Physicists Discover 13 New Solutions To Three-Body Problem

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.

Comments

Never thought it would be so hard to have a 3some

[oodaloop]

Though I'll admit it's entirely theoretical for me so far.

having said that

[etash]

would anyone care to explain how much accurate are the numerical analysis/numerical integration solutions ? ( which also apply to n-body problem, specific part of which is the 3 body problem ). Does the accuracy depend on how small is the dt we chose between each calculation ?

Re:having said that

[Anonymous Coward]

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.

Re:having said that

[etash]

so that actually means that for any dt, however small it is, given enough simulation time, there is a time point in the future after which the simulation is completely wrong ( for various values of "completely" )

Re:having said that

[cnettel]

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.

Well, for the same solver, it does. But the relative (and absolute) improvement realized by changing dt is quite dependent on what solver scheme you are using.

Re:having said that

[Anonymous Coward]

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

Re:having said that

[MickLinux]

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:having said that

[cgaertner]

Of course there's a theoretical solution and you can give it as a power series. The three-body problem just can't be solved via first integrals, and the power series is pretty much useless for practical purposes as it converges too slowly.

Re:having said that

[Noughmad]

Pretty much all integrators used for celestial mechanics have variable dt. The reason is that there are long periods where almost nothing happens, and then you come very close to a star (or two of the 3 bodies come very close together) where you have very rapid changes of velocity and you need very small dt. Because most of the newly found solutions include such close encounters, their accuracy may be questionable.

Re:having said that

[TapeCutter]

The clockwork metaphor of the universe fell apart about 100yrs ago. The universe is random at a fundamental level but even if it were deterministic one of the laws in your point (b) is that most systems in nature are mathematically chaotic, no mater how well you measure the starting conditions it can NEVER be accurate enough to reliably predict the behavior of the system past a certain point in the future.

The thing I find "odd" is that often (always?) the statistics of a chaotic system are extremely stable, eg: weather is chaotic and is difficult to predict more than a week into the future, climate (the statistics of weather) is not chaotic.

Re:having said that

[SomeKDEUser]

You misunderstand the laws of thermodynamics. They apply also at the quantum level, and deal mostly about the energy cost of transferring a bit of information. The trick being that the bit may or may not decay with some probability which depends on how much energy you put into preserving it. Where a "bit" is for example the excitation level of an electron.

The universe is truly nondeterministic. It really is a hugely complicated probability density function :)

Re:having said that

[semi-extrinsic]

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 evidence which falsify your hypothesis. Bonus: Zombie Feynman.

Re:having said that

[fredprado]

However weird the current accepted model is, and incompatible to what you want to believe in, if you really want to pursue science as a career or even as a hobby you need to understand that wanting things to be some way or feeling they should be some way are both hindrances to any scientist.

Science is the search for truth through logic and experiment, it accomplishes its goal mostly by ruling out the inconsistencies. Nobody can claim that the current statistical model is 100% correct, but what can be claimed with certainty is that a deterministic universe, reassuring as the idea may be, has been ruled out.

Re:having said that

[DMUTPeregrine]

Chaotic systems have attractors. Chaotic systems will be mostly stable around the attractors, it's the details (where around the attractor they are) that vary.

Re:having said that

[Rockoon]

The key there is 'from our viewpoint'

The Bell results only show that there are no hidden local variables. Non-local variables could never be proved to be impossible.
For all we know all quantum events are determined by a single 128-bit LFSR.

Re:having said that

[citizenr]

The universe is truly nondeterministic. It really is a hugely complicated probability density function :)

This is just an artifact of compression/optimization functions used to run the emulation.

Re:anonymous coward discovers new way to first pos

[K. S. Kyosuke]

naked and petrified!

You mean the paleolithic version of the three body problem?

Oh, you're talking about THAT three-body problem.

[QilessQi]

The one that *usually* keeps scientists awake at night is, "how can I get my girlfriend and her cute roommate into bed at the same time?"

See the actual orbits

[Anonymous Coward]

The orbit gallery

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

Very special cases

[tylersoze]

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:Very special cases

[K. S. Kyosuke]

I wonder what stability these solutions have. I.e., whether they are more like L1/L2 points (small deviations amplified over time) or more like L4/L5 points (small deviations lead to loops around the center).

Re:Very special cases

[BlackPignouf]

PROTIP: It isn't a "very special case" to get 3 coplanar bodies.

Re:Very special cases

[c0lo]

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:Oh, you're talking about THAT three-body proble

[Anonymous Coward]

I think just getting the girlfriend into bed (or having one, for that matter) is sufficient of a problem for most scientists.

Re:Never thought it would be so hard to have a 3so

[Anonymous Coward]

You obviously have funding issues for your research. Adequate funding will resolve this research deficiency.

Re:Oh, you're talking about THAT three-body proble

[K. S. Kyosuke]

"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:Oh, you're talking about THAT three-body proble

[K. S. Kyosuke]

I think just getting the girlfriend into bed (or having one, for that matter) is sufficient of a problem for most scientists.

Well, at least they've already solved in for a spherical girlfriend in vacuum.