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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.
Though I'll admit it's entirely theoretical for me so far.
Tic-Tac-Toe, Global Thermonuclear War, and relationships all have the same winning move.
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 ?
naked and petrified!
You mean the paleolithic version of the three body problem?
Ezekiel 23:20
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?"
Koans and fables for the software engineer
The orbit gallery
Click on an orbit and look at the "real space" diagram to see the actual paths of the planets.
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.
I think just getting the girlfriend into bed (or having one, for that matter) is sufficient of a problem for most scientists.
The paper is four pages. These could hardly be considered "solutions", there are no proofs at all.
You obviously have funding issues for your research. Adequate funding will resolve this research deficiency.
"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.
Ezekiel 23:20
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.
Ezekiel 23:20
No wonder you never get laid.
And they wont accept numerical solution: http://xkcd.com/613/
+1 Depressing Reality
... still waiting for this free-as-in-beer free beer I keep hearing about.
"how can I get my girlfriend and her cute roommate into bed at the same time?"
Get him drunk before you ask him.
systemd is Roko's Basilisk.
Get cracking, math guys. Until then, the universe is its own best simulator and it runs in real time - my lab. But it's kinda hard to trace the history of a single particle in that soup.
Why guess when you can know? Measure!
Or for that matter, keeping the girlfriend out of the bed if you're called Sheldon.
Wasn't this solved in 1951 as shown in that documentary "The Day The Earth Stood Still"?
LAst line for those who don't get the joke
the... a solution to the three body problem under a universal unidirectional inverse square law -- still the simplest case of the three body problem which one can analyse.
What if the force is dependent not on mass, which cannot be negative, but on electric charge, which can be? What about a hypothetical coloured force (like the stuff out of quantum chromodynamics) in which Red attracts Green and repels Blue, Green attracts Blue and repels Red, and Blue attracts Red and repels Green? What if there is a fourth party which may decide, from moment to moment according to as yet unspecified rules which way the attraction-repulsion cycle goes (so that the force is a kind of alternating dihedral force if you are familiar with the nomenclature of elementary group theory)?
Of course what the three body problem (and indeed gravitation and electromagnetism of two bodies) looks at is the continuous equivalent of modern game theory. A computational model, of course, then works in discrete time, so a computational model is an application of game theory (wearing a suitable disguise, such as a purple beard and greeny-grey glasses ;-) ).
John_Chalisque
The authors do not check the stability of the found peridioc orbits, which is a necessary condition for expecting such orbits in nature. When stable nearby orbits diverge typically linearly in time and stay similar to the periodic solution (like the planets in the solar system stay close to elliptic orbits), while when unstable the divergence is exponential and quickly the 3 bodies are widely separated.
It's strange how they don't mention the solutions of the 3-body problem explored in the 19th century by G W Hill: see e.g. "Hill's Lunar Equations and the Three-Body Problem": K R Meyer, D S Schmidt, Jnl of Differential Equations 1982, 44, 263-272 https://math.uc.edu/~meyer/jde82.pdf. Part of his work was one of the first things published in the American Journal of Mathematics, (G W Hill, in American Journal of Mathematics, Vol. 1, No. 1 (1878), pp. 5-26).
3 bodies can remain in static orbit according to lagrange: https://en.wikipedia.org/wiki/Lagrangian_point
Some of these orbit locations are "attractors", meaning that bodies close to these points will tend to "fall in" to the orbital points and remain stable. These solutions generally have 2 large bodies and one much smaller body. What I always wondered if it was possible for 2 black holes to orbit one another. If so, then they should have these lagrange orbital points where other objects would fall in and become "stuck" as the gravitational wells would be very strong and keep objects from falling out. Also, since these wells would be close to black holes gravitational feilds, objects inside them would experience time dilation. Meaning that time experienced inside of these locations would proceed more slowly then time at a distance away from the black holes. The reason I wonder about this, is because it seems it would allow objects and matter to fall partially into or near to a black hole, but never fall into either of the black holes. So if two black holes could remain in a stable orbit about one another, then there should be a fair amount of mass collected in these gravity wells that is "older" then all the other objects in the nearby space. Since time would flow at a slower rate, there should be objects in these wells that has not had as much time to age as the rest of the objects in the surrounding space.
It would be interesting in some far far future space exploration to visit a binary black hole system and then use the lagrange orbital paths to fly between the black holes and explore these gravity wells. It may be that some of the youngest old objects in the universe are hidden within them.
Of course, maybe black holes cannot have long stable orbits. And maybe these gravit wells are not close enough to create significant time dialation. Im just mentioning it because it would be interesting for someone with knowledge to think about it.
Well There's the:
Cool Threesome
Uncool Threesome
Wait, is my girlfriend/boyfriend gay
Wait, is my girlfriend/boyfriend straight
Is he only asking for this threesome because he no longer likes me and wants to get it on with that girl from work/the gym?
We just woke up and he/she was there
The Siamese (shudder)
No, I'm just here to watch (we saw how that went in basic instinct)
And so on. That's just arranging a suitable partner, we haven't even touched on the physicality of it. I think I'll have to do some research on that part.
Sorry, how did the scientist get a girlfriend? You lost me there.
Sure enough, the cow costume was hanging up next to the superhero outfit and sailors uniform. (S,Spud)