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Suppose there was a ternary system where the stars are effectively identical in mass, luminosity, radius, etc. These three stars circle a central point rather than two orbiting a larger third. At this central point is a planet.

My questions:

  1. Can this setup occur naturally (for example, a rogue planet is pulled into the center and held there by the combined gravity of the stars)?
  2. Is this setup stable from the perspective of the stars (for example, will one be consumed by the others)?
  3. Is this setup stable from the perspective of the planet (for example, the tidal forces of the stars balance out to leave the planet wracked, but whole)?
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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

  • $\begingroup$ Mass is the only important factor in maintaining the rosette. $\endgroup$ – Jim2B May 31 '15 at 1:25
  • $\begingroup$ @Jim2B Hm. Point. My question was originally going to go further than the three I posed. I may ask the other parts later. $\endgroup$ – Frostfyre May 31 '15 at 1:29
  • $\begingroup$ If you put a highly redundant active control system in there, you could still make it work... $\endgroup$ – Jim2B May 31 '15 at 1:38
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    $\begingroup$ Read this question on Physics.SE for a bit of the physics involved. In short, it would not be a stable system. $\endgroup$ – dotancohen May 31 '15 at 11:40
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What you describe is known as a Klemplerer Rosette. The configuration can be any regular polygon (triangle, square, pentagon, hexagon, etc.).

enter image description here

The star positions can be made statically stable by orbiting them around their common center of gravity. The problem is that the configuration is dynamically unstable - meaning if anything juggles the positions, the bodies will not return to their proper places.

Answers

  1. The configuration is unstable and will not occur naturally.
  2. No, it is unstable and the stars will eventually collide or wander off.
  3. No.

But if actively managed with a powerful method of moving stars around, a super science civilization could maintain the configuration.

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  • $\begingroup$ Beat me to it. Nice. $\endgroup$ – HDE 226868 May 30 '15 at 23:47
  • $\begingroup$ Haha, we probably both read Niven's books :) $\endgroup$ – Jim2B May 30 '15 at 23:48
  • $\begingroup$ I actually haven't gotten around to reading them. I really should. $\endgroup$ – HDE 226868 May 30 '15 at 23:48
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    $\begingroup$ Very fun books. I highly recommend them. $\endgroup$ – Jim2B May 30 '15 at 23:48
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Jim2B beat me to the best answer, but there are more solutions.

Analyzing a system like this is called the three-body problem, a case of the n-body problem. There are not many stable solutions to it, which kind of stinks for anyone wanting more exotic setups, like you. In most cases, it's best if two bodies are much more massive than the third. There are, however, exceptions.

Exotic solutions have been found (some recent ones are here; the paper is here), and these could be what you want. But they're awfully complicated.

Simpler solutions are given here. Trojan asteroids participate in such a system, but their mass is much less than that of Jupiter, let along the Sun. A non-trivial, very interesting one is the figure eight, in which three bodies of approximately equal mass travel in a shared orbit in the shape of a lemniscate.

Here's a gif, just for the fun of it:

enter image description here

You could have a planet that orbits in a straight line perpendicular to the plane, with a modified period such that it would not collide with any of the stars. That type of planet has been mentioned once before on Worldbuilding, though I can't recall its name.

This would be unlikely to form in nature, just as a Klemperer rosette would be unlikely to form.

The answers:

  1. Not really.
  2. Well, none will be "consumed by the others" unless there is a collision, but a small perturbation could throw the system off.
  3. I have no idea, though I'd wager not. It sounds like I have a new summer project, though.
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  • $\begingroup$ Very nice answer! IIRC the magic ratio is 9:1. For it to remain stable, Body 2 < .11 Body 1 & Body 3 < .11 Body 2. You can do lots with Lagrange points if you maintain the magic ratios. $\endgroup$ – Jim2B May 31 '15 at 0:06
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    $\begingroup$ From the answers, it looks like there's no natural solution to the problem of a planet being orbited by stars (which I suspected), which is too bad. Anyway, I thought this might draw you in. You've always provided great answers to planetary questions. $\endgroup$ – Frostfyre May 31 '15 at 0:12
  • $\begingroup$ @Frostfyre I've had to take a break from Worldbuilding in order to focus on other sites just getting into beta and outside things. I'm glad you like my answers. I can't resist these questions. $\endgroup$ – HDE 226868 May 31 '15 at 0:13
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    $\begingroup$ There's an outside? $\endgroup$ – Frostfyre May 31 '15 at 0:15
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    $\begingroup$ "That type of planet has been mentioned once before on Worldbuilding, though I can't recall its name." You might be thinking of my Sitnikov-planets answer although that was a simpler setup. If the dynamics are the same though, this would imply that the orbit of the planet is generally chaotic, so you couldn't really ensure that it never brushes one of the stars. $\endgroup$ – Martin Ender May 31 '15 at 14:55
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Perhaps one of the more exotic but still possible outcomes would be something like this, where if you imagine the earth is a star (a small one) and the sun is a star (a larger one), and 3753 Cruithne is the planet in orbital resonance with the smaller star. This might, (just maybe) have a survivable and mostly stable orbit where the 2 stars - certainly the smaller star would have odd movement. The seasons would be entertaining.

http://en.wikipedia.org/wiki/3753_Cruithne

enter image description here

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