# A planet ringed by stars

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)?
• Mass is the only important factor in maintaining the rosette. May 31, 2015 at 1:25
• @Jim2B Hm. Point. My question was originally going to go further than the three I posed. I may ask the other parts later. May 31, 2015 at 1:29
• If you put a highly redundant active control system in there, you could still make it work... May 31, 2015 at 1:38
• Read this question on Physics.SE for a bit of the physics involved. In short, it would not be a stable system. May 31, 2015 at 11:40

What you describe is known as a Klemplerer Rosette. The configuration can be any regular polygon (triangle, square, pentagon, hexagon, etc.).

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.

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.

• Beat me to it. Nice. May 30, 2015 at 23:47
• Haha, we probably both read Niven's books :) May 30, 2015 at 23:48
• I actually haven't gotten around to reading them. I really should. May 30, 2015 at 23:48
• Very fun books. I highly recommend them. May 30, 2015 at 23:48

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:

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.