The Three Body Problem and Exoplanets

Tired of all the politics and divisiveness in the news? Take a break with this cool space fact.

Yesterday my daughter (successfully!) defended her master’s thesis in astrophysics. Her jam is finding circumbinary exoplanets, which are planets that orbit binary stars — think of Luke’s planet Tatooine. Two suns, remember?

There are two kinds of such planets: s-type, where the planet orbits just one of the two stars; and p-type, where the planet orbits both of the stars. That’s the type we’re interested in today.

Binary stars orbit each other, like a perpetual dance whirling around each other. Between them somewhere is the center of their collective mass, and that’s the point they’re both really orbiting. It’s also the point around which any stable p-type planets are also orbiting.

But what if the planet is too close to the stars? It falls into their collective gravity well, and then the three of them get all joggled up. This would be an unstable circumbinary exoplanet. But if they are far enough away, that won’t happen, and they will continue to orbit their system’s center of mass, in stable orbits.

Here my own half-assed rendering of one of her slides from her thesis presentation:

The stability limit for a circumbinary exoplanet. NOTHING IN THIS IS REMOTELY TO SCALE.

What’s interesting here is that dotted line, the stability limit. Any planets orbiting inside that limit would be unstable and would fall into the gravity well and create a joggly mess; any planets outside that limit will remain in a stable orbit around both stars.

“Joggly mess” — just to be clear — is my own unsophisticated term. What it represents is the three-body problem, a term recently used as the title for a streaming series. When three bodies are orbiting each other in space, it is a chaotic system, and there is no mathematical equation that can solve it. Here is Wikipedia’s little animated depiction:

With this in mind, the question I asked during the public Q&A session was “How do we determine where the stability limit is?” By definition of the three-body problem, that distance cannot be calculated. It can be estimated, but never calculated. So how do we know where it is?

After the thesis presentation, one of the professors (whose name I did not catch) explained it to me. He’s one of the guys who determined this. It is done by modeling such a situation in the computer, thousands and thousands of such possible systems, and then running countless simulations. We can model it, we can simulate it, and we can see which starting positions of the planet fall into the gravity well and which do not. That way we can find out (approximately) where the stability limit is — We just can’t calculate it in advance.

In fact, that’s how the little above animation was able to be made. That’s a recorded simulation running; the positions could not have been calculated in advance.

So I think that’s pretty cool.