<p>The Wikipedia article you linked contains several other examples, both in <a href="https://en.wikipedia.org/wiki/Orbital_resonance#Laplace_resonance" rel="nofollow noreferrer">our own Solar system</a>, e.g. 18:22:33 for some of Pluto's moons, as for <a href="https://en.wikipedia.org/wiki/Orbital_resonance#Mean-motion_resonances_among_extrasolar_planets" rel="nofollow noreferrer">exoplanets</a>. 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 <em>why</em> there are so many:</p>
<blockquote>
<p>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.</p>
</blockquote>
<p><em>Technically</em>, one could say that Laplace ratios are always 1:2:4, but I assume that's not what you mean:</p>
<blockquote>
<p>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).</p>
<p>...</p>
<p>Three-body resonances involving other simple integer ratios have been termed &quot;Laplace-like&quot; or &quot;Laplace-type&quot;.</p>
</blockquote>

CC BY-SA 4.0
2021-08-18T20:37:20.033Z
Thanks! I threw the wikipedia link in late at night, not realising it mostly answered my question.
Ingolifs
CC BY-SA 4.0
2021-08-18T11:33:11.063Z
2021-08-18T11:33:11.063Z
Glorfindel
<p>Three of Jupiter's moons (Io, Europa and Ganymede) are in a 1:2:4 <a href="https://en.wikipedia.org/wiki/Orbital_resonance" rel="nofollow noreferrer">Laplace resonance.</a> Are there other possible resonances for a set of planets or moons, such as 1:3:9 or 1:4:16 that are stable?</p>

<orbital-resonance>
Are there other possible Laplace resonances? (e.g. 1:3:9)
Ingolifs
# Are there other possible Laplace resonances? (e.g. 1:3:9)

(Asked by: username_0 on 2021-08-18)

Three of Jupiter's moons (Io, Europa and Ganymede) are in a 1:2:4 [Laplace resonance.](https://en.wikipedia.org/wiki/Orbital_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?

**Tags:** orbital-resonance


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## 1 answers

### Answer by username_1 on 2021-08-18. Score: 3 | Accepted answer

The Wikipedia article you linked contains several other examples, both in [our own Solar system](https://en.wikipedia.org/wiki/Orbital_resonance#Laplace_resonance), e.g. 18:22:33 for some of Pluto's moons, as for [exoplanets](https://en.wikipedia.org/wiki/Orbital_resonance#Mean-motion_resonances_among_extrasolar_planets). 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".

> **Comments:**
> **username_0**: Thanks! I threw the wikipedia link in late at night, not realising it mostly answered my question.  

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