I saw this video a while ago, and recently it's gotten me thinking. Towards the end of Artifexian's video on gas giants and habitable moons, he mentions the idea of having 2 habitable moons in a horseshoe orbit. An example of a horseshoe orbit would be Saturn's moons Janus and Epimetheus. Once every 4 years, they swap orbital altitudes.

There's already been a question about seasons would work in this setup, so I'm going a different route.

What kind of tidal forces would 2 habitable moons in a horseshoe orbit exert on each other? Could it hinder the habitability of either moon?

When I say habitable, I just mean the usual stuff. Water, Breathable air, and somewhat Earth-like gravity. If it helps in forming answers, these parameters can be pushed. Never said humans had to live here.

I was imaging one moon as a mostly Earth-like planet, and the other as a mostly water world if that helps with answering this question.

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    $\begingroup$ What do you mean by habitable? $\endgroup$
    – Raditz_35
    Oct 17, 2017 at 14:52
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    $\begingroup$ Once again, a lot of close votes and NO COMMENTS FOR THE OP to help understand what makes the question weak. I disagree that this quesiton should be closed. It's very specific and well within the bounds of mathematics to answer. Just because it's hard doesn't mean it should be closed. $\endgroup$
    – JBH
    Oct 18, 2017 at 0:27
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    $\begingroup$ I think your statement that the two moons swap places every orbital period is unclear/inaccurate. It will usually take many orbital periods for two bodies to "swap places". Janus and Epimetheus, the moons of Saturn that are our best example of a horseshoe orbit, go around Saturn almost twice a day, but go about 4 years between swaps. $\endgroup$
    – Luke
    Oct 18, 2017 at 19:17
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    $\begingroup$ @guildsbounty It's not all that complicated... it's just darn near impossible to solve in closed-form. It's fairly trivial with numerical methods. The bigger problem, however, is that the phase space is very chaotic-ish. Relatively minor adjustments in the relative sizes of the moons and primary, orbit spacing, eccentricity, and so on change the answer a lot. $\endgroup$ Oct 19, 2017 at 2:16
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    $\begingroup$ @LoganR.Kearsley Yeah, I actually worked out/derived all the equations to compute the precise functionality of the system and to verify that it would be at least reasonably stable....then discovered that plugging numbers into the equations to produce something like a generalized solution was the gateway to madness. And gave up. $\endgroup$ Oct 19, 2017 at 13:44

1 Answer 1


Earth experiences pretty significant tidal forces, and it doesn't seem to affect habitability too much. The crust flexes, the oceans rush in and out, and we're fine. Some life actually relies on it.

Io, a moon of Jupiter, experiences significant tidal flexing, enough to generate serious heat and geological activity. So, it seems entirely possible for tidal forces to be strong enough to effect habitability. Constant volcanoes filling the air with ash and toxic chemicals, serious earthquakes moving dirt around and preventing plants from taking hold.

So, you're question really boils down to "How strong are the tidal forces experienced by horseshoe moons?" Which is a very difficult question. The strength of tidal force is mostly based on distance, and it can be very difficult to predict how close these moons get to each-other.

To get extremely close together, they would have a large difference between the innermost and outermost radius of their orbits. They would approach each other at a higher velocity. They would swap quickly. They would repeat their swaps more often. (relatively, we're still looking at several orbits to complete the swap and several hundred orbits between swaps)

A horseshoe orbit that never gets very close is pretty much the same thing, but slower. The two moons are always close to the same distance from the planet. The swap places at a greater distance from each other. Since they interact with each other more weakly, the swap takes longer. It might be tens of thousands of orbits between swaps.

tldr; It can probably be whatever you want, but the details are hard.


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