Physicists Discover a Whopping 13 New Solutions to Three-Body Problem

Science Now ^ | 3/8/13 | Jon Cartwright

[LibWhacker]

All the hubbub here is about 13 new solutions. I wonder if anyone has put an upper limit on how many there are?

[LibWhacker]

You know, regarding my question to Lonesome in Massachussets about a theoretical upper limit on the number of possible orbits, we may be looking at a situation where there are an infinite number of possible three-body orbits out there. Wouldn’t that be wonderful? Could you imagine the possibilities for life, and all the different environments it might inhabit?

[Lonesome in Massachussets]

There are clearly an infinite number of solutions, just as there are to the two body problem. My take is that they are finding new classes of solutions.

One example of the three body problem is the moon-earth-sun. The system is powerfully perturbed by Jupiter and Venus, so it’s not really a pure three body problem, but it is representative of one class of solutions: Ms >> Me >> Mm, where “>>” means “is sufficiently greater than” with the two smaller bodies body in a nearly Keplerian orbit, and their center of mass orbiting the most massive central body . Another class are the famous Lagrangian points, which include thousands of Trojan (no smirking) asteroids. Another is the horseshoe (only in Lagrangian coordinates) orbit. It was believed that horseshoe orbits were only possible theoretical constructs, until asteroids in horseshoe orbits around earth were discovered.

[Lonesome in Massachussets]

It looks like they are looking for periodic solutions, solutions that repeat.

Laplace, in Mécanique Céleste claimed to have "proven" that the solar system is stable. Newton thought that God had to intervene periodically to prevent chaotic disintegration of the solar system. When Napolean asked Laplace about the place of God in his universe, Laplace is said to have replied, "Sire, je n'ai pas besoin de cette hypothèse". (Sire, I have no need of that hypothesis.) We know now that Laplace was wrong, but wrong with style. He was very right about a great number of other things.

I don't think you can properly introduce the three body problem without at least a mention of Poincaré.

[LibWhacker]

Is there a limit on the number of classes of solutions?

Holy cow, my jaw dropped when I saw the MOTH III class. Maybe some science fiction writer of the future will set his novel in such a system? I hope so.

Poincaré... Way before my time and way over my head, lol!

[BenLurkin]

Something about the Kama Sutra, I think.

[BenLurkin]

So, astrogating around Pluto might be tricky?

[LibWhacker]

Absolutely! When your astronauts got to Pluto, it’d be a bummer to find out Pluto wasn’t where you thought it’d be when you sent them and was traveling 50,000 mph too fast in the wrong direction. Could make for a messy landing. Before climbing onboard, they’d want to know you got an A+ in celestial mechanics and not just some affirmative action diploma in it.

[BenLurkin]

Well, if it's me flying the thing I won't need any of that fancy stuf. 'Cause I don't understand it anyhoo.

I'll just use the 'ole seat 'o the pants.

Here we go!

[LibWhacker]

That’s best, anyway. If fuel is going to be in such short supply that I need to be shot out of a cannon, because liberal luddites quake in fear every time someone mentions the atom, I’d rather stay at home. Give me a nice powerful Orion class ship and I’d be happy to hop onboard with a seat-of-the-pants pilot. We’d get there quickly, and if Pluto doing what we thought it would be doing, we’d change course, catch up, etc., and not worry about running out of gas. The only way to travel!

[LibWhacker]

if Pluto doing what we

if Pluto WASN'T doing what we

[SunkenCiv]

Thanks LibWhacker.

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[SunkenCiv]

Thanks LibWhacker.

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[SunkenCiv]

Thanks LibWhacker. No, this three-body problem isn't about Obama and Benghazi.

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.

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[MHGinTN]

OR, the study of interacting conic sections. Think of each mass exercising its gravitational mass as a conic manifestation, with the larger portion of the cone representing the gravitational attraction spread over a larger volume of space, and the deeper into the cone toward the apex the more force is concentrated in the smaller volume of the cone. Now think of three body problem as the interaction of cones and conic sections of force ... hehehe

[Graewoulf]

Yes! What you wrote!