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There are various questions about the stability of multiple moons, how they affect tides and so on, but I don't think this one has been covered here:

If my planet has two moons, assuming they have separate orbits, is there a "typical" equilibrium that they are likely to find? Does a moon of a particular size tend towards a certain distance or orbital period, or are these more or less arbitrary depending on other parameters of the system?

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  • $\begingroup$ The only reason I have not purchased the Universe Sandbox simulator is the lack of any video I could find showing a stable system with 2 moons. I conclude it is very difficult to model. $\endgroup$
    – Willk
    Sep 26, 2017 at 14:45
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    $\begingroup$ Note that some of the planets in the solar system have many moons (e.g. Jupiter, Saturn, Uranus, Neptune). I assume these are in stable orbits since they have been around for a long time and have not collided yet. However, the planet is large an each of the moons is relatively small compared to the planet. Pluto is worth a look too. $\endgroup$
    – Jonathan
    Sep 26, 2017 at 20:31
  • $\begingroup$ Interestingly, the background image of worldbuiding shows two moons in what must be a stable orbit (as there are creatures inhabiting this world, which must have taken a long time to evolve) $\endgroup$
    – Stijn de Witt
    Sep 26, 2017 at 22:10
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    $\begingroup$ There's not much difference between a planet and multiple moons vs. a star and multiple planets. The physics works just the same. $\endgroup$
    – RonJohn
    Sep 26, 2017 at 23:07
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    $\begingroup$ The answers should be making it clear that there is no 'standard' answer. If you have a specific setup for how you want for your moons, I can use a program called Rebound to check for stability for you. That is a valid question on this site that I have answered before (example, here). Post as a different question then tag this comment to alert me and I'll give it a run. $\endgroup$
    – kingledion
    Sep 27, 2017 at 1:22

3 Answers 3

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There is no standard behavior for the orbits of multiple moons.

You've uncovered a problem that has plagued physicists since the 1600s when Newton was beginning to describe gravitational mechanics. This problem called the 3-body problem or more generally the N-body problem. To quote Wikipedia the N-body problem is described as:

Given the quasi-steady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times.

This is easily solved in cases of two objects (a planet and 1 moon). For all other cases there is no easy way to predict the future movements of every object.

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    $\begingroup$ The n-body problem lacks a known algebraic solution. It can still be solved by numerical integration, much the way our current universe does it. $\endgroup$
    – user
    Sep 26, 2017 at 13:48
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    $\begingroup$ @MichaelKjörling I had to smile at "current" universe. Current as opposed to... the previous one? :) (I agree with the comment; I just found it amusing.) $\endgroup$
    – Ghotir
    Sep 26, 2017 at 14:19
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    $\begingroup$ @Ghotir What can I say, except quote Douglas Adams from The Hitchhiker's Guide to the Galaxy? "There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened." Well, that, and... "In the beginning was the Creation of the Universe. This has made a lot of people angry, and has been widely regarded as a bad move." $\endgroup$
    – user
    Sep 26, 2017 at 14:24
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The size of the moon, as a celestial body, doesn't matter much in the orbital equations, stable orbital distances are determined, almost entirely, by the speed of the orbit alone. The Jovian moons do suggest that there are certain Harmonics that tend to emerge in multiple moon systems but that's one example only we don't have hard and fast rules for such things. Looking at the mechanics of Lagrange Orbits might give you some insight into the relationships between moons that may naturally develop. Do bear in mind Roche Limits when putting together your numbers.

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  • $\begingroup$ So a fast close orbit or a slow distant orbit tend towards stability? Or vice versa? $\endgroup$
    – glenatron
    Sep 26, 2017 at 15:04
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    $\begingroup$ Assuming atmospheric drag is a non-issue, so above 200km for Earth, then slower orbits mean a greater distance from the body orbited, objects in Low Earth Orbit (up to 2000km altitude) have a maximum orbit time of approx. 130min, in Geostationary Orbit (roughly 35,800km altitude) it's by definition a 24 Hours orbit time. As I understand it objects in unstable orbits (that aren't subject to drag) will either gain or lose altitude until they are at the orbital radius that matches their velocity/orbital period (barring gravitational interference from another object). $\endgroup$
    – Ash
    Sep 26, 2017 at 15:18
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    $\begingroup$ There are exception to the above comment, but generally it works. $\endgroup$
    – Ash
    Sep 27, 2017 at 9:04
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If the moons are very small and don't have a significant gravity field of their own, they are basically independent, e.g. Mars' moons. If they are large enough to have a significant gravity field of their own, two moons or more will perturb each others orbits. This leads to one of the moons being ejected from the system. There are exceptions, such as some orbital resonances as mentioned by Ash, but those depend on the size of the host planet compared to the moons. If the planet is much larger than the moons, orbits can be stable, e.g. if they are in resonance (e.g. the Jovian moons). I think multiple large moons would require a stable resonance for the system to be stable, but I'm not sure about that.

If the planet is not much larger than the moons, for example as with the earth-moon system, a stable system becomes very difficult, and likely all but one of the moons will be ejected.

If moons are in resonance that means their orbital periods are simple ratios, e.g. 1/2 or 3/5. So that is an in some cases standardised behavior, but the absolute orbits can be anything, there is no standard behavior for that. Also, if a moon and a planet are very close together, strong tidal forces will result, which will over time lead to tidal locking: the bodies will rotate around their axes in the same time that it takes to orbit each other. Pluto and Charon are tidally locked like that. The moon is also tidally locked to earth, which is why we only see one side of it. The earth is much larger so this hasn't happened for earth.

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