Three of Jupiter's moons (Io, Europa and Ganymede) are in a 1:2:4 Laplace resonance. Are there other possible resonances for a set of planets or moons, such as 1:3:9 or 1:4:16 that are stable?


The Wikipedia article you linked contains several other examples, both in our own Solar system, e.g. 18:22:33 for some of Pluto's moons, as for exoplanets. There are all kinds of ratios to be found (among two, three or even more bodies); instability is often caused (as far as I know) by a massive mass difference, not because of some 'unlucky' ratio. There's no reason to assume there's no 1:3:9 or 1:4:16 out there. The article also explains why there are so many:

Simulations have shown that during planetary system formation, the appearance of resonant chains of planetary embryos is favored by the presence of the primordial gas disc.

Technically, one could say that Laplace ratios are always 1:2:4, but I assume that's not what you mean:

A Laplace resonance is a three-body resonance with a 1:2:4 orbital period ratio (equivalent to a 4:2:1 ratio of orbits).


Three-body resonances involving other simple integer ratios have been termed "Laplace-like" or "Laplace-type".

  • $\begingroup$ Thanks! I threw the wikipedia link in late at night, not realising it mostly answered my question. $\endgroup$
    – Ingolifs
    Aug 18 at 20:37

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