# Planetary orbits in a Binary Star system.

http://spaceflightnow.com/news/n0210/11planet/

This is the only discovered planetary orbit around a close binary star that I know about.

I have some general questions about planetary orbits around or within close binary systems or even the further apart binary star formations or triples.

Considering how many binary systems (and triple) there are, I hope some Astronomers are making predictions about planetary orbits within them. I bet the math is complicated!

The idea of a planet in a binary system blows my mind.

All the different orbital possibilities are driving me crazy and I wonder if Astronomers are working on predictions for the Alpha Centauri AB and Proxima System (the Sun's closest stellar neighbors.) Also since Alpha A and B are not that drastically different in mass from eachother I get really puzzled by the idea of a planetary body near their center of mass however unlikely that would seem.

Some questions :

Would it be possible for there to be a Lagrange point between the binary stars where asteriods/planetoids, what-have-you remain somewhat fixed?!?

Also:
Is it possible for a planet to orbit both stars outside of the stars orbits with eachother? What would that orbit look like?

And a weird one: (please don't laugh) What about inside their orbits around both of them like a figure 8?

Or what about a regular circular orbit around one Star, but when the other star gets close (say there is a Eliptical orbit of one Star around another larger star ) the planetary orbit gets very distorted?
I realize that Jupiter doesnt have a distortion of Earth's orbit when it aligns but not every system is like ours (near circular). If Jupiter were closer or there were a much more massive Red Dwarf wouldn't it distort our orbit with the Sun when it passed close by? I have a tough time imagining what this orbit would look like.

This is racking my brain.

I have read that so far no Gas Giants have been seen around Centauri but this does not rule out smaller rocky ones or water worlds that could be detected with better equipment. I am anticipating a better understanding of Alpha AB and Proxima.

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Chronos
Gold Member
Distant planets could orbit the gravitational center of a binary system. Planets nearby would have to hug one or the other to preserve a stable orbit.

Filip Larsen
Gold Member
I am not an astronomer, but let me add a bit.

Would it be possible for there to be a Lagrange point between the binary stars where asteriods/planetoids, what-have-you remain somewhat fixed?!?
In the so-called circular restricted coplanar three body problem, the L4 and L5 Lagrange points are unstable saddle-points when the mass ratio of the smallest to biggest star is above a certain limit, that is, if we call the masses of the two stars for M1 and M2, then L4 and L5 are only stable if M1< 26.0 M2.

So for a binary star system to have stable L4 and L5 Lagrange points you would expect the the bigger of the stars to be at least 26 times move massive than its companion.

Is it possible for a planet to orbit both stars outside of the stars orbits with eachother? What would that orbit look like?

And a weird one: (please don't laugh) What about inside their orbits around both of them like a figure 8?

Or what about a regular circular orbit around one Star, but when the other star gets close (say there is a Eliptical orbit of one Star around another larger star ) the planetary orbit gets very distorted?
You can in general have all kinds of different orbits in such a system, but depending on the mass ratio of the stars and the planets "initial" orbital energy, some orbits will be stable, some will be unstable, and some will be "unreachable". Orbiting close around either star or orbiting far around both stars can be stable orbits, meaning that lacking perturbations from any other orbital body the planet would stay in certain regions around the star or stars. For other orbits where the planet have the orbital energy to change its orbit from around one star to the other should be possible, but I guess (without knowing exactly) that they should not be expected to be stable in the long term, that is, the planet orbit would probably only require small perturbations for the planet to be ejected or undergo similar dramatic change.

Considering how many binary systems (and triple) there are, I hope some Astronomers are making predictions about planetary orbits within them. I bet the math is complicated!
Yes and no. Writing the basic equation is quite simple. You just calculate the gravitational force between the objects. However, it's one of those problems that gets very interesting very quickly.

Would it be possible for there to be a Lagrange point between the binary stars where asteriods/planetoids, what-have-you remain somewhat fixed?!?
Yes. However, the Langrangian solution to the three body problem assumes that you have two binary stars/planets/whatever in circular objects, with a third body. If the two stars aren't in circular orbits things get interesting.

Is it possible for a planet to orbit both stars outside of the stars orbits with eachother? What would that orbit look like?
Yes.

And a weird one: (please don't laugh) What about inside their orbits around both of them like a figure 8?

In the case of the simplest restricted three body problem, that doesn't happen. Either the planet is captured by one star, or is in a common orbit around both of them. Now if you make things just a little different, this does happen, and if you make things not much different you can have the small object flip between the two larger objects chaotically.

Or what about a regular circular orbit around one Star, but when the other star gets close (say there is a Eliptical orbit of one Star around another larger star ) the planetary orbit gets very distorted?
Yup that happens.

This is racking my brain.
The first thing to do is to come up with a simple problem. If you assume that the two big objects are in circular orbits around each other and that the third object is too small to change the situation, you end up with not too complicated ways of thinking about it.

This is one area where things are a lot simpler if you can see pictures of what is going on.