly better question is "for how long"? A year? Easy. A hundred billion? Not so easy. In between is, well, in between.
 
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...
 
A map of a four-dimensional planet is three dimensional, so such can exist in our Universe. I made one and posted a video to the Internet. This is all based on William Kingdon Clifford's math from the 19th century. It works like this. A 4D planet has two perpendicular planes of rotation. The intersection of such a plane with the surface of the planet is a great circle. We can define latitude as the arctan( distance from one plane/distance from the other plane). The set of all points...

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