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Is it possible for a planet to orbit a binary star system in a figure of eight? And is it possible for such an orbit to be stable?
Ron Dippold
San Diego, California, US
In theory, it could happen – one of the very first solutions to the three-body problem was this scenario. But it is very unlikely to be stable over time. You need the stars to have near equal mass and the star system to have nothing else going on, like the presence of other planets. The problem comes when your planet crosses the X and goes from orbiting one star to orbiting the other. This is near the inner Lagrange point between the stars, where gravity between them cancels out – any tiny nudge here can just send your planet flying off because neither star has a good hold on it.
But we have seen stable planets in a binary star system. There are S-type, where the planet orbits only one of the stars, and P-type, where the planet is further out and orbits both of them. We just haven’t seen a figure of eight configuration because it wouldn’t last long.
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In theory, a figure-of-eight orbit in a binary star system could happen, but it is very unlikely to be stable over time
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Mel Earp
Macclesfield, Cheshire, UK
This is an example of the three-body problem. Unlike the two-body problem, for which an exact mathematical solution has been around since the 1600s, courtesy of Johannes Kepler, Isaac Newton and others, there is no known general exact solution. Even the restricted problem, with the planet assumed to be of negligible mass compared with the stars, is chaotic in the mathematical sense. There are, however, some families of very specific stable solutions, some quite complex and bizarre paths that almost certainly wouldn’t exist in reality. One of the simplest solutions is a figure of eight, but in this, all three bodies are of equal mass and are following each other around the path. There appears to be no exact solution that has been found for a body orbiting two others in a figure of eight.
There have been two observed planetary configurations in binary star systems: S-type, where a planet orbits just one of the binary pair, and P-type, where a planet orbits the barycentre (centre of mass) of the pair and outside both. There are simulations that show a planet in an S-type orbit around one of the binaries, which then flips at some point to an S-type orbit around the other binary and back again in a stable repetition. During the transition from one star to the other, it is possible that the planet follows part of a figure of eight but doesn’t complete it. This simulation has never been observed in a real binary system, because the timescales of the orbits are so long that we haven’t been watching long enough.
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