A planet ringed by stars

Question

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)?

Answer 1

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.

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.

Answer 2

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.

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.

Answer 3

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