The figure 8 orbit is the only known stable orbital configuration for 3 bodies of equal mass. Are there islands of stability, analogous to Lagrange points for 2 orbiting bodies, that trace their way around the figure 8?
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2$\begingroup$ There are other stable orbits for three bodies, such as a central body and two planets, or a central body, a planet and a moon. $\endgroup$– James KCommented Apr 19 at 21:20
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1$\begingroup$ @JamesK edited, thanks $\endgroup$– user121330Commented Apr 20 at 2:34
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1$\begingroup$ Is the figure of 8 orbit stable? The paper linked doesn't claim that (just read the conclusion). It states that if some of the initial conditions are perturbed collectively in the right way it keeps the same configuration. But an orbit is only considered stable if all possible small perturbations keep the orbit closed. $\endgroup$– ScienceSnakeCommented Apr 20 at 10:33
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1$\begingroup$ @ScienceSnake it's a good point. I can hear the joke now CARSON: the figure-eight orbit is so stable... AUDIENCE: (in unison) How stable is it?" I think that in orbital there are several different flavors of stability; for example see the first paragraph of Wikipedia's Lyapunov stability $\endgroup$– uhohCommented Apr 20 at 15:44
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1$\begingroup$ @uhoh Yes, it's always more complicated... But stability always means something like being at the bottom of a potential valley such that the system is self restoring under any small perturbation (or, at least, not exponentially diverging). The paper cited (and my own limited understanding of 3-body dynamics) suggests that the figure-8 orbit is more like a saddle point, with a few directions in phase space 'curving up' and many more curving 'down'. Proving that that's not the case and it is in fact a stable 3-body solution would be a major result, I believe. $\endgroup$– ScienceSnakeCommented Apr 21 at 14:20
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