pssst!...gotta problem with 3 bodies?

[Vraith]

so everyone knows by now that AFAWK, there isn't and never can be a general solution to predicting 3 bodies orbiting...there are only specific solutions.
And only 3 of them found over the last couple hundred years...3 pretty simple ones.

UNTIL NOW: 13 more solutions have been found! The link below isn't to the article, it's to diagrams of the 16 known solutions.
Some of them are pretty nifty looking, I'd love to see an actual system that had them!

suki.ipb.ac.rs/3body/

[Hashi Lebwohl]

That is completely amazing! The Three-Body Problem has been one of the great unsolvable problems in mathematics and physics. Although not a general solution, these specific solutions are more than we have had before.

[Avatar]

So wait a second...

These are 16 of the ways that three bodies (quantum particles) can orbit?

But the problem is actually how to predict their orbit from their velocity and position? Which this doesn't do, instead just showing ways in which they could orbit?

--A

[Hashi Lebwohl]

Correct. The general solution to the three-body problem is, I think, impossible but certain specific solutions can be found; these 16 are some of those specific solutions in that they are periodic--at some point the three particles wind up in their original starting positions and then the pattern repeats. There are other solutions that would not be periodic and we cannot find those.

[Vraith]

So wait a second...

These are 16 of the ways that three bodies (quantum particles) can orbit?

But the problem is actually how to predict their orbit from their velocity and position? Which this doesn't do, instead just showing ways in which they could orbit?

--A

Not sure if the application is identical or not for quantum 3 body, but this particular case they were talking macro-scale. Planets and such.
And it does do what you say it doesn't...IF you set the initial conditions in one of the 16 ways, you can predict their orbits pretty much forever.
And IF you know the velocity and position of 3 bodies, you can easily tell if they match one [and only one] of the 16 solutions...so you can calculate back and predict forward. [all other cases, so far anyway, remain insoluble]

[Avatar]

But each one is only true if the bodies happen to have that particular vector. So if you can match position and velocity to one of the models, then it will describe it.

I wouldn't call it so much a solution as a description of 16 possible paths for a 3 body orbit.

--A

[Vraith]

But each one is only true if the bodies happen to have that particular vector. So if you can match position and velocity to one of the models, then it will describe it.

I wouldn't call it so much a solution as a description of 16 possible paths for a 3 body orbit.

--A

Heh...I'm not sure there's a difference between description/solution when it comes to math. A solution is just a description that works. But that's a different kind of discussion....and maybe not true in any technical sense.

The key is it is calculable...if you have the variables[vectors] you can solve the orbits. [if it is one of the 16] or not [if it isn't].
AND if you observe a system, you can reverse it and solve/predict the vectors [if it is one of the 16] or not [if it isn't].

[Hashi Lebwohl]

Heh...I'm not sure there's a difference between description/solution when it comes to math. A solution is just a description that works.

No, there is no difference. The 16 paths listed on that link are solutions to the three-body problem. The full solution set is most likely infinite (and probably uncountably infinite, which is different than countably infinite) which is why the general solution is impossible.

The other thing to consider is that these 16 solutions probably only work with three bodies that have the same mass and thus the same gravitational pull. If one of the bodies were twice as massive as the others the orbits would not work as listed.

[Vraith]

The other thing to consider is that these 16 solutions probably only work with three bodies that have the same mass and thus the same gravitational pull. If one of the bodies were twice as massive as the others the orbits would not work as listed.[/color]

I'm not sure from the article if that is the case or not for the new solutions. It doesn't mention it. It probably does in the actual study, but I can't get that, and it's probably all over-my-head math anyway.
It does call them "families" though...which I take to mean they're like similar geometry shapes...size doesn't matter, only the relationships...so IF a "yarn" solution works with [I'm just making simple numbers up...nothing to do with real] a 1/2/3 system, you will ALSO see "yarn" in a 2/4/6 system.
It also mentions that the only commonly accepted stable one is of the LaGrange-Euler type...Sun, Jupiter, and a Trojan asteroid...and those are far from same mass.

[Hashi Lebwohl]

hrm...I have to admit that I haven't read the actual study yet but I suppose the solutions might actually be independent of body mass.

[I'm Murrin]

I would have thought it'd be specific to certain mass ratios, surely?

[Vraith]

specific ratios of mass, yes...but not ONLY mass.
the problem involves 10 or 12 integrals of 3 or 4 different kinds.

IIRC, one of the first/oldest solutions only works [like the one known actual system] if one of the bodies has insignificant mass [SUN,JUPITER, asteroid].

I assume the new solutions, each family will be similar, as I said...have the same multi-variable relationships...but not identical values.