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I'm going to keep it simple, so I can maybe get an answer. Can you have two habitable terrestrial sized moons of a gas giant or brown dwarf in a stable horseshoe orbit (50+ million years) that is also eccentric (eccentricity of maybe .2-.4)? If so, what is the limit of how eccentric the orbits can be, and if not, why not? If so, does this effect the formation of other things like rings or additional moons and how so? As a side note, it doesn't matter how the system came to be for what I'm wanting, just so long as it can feasibly stay stable for the allotted period.

I have already reviewed the closest post to this here (Two planets in a stable horseshoe orbit?), and was not able to extrapolate a satisfactory answer. Because of the nature of how the questions here were proposed, no one answered the more general questions, and tailored their answers specifically to the defined perameters of the asker. The person who got the most up votes even assumed a near zero eccentricity without explaining or answering the question because it was buried in a wall of text. Also, the most viable answer to that question was limited by the habitable zone of a star, whereas the only limits of my system is the outer limit of a satellite orbiting the much less massive body of a large gas giant or brown dwarf (the hill sphere).

A video here (https://youtu.be/Evq7n2cCTlg) explains a lot of the horseshoe orbit, and conceptualizes what I want, but it says that the eccentricity must be low at one point, but it doesn't explain why.

LanceLercher
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  • I tried to delete my original question, so hopefully this one meets the criteria better. – LanceLercher Oct 16 '17 at 16:37
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    If you want to know why I'm asking this question, it is so that I can quantify having a higher spin orbit resonance than 1:1 (tidal lock) in this type of system similar to mercury with its 3:2 resonance. – LanceLercher Oct 16 '17 at 16:40
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    You do realise that a horseshoe orbit is in fact an optical illusion depending entirely on your point-of-view? – Ash Oct 16 '17 at 16:48
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    Do note that these earth-like moons that I am proposing will not have satellites of their own. And yes, I am fully aware of the actual mechanics of a horseshoe orbit in that the moons don't actually orbit in horseshoes, but rather appear to be in relation to their primary. – LanceLercher Oct 16 '17 at 16:58
  • @Ash I read into that post, and the post itself was very specific to the asker's questions and circumstances, and people didn't address the general nature of orbit eccentricity, and rather tried to run with numbers close to that proposed by the asker, and whether their scenario was viable. I'm just asking if eccentric orbits in general are possible with horseshoe orbits, and if so what are the limiters, and if not, why. – LanceLercher Oct 16 '17 at 18:51
  • Can someone please explain to my why this is a duplicate? I've combed over the other post multiple times, and although the same question is asked buried deep in the post, not a single person addresses it in the answers because the post itself had so many questions to answer from. – LanceLercher Oct 16 '17 at 20:16
  • This is probably being marked as a duplicate because your question was essentially answered there: that question's best answer basically says that you can't get a stable horseshoe orbit with two planets around a star, as one will slingshot the other out of that orbital path. Your extension to an eccentric orbit (which was in fact done as the other question's third case) is thus irrelevant. – Palarran Oct 16 '17 at 20:53
  • @Palarran My question doesn't involve a sun, but rather terrestrial sized moons around a massive gas giant. Beyond that, the circumstances you're implying insist that horseshoe orbits in general don't work because they would fling each other out, however this isn't true because Janus and Epimetheus of Saturn have such a relationship. The main difference for my post is that I'm not limiting the orbital distance from my primary by having to stay in the "habitable zone" of a star. – LanceLercher Oct 16 '17 at 23:25
  • Comments aren't the place for discussions. I'll simply point out how that answer stated that the Janus/Epimetheus scenario had a mass difference between the moons and the planet of about 10^9, whereas anything the size of a planet orbiting a gas giant will not reach those proportions (orbiting a sun resulted in a gap of about 10^6, or 1000 times larger relatively, and gas giants are far smaller than suns) and that this was probably the reason why the horseshoe orbit was impossible. How does that answer not apply to your question? – Palarran Oct 17 '17 at 01:53
  • @Palarran I understand comments aren't the place for discussion, I'm just trying to establish a basis that my post is not a duplicate to yours. You are basing my question on an answer that is tailored to your question. My question posits the relationship with less regard to orbital distance than yours doesYours is framed around mass of the primary vs it's satellites, and although this does play a significant role in the answer to both our questions, mine might allow more varied orbit distances. Also, I was not able to find an answer that definitely said how much mass matters, just speculation. – LanceLercher Oct 17 '17 at 03:48
  • @LanceLercher Have you looked at the second answer to the duplicate? The resources there will give you the answer to your question. "Duplicate" doesn't mean it's the same question it means the resources provided by an existing question's answers will give you what you need. – Ash Oct 17 '17 at 09:46

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