## Physicists Discover 13 New Solutions To Three-Body Problem 127

sciencehabit writes

*"It's the sort of abstract puzzle that keeps a scientist awake at night: Can you predict how three objects will orbit each other in a repeating pattern? In the 300 years since this 'three-body problem' was first recognized, just three families of solutions have been found. Now, two physicists have discovered 13 new families. It's quite a feat in mathematical physics, and it could conceivably help astrophysicists understand new planetary systems."*The paper is available at arxiv.
## See the actual orbits (Score:5, Informative)

The orbit gallery [ipb.ac.rs]

Click on an orbit and look at the "real space" diagram to see the actual paths of the planets.

## Re:having said that (Score:4, Informative)

would anyone care to explain how much accurate are the numerical analysis/numerical integration solutions ?

They are as accurate as you care to make them. The problem is that increased accuracy over a long period can

require an exponential increase in cost.

Does the accuracy depend on how small is the dt we chose between each calculation ?

Precisely.

## Very special cases (Score:5, Informative)

While the results are interesting, it looks like the 13 new solutions all involve 3 equal mass bodies with total zero angular momentum and coplanar. Of course, all the periodic solutions are probably special cases of some sort.

## Re:having said that (Score:5, Informative)

## Re:Oh, you're talking about THAT three-body proble (Score:5, Informative)

"how can I get my girlfriend and her cute roommate into bed at the same time?"

Try turning the lights off and leaving the room.

## Re:having said that (Score:2, Informative)

It really just means no closed form solution... falls under advanced algebra. Interesting results, boring class.

## Re:having said that (Score:5, Informative)

I don't think they did it that way, rathe, they are using the computer to help them predict repeating lissajous patterns (for want of a better term) on their transformed sphere-space.

That then relates back to a specific repeating orbit in 3-space.

This is rather interesting, in that it is quite similar (methinks) to the knot classification problem.

But looking at the lissajous figures, it doesn't really seem to me that there are fourteen new classes, unless the lagrange solutions -- which are all a single class -- were counted as five.

But it's no less impressive, what they have done. They have started to transform from physicists to mathematicians.

## Re:Very special cases (Score:5, Informative)

While the results are interesting, it looks like the 13 new solutions all involve 3 equal mass bodies with total zero angular momentum and coplanar. Of course, all the periodic solutions are probably special cases of some sort.

From the point of view of "conceivably help astrophysicists understand new planetary systems" (TFA claim): the zero angular momentum doesn't bother me that much: it'd be a planetary system that rotates in time. The coplanar... mmmhh... maybe an acceptable approximation. It is the mass equality that one doesn't see too often.

## Re:having said that (Score:4, Informative)

It's not that a particle has a theoretical probability of being somewhere with some probable momentum, no it will be at a very real place at a very real time with a very actual momentum. It's just that practically it's so complicated to predict it, that the best way we have come up till now are quantum mechanics .

Nope, you're wrong. Here are the experimental [aps.org] evidence [aapt.org] which falsify [sciencemag.org] your hypothesis. Bonus: Zombie Feynman [xkcd.com].