Didn’t want to hijack the Jupiter-as-star thread.
In a double-star system, would it be possible for a planet to orbit the stars in a stable figure-8 orbit, rather than an elliptical orbit around both stars? What would it take, during system formation, for such an orbit to be established?
I suspect that, while it’s possible, it’s extremely unlikely. If you envision your system in terms of gravity wells, then you can easily see that, if your planet has sufficient energy to not orbit one star or the other, most stable orbits are going to be big elliptical orbits around both stars, with figure 8 orbits only possible in a narrow range of energies. they’d be easily perturbed out of that figure-eight state – if they had the right energy and velocity to be there in the first place – by just about anything besides those two stars and the object itself.
In othger words, I think it’s unlikely to be the orbit that develops – although, given a pair of stars with a lot of “solar system” matter, some objects should fall into that orbit – but that it would be very easy to be perturbed out of the orbit, so that items orbiting that way will likely not be, af5ter a while. And that it’s less likely to drop out of such an orbit that to drop into it.
Such an orbit is possible, but would not be stable under any circumstances.
You can imagine a gravity well as similar to a dip in a flat table. (say, a parabolic depression) An orbit is something rolling in a circle or an ellipse in that depression. Sort of like those coin donation things where the coin rolls in a circle for quite a while before it reaches the bottom (damn friction!!).
So could you imagine a double-dip setup where the marble or whatever rolls in turn through one dip then the other? Maybe; I’m not a math major. But… the other problem is the mother stars are not standing still. This isn’t a figure 8 around 2 staionary masses; they too are circling their common center of gravity; and to make matters worse, most likely an elliptical orbit to some degree so their location varies too; this makes the distance these two masses are from the eight-ball planet and each other quite erratic. Plus, odds are very likely one is a significantly larger mass than teh other, thereby also messing up the calculations.
I suspect the planet is less likely to do a figure 8 than to perform odd erratic maneuvers where as it reaches max distance one way, it is captured by the other and thrown in a different toally random direction.
Remember - an orbit is either elliptical (less than escape velocity) or hyperbolic (greater) or in rare circumstances, parabolic (exactly escape velocity). When the upper end of an elliptical orbit intrudes into the next star’s sphere of influnce, it now has to determine it’s trajectory around that star. Sooner or later these random pertrubations will result in either being thrown clear or hitting the star.
It was a bit of trivia mentioned by Isaac Asimov, I think, and used in one of his earliest stories; the stable L3 or trojan point (60 degrees ahead or behind an orbiting body) is only stable to a certain point - IIRC when the mass of the orbiting body is a significant fraction of the central mass, like 10% or something, L3 stops being stable.
Saturn’s braided F ring is freakier than a figure-8, so it’s possible, I guess.
An earlier thread on the subject (with a link or two and some helpful discussion)