# Can a binary star optically "orbit" a planet?

I was watching a science fiction anime from the mid 70's. In it, there was a star orbiting a planet. Since this seemed impossible, and I had never heard of it, I looked on the internet to see if this could be possible in a very unlikely situation or in theory.

On a similar question on Quora, after many no, no, no, no answers from astronomers/astrophysicists, some of them with very detailed models and theories with different scenarios and equations, one answer read,

Absolutely.

If there were two stars of identical mass orbiting each other in equilibrium, then you could throw a planet of any size at the barycenter of the two stars. Then optically you'd have not just one, but two stars orbiting a planet. The planet would be equidistant from the two stars at all moments in time, and would experience identical gravitational pull in two diametrically opposite directions and hence never deviate from the barycenter. This system would not be in a stable equilibrium though, and a passing celestial object of any mass could disrupt this system. Hence, this is probably something that is unlikely to be observed.

Is this possible?

• I'm not an astrophysicist so I can't give you a proper answer with math, hence this as a comment. I'd bet that the answers you'd get here will be along the lines of "that is too unstable to last for any period of time. Even the slightest perturbation would eventually send the planet into one of the stars, or away from both of them". I bet you your quoted answer is from a pure math, ignore-unnecessary-variables point of view, not a this-can-really-happen point of view. Related, you'll find this article interesting: spaceplace.nasa.gov/barycenter/en
– Cody
Commented Jul 20, 2017 at 0:02
• Interesting question, as @Cody says the answer probably lies in some mathematical model of the 3 body problem as to how stable such an orbit would be.
– Dean
Commented Jul 20, 2017 at 12:13
• But as far as I know there are astrophysicts here, someone could answer that or it's too difficult? I honestly ask because I have no idea, it could be very easy to calculate or not since I dont have the knowledge I can't tell Commented Jul 20, 2017 at 12:16
• Cody is correct. You don't need to be an astrophysicist either. A basic understanding of orbits will tell you that 2 large bodies orbiting a 3rd smaller one isn't stable because the central body would slip out of place and there's no force keeping it in the center but once off center, there would be forces to toss it about. Like a pencil balancing on it's point in the wind. It's not stable. (if anyone wants to answer with pictures and saddle points, feel free), but that particular solution is clever, unrealistic and temporary. Commented Jul 20, 2017 at 12:47
• Not really, and the answer could probably range from 5 minutes to 100,000 years. There's too many unknowns and too many variables to say anything like that for certain. To use userLTK's analogy, you could stand a pencil precisely on it's point, but who's to say how long it will be until it falls? Can you account for all slight Earth tremors or slight gusts of wind? Besides, based on known formation processes, there's no natural way for a system like that to have ever formed. It'd have to be purposefully designed like that and who's going to do that? Commented Jul 20, 2017 at 15:09

Planets don't orbit stars. Stars don't orbit planets.

Whenever there are two bodies bound by gravity, they are both orbiting their common center of mass. For example, both the Earth and the Moon orbit their common center of mass - but that's pretty close to the center of the Earth actually, so it seems like the Moon orbits the Earth.

For a star to seem to orbit a planet, that would mean the planet is much heavier than the star. As far as we know, that's impossible. Their common center of mass would be much closer to the star, so it would seem like the planet is orbiting the star, as usual.

If you have two stars orbiting each other (actually, orbiting their common center of mass) very closely, then you could have a planet circling around both. If the planet is circling around too closely, its orbit would not be stable.

But if the planet's orbit is far enough from the pair of stars, the orbit could be stable a very long time. The minimum distance it at least 2x ... 4x the distance between stars, ideally much bigger. We have discovered such planets. Kepler-47c is a gas giant in the circumbinary habitable zone of the Kepler-47 system.

This wiki page has more details:

https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems

EDIT: If you have a closely-bound binary star, with a planet right in between them, in the barycenter of the two stars, that's not a stable system. Any slight perturbation would pull the planet out of there, and then the net force would be pulling it further out. It would eventually fall into one of the stars. It's not self-stabilizing.

I can't even imagine any conceivable mechanism that would put the planet in there to begin with.

• yes, that's why I added the quotations marks to the word orbit when I made the question. But you get the meaning. But I think you didnt answer if it's possible for a planet to be in the barycenter of the 2 stars. Commented Jul 20, 2017 at 18:57
• @Pablo - I see now what you mean. I've made an edit at the end of the answer. Commented Jul 20, 2017 at 19:14
• I'll leave the question open for a while. If no one comes with a mathematical explanation of how much slightly a perturbation force would have to be to thrown a planet out of there (which nobody conceives how could it have reached there) I'll accept your answer. Commented Jul 20, 2017 at 19:17
• Almost no math is needed. Planet is in barycenter: net force is zero. Planet is slightly out of barycenter (just random fluctuations would do that), net force is away from the barycenter, towards the closer star (because the star that's closer now exerts a greater force than the other star). That's the problem. The net force acting on the planet never points at the barycenter, it points away from it. So it never returns to equilibrium, but it runs away from it. The planet is like a bowling ball sitting on top of a round dome - eventually the slightest breeze will push it downhill. Commented Jul 20, 2017 at 19:25
• @FlorinAndrei of course math is needed! This is a three body dynamical problem. Your conclusion may be right but your explanation is not QED. You need to be careful using analogies of a simple potential surface running downhill. This famously fails when people try to explain why orbits near the triangular CR3BP Lagrange points L4 and L5 are stable even though the simplistically drawn potential energy surface is convex. The problem is that the pseudopotential in the rotating frame contains velocity dependent terms and some people set those to zero before plotting.
– uhoh
Commented Dec 14, 2017 at 11:16