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update: The BBC News article Citizen science bags five-planet haul announces the system K2-138, also described as a "resonant chain" of planets. However, see the actual paper in ArXiv and Ast. J. where the title calls it only a "near-resonant chain" instead; The K2-138 System: A Near-Resonant Chain of Five Sub-Neptune Planets Discovered by Citizen Scientists

The Phys.org news item Discovery of new planet reveals distant solar system to rival our own outlines the recent announcement of results using AI to help search Kepler photometric (transit-method) data for exoplanets. Near the end is the paragraph:

Kepler-90i wasn't the only jewel this neural network sifted out. In the Kepler-80 system, they found a sixth planet. This one, the Earth-size Kepler-80g, and four of its neighboring planets form what is called a "resonant chain," where the planets are locked by their mutual gravity in a rhythmic orbital dance. The result is an extremely stable system, similar to the seven planets in the TRAPPIST-1 system, so precisely balanced that the length of Kepler-80g's year could be predicted with mathematics.

My question is about these "resonant-chains" of planets. If I understand correctly this would be a group of planets where due to mutual perturbative effects they are in orbits who's periods are in mutual rational number ratios, e.g. 3:2 or 7:9.

Is it known yet how long-lived (time domain) or narrow (frequency) domain these resonances are, or are likely to be? In other words, are they thought to be really "locked" into these fixed ratios for say tens or even hundreds of millions of orbits, or are the orbits just really close, but with occasional, irregular "slippage" events?

Since the span of data and its precision is limited, I would expect that one can not conclude from the data alone, and it's likely some modeling has been done on resonant-chains of planets to improve the understanding of the phenomenon, so I'm asking to understand what's known and believed, rather than a precise answer about a given system. Since the problem is mostly orbital mechanics it lends itself more easily to simulation than most problems.

As background, Wikipedia addresses "locked" orbital resonances:

Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. (emphasis added)

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  • $\begingroup$ I am not an expert, so this is not an answer and may be totally wrong. From what I understand, orbiting objects "gravitate" toward the more stable orbital resonances and do it more quickly the more elliptical the orbits are. I believe they also trend toward more circular orbits. Collisions (which don't necessarily imply "impacts") upset these stable situations for a while. Therefore I am thinking that systems with planets not in resonant periods are working their way there, some faster than others. I believe our system is one of these. Also, not an answer since I don't have definitive sources. $\endgroup$ – Jack R. Woods Dec 18 '17 at 19:11
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    $\begingroup$ I'm also not an expert, but I think with red-dwarf systems with closer planets, resonance is more likely because the planets have greater influence on each other, similar to Jupiter's large inner moons have on each other. In solar-systems like ours, the planets are mostly pretty far apart. $\endgroup$ – userLTK Jan 14 '18 at 9:50
  • $\begingroup$ @userLTK that certainly makes sense. I'm really after how narrow the resonances are thought to be; either via measurements or simulations. How likely is it that these known planetary systems are actually locked into rational fraction ratios as the Jovian satellites, or just near-resonant, where they might occasionally "skip a beat" so to speak. $\endgroup$ – uhoh Jan 14 '18 at 11:11

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