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I'm designing a moon system for a fictional setting, and recently came across the idea of horseshoe orbits.

The gist of my question is how many objects can share a horseshoe orbital at a time?

I need to have roughly a dozen Earthlike moons in orbit around a planet. Originally, I was thinking about having them spaced out on the same orbital, or just on different orbitals, but a horshoe setup would be near perfect for multiple reasons I won't get into.

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  • $\begingroup$ This is a worldbuilding question. $\endgroup$ – James K Apr 10 '18 at 10:22
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    $\begingroup$ @JamesK ultimately, it is, but the OP is asking for solid physics to justify a more realistic situation. $\endgroup$ – Carl Witthoft Apr 10 '18 at 15:41
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A horseshoe orbit requires a central body (eg a star) a large orbiting body (a planet) and a small co-orbiting body (an asteroid). If the asteroid has too much mass. The orbit "works" because the large body isn't affected by the small co-orbiting body much.

You have a central body (a planet) and multiple mid-sized co-orbiting and 12 mutually interacting bodies (moons). This isn't stable.

There are some special orbits like that of Janus and Epimetheus, which can be stable for a while. It may be possible to design orbits with more than two bodies in this form, but the region of stability would become very small, and subject to perturbation from the sun and other planets. 12 major co-orbiting bodies would not be a naturally occurring configuration.

A sufficiently large planet could have 12 large moons, providing they are on sufficiently different orbits.

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  • $\begingroup$ Thanks, James. What do you think about having the planet as the large orbiting body, instead of the central body? That's another idea I was playing with. It being sufficiently large would be a more plausible horseshoe setup, but could it have multiple smaller partners, instead of just one? $\endgroup$ – user49466 Apr 10 '18 at 11:53
  • $\begingroup$ I don't understand, but 12 large bodies on the same orbit isn't going to be stable $\endgroup$ – James K Apr 10 '18 at 12:35
  • $\begingroup$ If you were to (over at WorldBuilding) premise a clone of Ringworld Engineering, these moons could be actively stabilized. $\endgroup$ – Carl Witthoft Apr 10 '18 at 15:43
  • $\begingroup$ @James: To clarify, the original setup was a star, orbitted by a planet, which is, in turn orbitted by moons on a horseshoe around it. What I'm saying is would it be more feasible to have a star, which is orbitted by one large mass + other objects sharing a horshoe orbital with that large planet, rather than being it's satellites? Switch it from them as moons, to a series of planets on orbital with a giant. Usually the horseshoe orbit would only have two objects, but is that necessarily the case? Could it, instead be one large object with multiple smaller ones? $\endgroup$ – user49466 Apr 11 '18 at 1:11
  • $\begingroup$ 12 is not going to be naturally occuring, too many n-body interactions. A couple of trojans might be possible, but not 12 $\endgroup$ – James K Apr 11 '18 at 9:13
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Answering your comment, but it's very related to your question

To clarify, the original setup was a star, orbitted by a planet, which is, in turn orbitted by moons on a horseshoe around it. What I'm saying is would it be more feasible to have a star, which is orbitted by one large mass + other objects sharing a horshoe orbital with that large planet, rather than being it's satellites? Switch it from them as moons, to a series of planets on orbital with a giant. Usually the horseshoe orbit would only have two objects, but is that necessarily the case? Could it, instead be one large object with multiple smaller ones?

If you want a planet with a lot of moons, increase the planet's hill sphere. That can be done by increasing the planet's mass or moving the planet further away from it's star. If you need your planet to be in the Goldilocks zone, make the star bigger, just don't make the star too big because it's life will become too short for habitable planets to happen. If your star is over 2.5 or 3 solar masses it's life may be to short for the planets to form and moons to cool.

Even with a bigger hill sphere, A dozen is pushing it. Orbits need distance between them for long term stability and 12 probably too many. If you multiply each distance by 3/2 for resonance and even if you don't have resonance, that's a fair enough ballpark estimate, then the outermost moon is 130 times as far from the planet as the innermost and the innermost moon can't be too close to a large planet, or should undergo fairly rapid tidal forces drawing it inwards or outwards.

If you make some of them teeny and distant then 12 moons is easy. Jupiter has dozens of moons, but just 4 large ones.

Sharing orbits in a horseshoe (or Trojan) doesn't help you add moons because a horseshoe orbit would be perturbed by near-by large orbiting objects. In other words, you need to create extra space around two moons sharing an orbit, so you've not really increased the total number of stable orbits for large moons by putting two in a horseshoe. Now if you do large and tiny, you can have several tiny, but large and large and some measure of stability, two is the limit.

A horseshoe orbit is very similar to a Trojan orbit. If the two moons orbital periods are close enough, they get caught in each other's saddle points and never cross. If they're a little bit further apart from each other, then the catch-up moon can pass through the saddle point and the two moons can switch places (kinda-sorta), as they undergo the horseshoe dance.

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