Physicists Discover 13 New Solutions To Three-Body Problem

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Physicists Discover 13 New Solutions To Three-Body Problem

Posted by Unknown on Saturday March 9, 2013 @07:33AM from the mystical-spheres dept.

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.

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Never thought it would be so hard to have a 3some by oodaloop · 2013-03-09 07:42 · Score: 5, Funny

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.
having said that by etash · 2013-03-09 07:45 · Score: 2

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 ?
1. Re:having said that by Anonymous Coward · 2013-03-09 07:51 · 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.
2. Re:having said that by etash · 2013-03-09 07:55 · Score: 4, Informative
  
  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" )
3. Re:having said that by cnettel · 2013-03-09 07:57 · Score: 2
  
  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.
4. Re:having said that by etash · 2013-03-09 08:06 · Score: 1
  
  what troubles me is the impossibility of a theoretical solution because it undermines my belief in a deterministic universe. There _must_ be some theoretical solution which can 100% accurately predict any future status of the n body problem!
5. Re:having said that by Anonymous Coward · 2013-03-09 08:10 · Score: 1
  
  Your inability to predict something doesn't mean it isn't deterministic.
6. Re:having said that by etash · 2013-03-09 08:13 · Score: 1
  
  IF the universe IS deterministic there should be a THEORETICAL solution to predict any future state of the universe provided that you a) know an initial state and b) know all the laws of the universe.
7. Re:having said that by Anonymous Coward · 2013-03-09 08:13 · Score: 2, Informative
  
  It really just means no closed form solution... falls under advanced algebra. Interesting results, boring class.
8. Re:having said that by khallow · 2013-03-09 08:31 · Score: 1
  
  Quantum mechanics rules out a deterministic universe from our point of view.
9. Re:having said that by etash · 2013-03-09 08:48 · Score: 1
  
  i know, but quantum mechanics is not necessarily how the universe functions, it's just a probabilistic approximation just like the laws of thermodynamics. p.s. i think the universe cannot be non deterministic unless you believe in flying spaghetti monsters of pink unicorns
10. Re:having said that by MickLinux · 2013-03-09 08:59 · Score: 4, 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.
  
  --
  Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
11. Re:having said that by MickLinux · 2013-03-09 09:05 · Score: 1
  
  Actua\ly, not always. Accuracy is often dependent on getting convergence at all (existance and uniqueness), and then on not getting an infinitely slow convergence (iirc, the mcLauren/Taylor solution to the ATAN function is an example.)
  After that, you are limited in a very real way by computing power. Thus, any time you can eliminate whole swathes of calculation by refining your model -- or coming up with an exact solution -- it's always a big plus.
  
  --
  Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
12. Re:having said that by cgaertner · 2013-03-09 09:11 · Score: 2
  
  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.
13. Re:having said that by osu-neko · 2013-03-09 09:18 · Score: 1
  
  p.s. i think the universe cannot be non deterministic unless you believe in flying spaghetti monsters of pink unicorns
  The difference here being that unicorns are compatible with our understanding of the universe, and are thus a more reasonable thing to believe in based on the evidence than say, a flat earth, Biblical creation, or a deterministic universe. The latter three fly in the face of science, instead of simply being unsupported by evidence ala unicorns and spaghetti monsters.
  
  --
  "Convictions are more dangerous enemies of truth than lies."
14. Re:having said that by Noughmad · 2013-03-09 09:35 · Score: 2
  
  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.
  
  --
  PlusFive Slashdot reader for Android. Can post comments.
15. Re:having said that by __aaltlg1547 · 2013-03-09 09:36 · Score: 1
  
  True, and I want to point out that flying spaghetti is totally consistent with string theory and a fully stochastic (and messy) universe.
16. Re:having said that by TapeCutter · 2013-03-09 09:40 · Score: 2
  
  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.
  
  --
  And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
17. Re:having said that by SomeKDEUser · 2013-03-09 09:45 · Score: 1
  
  Sorry, but this is not the way it works. You have problems such that you can prove there exists an optimal algorithm to solve them, and simultaneously prove you cannot actually write it.
  Or for cases such as this, there may not be a finite number of solutions. In fact, there may not be a countable infinity of solutions. At which point, since the axiom of choice may not be true (your choice!) it may be that you may not be able to pick all the solutions which are true and exist, nor even write them as families of solutions.
  The universe may still be deterministic, but it may not be computable (in fact, I suspect that). this means that even is all events are perfectly defined from the past, you may not make a prediction about future events in general.
18. Re:having said that by SomeKDEUser · 2013-03-09 09:50 · Score: 4, Insightful
  
  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 :)
19. Re:having said that by Waffle+Iron · 2013-03-09 10:04 · Score: 1
  
  what troubles me is the impossibility of a theoretical solution because it undermines my belief in a deterministic universe.
  
  As they say: The universe doesn't care what you believe.
  We don't have enough information to know whether it's deterministic or not. Whatever the case, it is what it is. And if it is deterministic, that still doesn't necessarily imply that predicting the future is actually computationally feasible.
20. Re:having said that by etash · 2013-03-09 10:29 · Score: 1
  
  i tend to disagree. I don't think that subatomic particles have their own mind. every particle moves under the influence of all the known forces ( 5 - or maybe more ) of all subatomic particles in the universe and its position and momentum is certain despite the fact that it's impossible ( computationally ) for us to determine it. The laws for gases ( pressure etc. ) and quantum mechanics are just stochastic simplifications of the actual movements of the molecules ( or subatomic particles in the case of quantum mechanics ).
  
  what i'm saying is: 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 and generally speaking, stochastic laws which only approximate for practical purposes. A theory constructed to give practical approximations does not have a say on the actual theoretical position/momentum of the particles.
21. Re:having said that by Anonymous Coward · 2013-03-09 10:33 · Score: 0
  
  I don't know enough about orbital simulations, but what you say is not true in general. A numerical simulation's error may be bounded. In fact, a simulation with unknown, unbounded error is useless. The question is whether the error increases with time (number of simulation steps.) For chaotic systems, it definetly does. For others, it may as well be bounded, independent or decreasing. It depends on whther there is a single, non-chaotic attractor and whether the simulation is numerically stable. As an example consider "orbit" of a falling stone, if the simulation is stable, the fall ends on the ground regardless of accuracy of positions in the interim.
22. Re:having said that by etash · 2013-03-09 10:35 · Score: 1
  
  How can something be possibly random at a fundamental level ? it would go against the law of conservation of motion. In my opinion there is no randomness at all. It's just that every particle in the universe is affected by every other particle ( nomater how small those forces may be ), thus the particles' movement seem random to us.
  
  the practical difficulty in computing does not mean that there is a chaotic or random factor. It's just means the factors that affect the particular phenomenon so many, that it becomes too complex to compute/comprehend.
23. Re:having said that by etash · 2013-03-09 10:44 · Score: 1
  
  i know that the question is still open and i'm not sure myself. However I cannot "see" how it can be non deterministic. Stochastic theories are always approximations when it's too difficult to compute each element. The fact that we have built a stochastic theory which gives accurate results more or less on a "whole" level ( of the phenomenon we are studying ) does not mean that this stochastic theory reflects reality. It's just a tool to get practical results ( just like feynman's on the back of the hand calculations ).
  
  if it is determiinistic and we had a massive supercomputer outside the boundaries of the universe, knew all the laws and had an initial state, we could simulate/predict any future/past state
24. Re:having said that by etash · 2013-03-09 10:47 · Score: 1
  
  i'm not sure i understood your last point on whether it could be not computable. If it is deterministic and we had all the initial data and the laws we could "replay" the whole thing out. Of course we would have to have a massive supercomputer outside this universe, so as not to affect the prediction.
25. Re:having said that by RandomFactor · 2013-03-09 11:07 · Score: 1
  
  the practical difficulty in computing does not mean that there is a chaotic or random factor.
  
  Are you sure?
  
  --
  --- Mercutio was right.
26. Re:having said that by semi-extrinsic · 2013-03-09 11:09 · Score: 3, 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 evidence which falsify your hypothesis. Bonus: Zombie Feynman.
  
  --
  for i in `facebook friends "=bday" 2>/dev/null | cut -d " " -f 3-`; do facebook wallpost $i "Happy birthday!"; done
27. Re:having said that by fredprado · 2013-03-09 11:10 · Score: 2
  
  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.
28. Re:having said that by DMUTPeregrine · 2013-03-09 11:25 · Score: 2
  
  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.
  
  --
  Not a sentence!
29. Re:having said that by DMUTPeregrine · 2013-03-09 11:29 · Score: 1
  
  Actually, even if it is deterministic there can be problems with no solutions, such as the Halting Problem. Predicting the future in all cases is impossible, even in a fully deterministic universe.
  
  --
  Not a sentence!
30. Re:having said that by Anonymous Coward · 2013-03-09 11:31 · Score: 1
  
  --
  And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
  "Meek and obedient you follow the leader down well-trodden corridors into the valley of steel" - Ditto
31. Re:having said that by Anonymous Coward · 2013-03-09 11:33 · Score: 0
  
  The theoretically perfect solution is to use a numerical scheme with infinitely small time steps.
  You did say theoretical, and not practical, right?
32. Re:having said that by Rockoon · 2013-03-09 11:58 · Score: 2
  
  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.
  
  --
  "His name was James Damore."
33. Re:having said that by HiThere · 2013-03-09 12:36 · Score: 0
  
  Yes it is. We can't show which side of the sun the Earth will be on exactly 10,000,000 years from now (measured in standard seconds, etc.) And we can't show that it will still be orbiting the sun some number of years after that. The errors increase without limit, but slowly.
  Note that some, but only a small part, of the error is due to unknowns, say astroids we haven't mapped the orbit of. Most of it is due to chaos. The calculations are EXTREMELY sensitive to initial conditions AND to errors in calculation at each step. We don't have analytical solutions, only recursive approximation solutions.
  But do note that we can't measure the error in our predictions of where the Earth will be exactly one year from now. The errors are both cumulative and unnoticably small in each step.
  
  --
  
  I think we've pushed this "anyone can grow up to be president" thing too far.
34. Re:having said that by Cracked+Pottery · 2013-03-09 12:48 · Score: 1
  
  If you believe in free will, you have to admit the possibility that the Universe isn't deterministic. It might not be possible to prove that any posited set of laws is ultimate, so that question might remain unsettled for a long time.
35. Re:having said that by Your.Master · 2013-03-09 13:05 · Score: 1
  
  Well, not with absolute certainty. There's still the superdeterminism loophole. It's just that this is even weirder and less satisfying to many people than just dropping determinism, especially since, philosophically, it suggests that science is meaningless and anything we discover through the scientific method is coincidence that could change tomorrow, because literally every experimental result you've ever had is a part of a vast conspiracy of all the particles in the Universe.
36. Re:having said that by MickLinux · 2013-03-09 13:06 · Score: 1
  
  We do have analytical solutions to the orbital problem,look up the parker sochacki solution to the picard iteration.
  http://csma31.csm.jmu.edu/physics/rudmin/parkersochacki.htm
  But there are limitations of how good our understanding of the initial position/velocity vectors are, so yes, we are also limited on the value of the results.
  
  --
  Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
37. Re:having said that by lazy+genes · 2013-03-09 14:36 · Score: 0
  
  Everything that exists is a tree body system. All things broken down to their fundemental properties have three parts. Its because the fabric of spacetime is hexagonal.It is only deterministic for a short time,time in the quantum world is very different so we do live in a deterministic universe.
38. Re:having said that by fustakrakich · 2013-03-09 14:45 · Score: 1
  
  Flip a coin
  Heads or tails?
  
  --
  “He’s not deformed, he’s just drunk!”
39. Re:having said that by citizenr · 2013-03-09 15:25 · Score: 2
  
  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.
  
  --
  Who logs in to gdm? Not I, said the duck.
40. Re:having said that by Anonymous Coward · 2013-03-09 15:28 · Score: 0
  
  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.
  ^Pun Intended???
41. Re:having said that by Anonymous Coward · 2013-03-09 15:34 · Score: 0
  
  Your opinion is in conflict with what a lot of very smart people have determined experimentally. The universe doesn't work the way you want it to just because you feel it must.
42. Re:having said that by fredprado · 2013-03-09 16:13 · Score: 1
  
  To say that superdeterminism is extremely implausible is to understate it. Furthermore as you said if that was so Science would be a pointless endeavor, and therefore by ignoring the possibility we don't really lose anything. We can also ignore the Flying Spaghetti Monster theory with similar results.
43. Re:having said that by Anonymous Coward · 2013-03-09 19:19 · Score: 0
  
  But the orbit of the Earth is a chaotic system.
44. Re:having said that by Anonymous Coward · 2013-03-09 19:40 · Score: 0
  
  Everything that exists is a tree body system. All things broken down to their fundemental properties have three parts. Its because the fabric of spacetime is hexagonal.
  But why hexagonal? Do you think, a hexagon is the shape of the spacetime? No, only in 3 dimension, because hexagon is the projection of a cube from diagonally opposite corner. The TRUE shape of 4-dimension spacetime is the TIME CUBE, and the SPACE HEXAGON is only a shadow!
45. Re:having said that by hazem · 2013-03-09 21:24 · Score: 1
  
  But don't forget that pretty much any numerical analysis will take place on a computer with a limited ability to represent floating point numbers. There will be a diminishing point of returns when decreasing dt when the increased precision from the smaller dt is eaten up by the increased errors in the floating point numbers.
  One of my favorite descriptions of this problem comes from RW Hamming's book, "Numerical Methods for Scientists and Engineers": http://books.google.com/books/about/Numerical_Methods_for_Scientists_and_Eng.html?id=Y3YSCmWBVwoC
46. Re:having said that by jouassou · 2013-03-09 23:00 · Score: 1
  
  Depends on what you mean with completely wrong. There is a class of numerical algorithms called Symplectic Integrators, which make sure that energy is conserved. You can also choose algorithms with an adaptive stepsize, which means that the simulation should converge to within a given error tolerance. (The simulation can still suffer from e.g. accumulated floating point errors, though.)
  
  The classic example of a simulation gone completely wrong, is the Flying ice cube problem...
47. Re:having said that by Anonymous Coward · 2013-03-10 00:52 · Score: 0
  
  Your choice to believe that is not founded in evidence. It is based on a stubborn insistence that the universe be simple enough that you can comprehend it. The universe is not obliged to conform to what you consider plausible.
  For example, with respect to photons reflecting off a surface; there is some probability distribution on whether that photon will reflect or be transmitted through the medium. What you're insisting upon is that there is some hitherto unknown cause for some to be reflected and some not to be. That may well be true, but there is absolutely no evidence to support that, it is just you trying to push your will on the universe.
48. Re:having said that by Carewolf · 2013-03-10 00:58 · Score: 1
  
  How can something be possibly random at a fundamental level?
  Because nothing has a fixed position or speed. Everything is at a fundamental level a probability wave, that only collapses to a fixed position or a fixed speed when interacting with other probability waves.
49. Re:having said that by dkasak · 2013-03-10 01:13 · Score: 1
  
  Except that it was proven impossible for a local hidden variable theory (which is what you are suggesting) to reproduce the results of quantum mechanics. This result is called Bell's theorem. This means that either the universe is non-deterministic or it is not completely local (i.e. there are effects which cannot be attributed to a local force). Either that or counterfactual definiteness does not hold, which would essentially mean that the result of any experiment and the choice of measurement the experimenter made for that experiment are both inseparably linked by being caused by the same deterministic factors (i.e. the experimenter got result A when doing a measurement Q and it makes no sense to ask "what would have happened if he chose measurement P instead?" since his choice of measurement was predetermined by exactly the same factors that made the result A). This is possible, but very implausible.
50. Re:having said that by Anonymous Coward · 2013-03-10 01:32 · Score: 0
  
  No. You're wrong.
  Particles as little solid balls with a defined (albeit perhaps unknowable) momentum and position do NOT exist*. See Bells Theorem.
  Only wave-functions exist and it's mathematically impossible to have a wavefunction with a distinct location (delta-function) and a distinct linear momentum (sine wave). This is Heisenbergs uncertainty principle.
51. Re:having said that by Anonymous Coward · 2013-03-10 01:58 · Score: 0
  
  i know, but quantum mechanics is not necessarily how the universe functions, it's just a probabilistic approximation just like the laws of thermodynamics.
  My understanding is that the probablistic view of QM is looking increasingly physically wrong. Some good experimental evidence: recent observation of a macroscopic object existing in two quantum states at once means quantum states are physically real and are not mere statistical abstractions that don't exist. Quantum teleportation and therefore Bell's Theorem and entanglement are physically real - can you explain those purely as statistical events? CNOT gates are real. Could quantum computing work in a purely statistical QM? QM is a very different mathematical construct to classical thermodynamics, it's not a good analogy,
52. Re:having said that by Anonymous Coward · 2013-03-10 02:04 · Score: 0
  
  Many people make this mistake. Don't confuse chaos theory with non-determinism. Chaos theory - ie error amplification in non-linear systems - is entirely deterministic.
53. Re:having said that by dkasak · 2013-03-10 02:10 · Score: 1
  
  Except that it has been proven impossible for a local hidden variable theory (which is what you are suggesting) to be able to replicate all of the results of quantum mechanics. This result is called Bell's theorem. This essentially means that either the universe is non-deterministic or it is not completely local (i.e. there are effects not caused by local forces). Either that or counterfactual definiteness does not hold (since Bell's theorem relies on it) due to the results of any experiment and the choice of measurement procedure for that experiment being inseparably linked through exactly the same deterministic factors. In other words, counterfactual definiteness being false means that, given an experiment producing a result A through measurement P, it makes no sense to ask "what would have happened if we chose measurement Q instead?" since the very same deterministic factors that caused result A also caused the experimenter to choose measurement P. While this is possible, it is extremely implausible.
54. Re:having said that by Anonymous Coward · 2013-03-10 03:51 · Score: 0
  
  if it is determiinistic and we had a massive supercomputer outside the boundaries of the universe, knew all the laws and had an initial state, we could simulate/predict any future/past state
  Provably false. It can still be deterministic, but not computable. Read up on halting problem.
55. Re:having said that by HiThere · 2013-03-10 06:50 · Score: 1
  
  I'm not sure that you can express the initial conditions as a finite series. If you can, then it looks as if you might be right. (Which doesn't say it would be possible to solve it in any feasible time on any feasible equipment.)
  So, OK, MAYBE there is an analytic solution. But I doubt it, because I don't think the initial conditions can be satisfied. (OTOH, it's been decades since I even *looked* an a differential equation, so my opinions aren't worth weighing heavily.)
  Even then, though, as we agree, the chaos in the system makes it so sensitive to initial conditions and perturbations (passing stars, e.g., even at multiple light years) that accurate prediction in detail isn't possible, which at a later time becomes much more general.
  
  --
  
  I think we've pushed this "anyone can grow up to be president" thing too far.
56. Re:having said that by peawormsworth · 2013-03-10 15:42 · Score: 1
  
  With a two body problem like the sun and the earth, we can accurately know exactly where the earth will be in 10,000,000 years. Because we will assign an exact number to its location and speed and exact numbers to the mass of the bodies and such. So the answer in relation to the article... is YES, we know exactly how to calculate 2 bodies in gravitational orbit. Of course, in reality, we dont know everything perfectly, so HiThere is correct in saying that in practice we cannot perdict that far out because there are other variables involved which are not related to a simple two body orbit. But the theoretically answer is that we DO know how to determine the location of the earth and sun exactly to an infinite point in the future, if all we had was exact initial conditions and nothing else to disturb it.
  I think you should consider the earth and sun as a perfect two body system, because this is what the article is referring to. It is not including all the other unknowns and limits of our measuring abilities. The 3 body problem does not include ouside considerations. It is difficult all on its own. It is a formula where 3 perfect bodies are set in motion appart from anything else. It is not a limitation of our ability to measure mass, distance, location or speed. So bringing our limitations of measurement of the earth and sun and future unknown possibilities over a 10 million year span has little to do with the considerations of the above article.
57. Re:having said that by Ultracrepidarian · 2013-03-10 19:28 · Score: 1
  
  In the real world, there are only n body problems where n is a very very large number.
58. Re:having said that by HiThere · 2013-03-11 03:53 · Score: 1
  
  If there weren't anything but the earth and the sun, you would have a point. But you've left out not only the rest of the solar system, but even the moon. This doesn't work.
  N.B.: You can't ignore both Jupiter and Saturn and have a prediction that's even good for a few decades.
  
  --
  
  I think we've pushed this "anyone can grow up to be president" thing too far.
59. Re:having said that by MickLinux · 2013-03-11 13:49 · Score: 1
  
  It's not as bad as you think, but the paper does discuss that towards the end. And yes, the author did use it elsewhere to show that the trojan asteroids cycled around their -- well, I'd actually call it their lagrangian spots on Jupiter's orbit.
  
  --
  Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's
60. Re:having said that by Kartu · 2013-03-17 04:53 · Score: 1
  
  Mm, but Bells result only show that there are no hidden local variables assuming function can be written in form blahttp://en.wikipedia.org/wiki/Local_hidden_variable_theory#Local_hidden_variables_and_the_Bell_tests
  So strictly speaking it doesn't prove that no hidden local variables theory is possible. (even though hidden local vars functions that could be chosen to match quantum results do not "feel natural")
Re:anonymous coward discovers new way to first pos by K.+S.+Kyosuke · 2013-03-09 07:47 · Score: 5, Funny

naked and petrified!
You mean the paleolithic version of the three body problem?

--
Ezekiel 23:20
Oh, you're talking about THAT three-body problem. by QilessQi · 2013-03-09 07:48 · Score: 4, Funny

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
See the actual orbits by Anonymous Coward · 2013-03-09 07:50 · Score: 5, Informative

The orbit gallery
Click on an orbit and look at the "real space" diagram to see the actual paths of the planets.
1. Re:See the actual orbits by Nivag064 · 2013-03-09 09:35 · Score: 1
  
  This is essentially 'Experimental Mathematics' at its best - the conclusions are (I assume) valid, but no theoretical framework is provided to show that there are no other solutions. I think their work is very important, but it lacks mathematical elegance; it may be that we will never find a practical and elegant mathematical theory to cover this - I hope I am wrong!
  I know of no proof that determines if the number of solutions (disregarding symmetries and topological invariant transformations ,,,) is finite or not.
  Looking at the method of how the new ones were found, I suspect that there are an infinite number of (disregarding symmetries and topological invariant transformations ,,,).
Very special cases by tylersoze · 2013-03-09 07:53 · Score: 4, 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.
1. Re:Very special cases by K.+S.+Kyosuke · 2013-03-09 08:02 · Score: 2
  
  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).
  
  --
  Ezekiel 23:20
2. Re:Very special cases by BlackPignouf · 2013-03-09 09:56 · Score: 2
  
  PROTIP: It isn't a "very special case" to get 3 coplanar bodies.
3. Re:Very special cases by c0lo · 2013-03-09 10:02 · Score: 4, 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.
  
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4. Re:Very special cases by K.+S.+Kyosuke · 2013-03-09 11:21 · Score: 1
  
  The coplanar... mmmhh... maybe an acceptable approximation.
  I'd say that depends on the stability of those systems. It's not just about point solutions in the parameter space, for astronomers, it's more about stable regions, like the L4/L5 Lagrangian solution. You simply won't hit a point solution with real objects, be it the mass or coplanarity, it doesn't matter.
  
  --
  Ezekiel 23:20
5. Re:Very special cases by Anonymous Coward · 2013-03-09 12:09 · Score: 0
  
  PROTIP: It isn't a "very special case" to get 3 coplanar bodies.
  Right, it's impossible. In the real world, nothing lines up that perfectly. PROTIP: Don't be an asshole and others won't treat you like one.
6. Re:Very special cases by Insightfill · 2013-03-09 16:16 · Score: 1
  
  PROTIP: It isn't a "very special case" to get 3 coplanar bodies.
  Right, it's impossible. In the real world, nothing lines up that perfectly. PROTIP: Don't be an asshole and others won't treat you like one.
  GP's point is that three bodies DEFINE a plane. They're always coplanar. It's the fourth body that gets you in trouble.
7. Re:Very special cases by Anonymous Coward · 2013-03-09 19:45 · Score: 1
  
  PROTIP: It isn't a "very special case" to get 3 coplanar bodies.
  Right, it's impossible. In the real world, nothing lines up that perfectly. PROTIP: Don't be an asshole and others won't treat you like one.
  GP's point is that three bodies DEFINE a plane. They're always coplanar. It's the fourth body that gets you in trouble.
  Which is missing the point, since OP clearly meant that all the velocity vectors lie in the same plane as the three bodies, so that they remain in the same plane.
8. Re:Very special cases by c0lo · 2013-03-10 00:19 · Score: 1
  
  The coplanar... mmmhh... maybe an acceptable approximation.
  I'd say that depends on the stability of those systems. It's not just about point solutions in the parameter space, for astronomers, it's more about stable regions, like the L4/L5 Lagrangian solution. You simply won't hit a point solution with real objects, be it the mass or coplanarity, it doesn't matter.
  You reckon?
  1. when you speak stability of the system, what reference of duration you think of? Because, look, I'm pretty sure the Solar System is mathematically unstable in the absolute sense, however the changes in the planet orbits are so minute on millennial scale that we can consider it "pretty stable" even if, hundreds of millions of years the changes would be notable (my point: unless catastrophically unstable to exist, a real astronomical star system does not impose/require stability in the absolute sense)
  2. I don't know why I remember 3 points always define a plane, at least in 3D Euclidean geometry. Now, it's highly likely a system to have a central star that is more massive than the planets; thus, the planets will rotate more or less around the star (that means the mass center is much closer to the start); such a system will not have a null angular momentum (that's why the second Kepler law holds so well). By the conservation of angular momentum, it means that - at least for an 3 body isolated star system (e.g. not too close to a black hole to avoid precession/nutation), this plane is likely will be stable (or become stable by exchange of angular momentum) or the system is unstable on long term. (my point: I wouldn't be dismissing the coplaneity and the difference of masses as not significant)
  But... don't get me wrong, I do agree with you if you say what the guys did is sort of intellectual masturbation with little applicability for real life astronomy (maybe we may differ on the reasons why we consider their indulgence as such).
  Funny thing, they are not even the first to fool around with that
  
  --
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9. Re:Very special cases by nedlohs · 2013-03-10 01:27 · Score: 1
  
  Except that you'd have to make an effort to think he meant just the positions of the objects rather than the velocity vectors that he obviously did.
10. Re:Very special cases by complete+loony · 2013-03-10 02:08 · Score: 1
  
  I believe that stability is exactly what this team will be investigating next.
  
  --
  09F91102 no, 455FE104 nope, F190A1E8 uh-uh, 7A5F8A09 that's not it, C87294CE no. Ah! 452F6E403CDF10714E41DFAA257D313F.
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 07:55 · Score: 5, Funny

I think just getting the girlfriend into bed (or having one, for that matter) is sufficient of a problem for most scientists.
um by Anonymous Coward · 2013-03-09 07:56 · Score: 1

The paper is four pages. These could hardly be considered "solutions", there are no proofs at all.
1. Re:um by cnettel · 2013-03-09 08:00 · Score: 1
  
  True, but now when you know where to look, it is far easier to retrofit proper theory. The presence of the solutions could trivially be verified in any (really well-written) independent numerical simulation.
2. Re:um by Anonymous Coward · 2013-03-09 08:06 · Score: 0
  
  The paper is four pages. These could hardly be considered "solutions", there are no proofs at all.
  Yeah, and being an electronic web page, it's not really even a paper. Those lying cock-suckers!
3. Re:um by Noughmad · 2013-03-09 09:42 · Score: 0
  
  There are no proofs in physics, only experiments. Experiments are difficult in this case, so these solutions were found with numerical simulation. Additional simulations by other physicist (and for this problem, there will be many) will show whether these are proper solutions or caused by the authors' mistakes.
  As sibling above points out, people will probably try to find analytical solutions that match these.
  
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4. Re:um by marcosdumay · 2013-03-09 11:05 · Score: 1
  
  There is a class of problems named NP. Have you heard about them?
  
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  Rethinking email
5. Re:um by Anonymous Coward · 2013-03-09 11:41 · Score: 0
  
  There are proofs in theoretical physics all the time. Consider many theories in physics are governed by simple, mathematical rules, you get a lot of proofs just to show what the implications of such rules are, such that they can be later tested, etc.
6. Re:um by MickLinux · 2013-03-09 13:48 · Score: 1
  
  Yes, but not all problems are Np. For example, the Parker-sockaki has allready passed existence and uniqueness, but AFAIK, NP is still out there. it would be nice to know that it was NP, but right now it only might be.
  
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7. Re:um by Noughmad · 2013-03-11 05:44 · Score: 1
  
  Yeah, I felt a bit stupid after posting that. This is one of those example where the problem has a complete and simple mathematical formulation. An analytical solution can be proved to be periodic. What these guys did was find numerical solutions. However, now that they have some ideas where to look, it should be easier to come up with analytical orbits.
  
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8. Re:um by marcosdumay · 2013-03-11 14:54 · Score: 1
  
  Solving differential equations (like this one) is NP.
  
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  Rethinking email
Re:Never thought it would be so hard to have a 3so by Anonymous Coward · 2013-03-09 08:02 · Score: 0

It is so abhorrent to the universe that it already never happened before it never had the chance to.
You are stuck in a self-correcting closed timelike curve of 3some virginity.
I'll give you a wave when I pass you aga
Neat, but not relevant to the real world. by Anonymous Coward · 2013-03-09 08:05 · Score: 0

Mathematically interesting, in particular the way they classified the orbits they found, but in terms of real world impact this discovery is of little utility. In general, few systems consist of 3 bodies of equal mass, all co-planar and with non zero angular momentum.
A much more interesting problem is the n-body problem, of which the 3 body problem is a special case. There is a large amount of work being done by Mathematicians and Computer Scientists on simulating the problem, it turns out it lends itself well to parallelisation (and the use of GPUs). The real world impact is mostly on cosmological problems (galaxy formation etc) but can also be applied to fluid dynamics, electrostatic systems etc.
Re:Never thought it would be so hard to have a 3so by Anonymous Coward · 2013-03-09 08:09 · Score: 3, Funny

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 by K.+S.+Kyosuke · 2013-03-09 08:09 · Score: 4, 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.

--
Ezekiel 23:20
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 08:10 · Score: 0

How can you call yourself a scientist if you don't experiment?!
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 08:16 · Score: 0

The one that *usually* keeps scientists awake at night is, "how can I get my theoretical girlfriend and her theoretical cute roommate into bed at the same time?"
FTFY
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 08:27 · Score: 0

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

Let's see. All scientists have difficulty getting laid. Check.
All blacks are violent gang members and obsessed with basketball.
All Jews are materialistic, greedy penny pinchers.
All whites are oppressive slave-owners.
All women are fickle and can't drive.
All Asians have small penises and tiny breasts.
All Americans are stupid and fat.
All English have shitty teeth.
All Hindus have sexual feelings towards cows.

Oh wow stereotypes are so much fun! Course we COULD be hypocritical bastards and get offended at some of those. Glad we're better than that around here!
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 08:35 · Score: 0

Other than the whites, yeah, pretty much.
Re:Oh, you're talking about THAT three-body proble by K.+S.+Kyosuke · 2013-03-09 08:40 · Score: 5, Funny

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
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 08:57 · Score: 1

No wonder you never get laid.
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 09:25 · Score: 0

Well, at least they've already solved in for a spherical girlfriend in vacuum.
In a non-accelerating frame of reference and well above the Planck scale in Euclidean space-time. On a wet Tuesday afternoon.
Re:Oh, you're talking about THAT three-body proble by godrik · 2013-03-09 09:29 · Score: 1

And they wont accept numerical solution: http://xkcd.com/613/
Re:Oh, you're talking about THAT three-body proble by Kreigaffe · 2013-03-09 09:29 · Score: 1

+1 Depressing Reality

--
... still waiting for this free-as-in-beer free beer I keep hearing about. :|
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 09:30 · Score: 0

What does your mom have to do with anything?
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 09:31 · Score: 0

I suppose so. Most of the scientists I know have settled on a two-body solution. (They're married.)
Re:Oh, you're talking about THAT three-body proble by wonkey_monkey · 2013-03-09 09:32 · Score: 1

"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.
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-09 09:37 · Score: 0

You trying to kill a cat?
vacuum by itself. by Anonymous Coward · 2013-03-09 10:26 · Score: 0

re: Well, at least they've already solved in for a spherical girlfriend in vacuum.
;
Well, there are some men-folk that use the vacuum alone as a substitute for the girlfriend. Vacuums suck, eh? ;>)
I have one name for you by Anonymous Coward · 2013-03-09 11:41 · Score: 0

Karl Frithiof Sundman
At least a beginning by DCFusor · 2013-03-09 12:25 · Score: 1

I've been told by software simulation vendors that no way can their stuff - even if it was running on every supercomputer on the planet for years, could solve the 10e19 body problem I have simulating a fusor's emergent behavior. The math guys have let us down here in science-ville. And if you can't even really do it feedforward for 3 bodies that only attract (vs ions, electrons, charge exchange, and neutrals) I don't have any hope of it being done for my field in my lifetime.
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!
1. Re:At least a beginning by Anonymous Coward · 2013-03-09 16:12 · Score: 0
  
  I've been told by software simulation vendors that no way can their stuff - even if it was running on every supercomputer on the planet for years, could solve the 10e19 body problem I have simulating a fusor's emergent behavior. The math guys have let us down here in science-ville. And if you can't even really do it feedforward for 3 bodies that only attract (vs ions, electrons, charge exchange, and neutrals) I don't have any hope of it being done for my field in my lifetime.
  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.
  A terrabyte is only 10^12 bytes. Assume each particle could be simulated in a byte (unlikely). Now you need a 10 billion terrabytes of memory (not disk) just to represent the variables unless you want to swap them in and out of disk continually. For each time step you're going to have to involve each particle. so that's 10^19 calculations you have to do just for one time step. Dude if you are relying on this coming about in your lifetime, you're going to need a brand new method, and it probably won't be as accurate. Even observing that many particles is going to present similar problems. If you're doing it in the lab you then need to observe macro behaviour or specific particles. That is unlikely to change in your lifetime.
Re:anonymous coward discovers new way to first pos by Anonymous Coward · 2013-03-09 12:33 · Score: 0

Rule 34 confirmed... redefining "skeletons in the closet".
Re:Oh, you're talking about THAT three-body proble by martin-boundary · 2013-03-09 12:46 · Score: 1

Or for that matter, keeping the girlfriend out of the bed if you're called Sheldon.
Rocheworld by Anonymous Coward · 2013-03-09 15:35 · Score: 0

I thought one of the Flouwen had already solved that problem (I think it was Clear+White+Whistle)
See groundbreaking work by Klaatu et al. by 91degrees · 2013-03-09 20:26 · Score: 1

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
This is of course ...the by John+Allsup · 2013-03-09 20:55 · Score: 1

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 ;-) ).

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John_Chalisque
Stability of the solutions by Framboise · 2013-03-09 21:47 · Score: 1

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.
1. Re:Stability of the solutions by Required+Snark · 2013-03-09 22:20 · Score: 1
  
  From the article:
  
  The next step for the Belgrade physicists is to see how many of their new solutions are stable and will stay on track if perturbed a little. If some of the solutions are stable, then they might even be glimpsed in real life.
  
  The authors are, in fact, smarter then you. They are well aware of this issue. RTFA. You just make yourself look stupid when you post the obvious.
  My sig says it all:
  
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2. Re:Stability of the solutions by Framboise · 2013-03-10 02:24 · Score: 1
  
  Did I say they were not aware? To me the authors look amateurish because checking stability is rather trivial once you know how to integrate ordinary differential equations.
  The other aspect that should be said is that in such hamiltonian systems periodic orbits are dense in phase space, but most of them are unstable. So actually one should expect an infinity of such orbits, most of them are not interesting for practical applications. So the minimum the authors could have checked stability before publishing rather unsurprising results.
3-body by Anonymous Coward · 2013-03-10 02:36 · Score: 0

Facinating. Like a 3-D spirograph
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-10 04:12 · Score: 0

Stereotypes are not about "ALL". They reflect the perceived average of a group. So of course, not all Scots are thrifty, but there are many who are, and there are scientists that do not have difficulty getting laid, but for your typical scientist it might be difficult.
Did the authors forget some known solution work? by waterbear · 2013-03-10 04:33 · Score: 1

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 body lagrange problem by peawormsworth · 2013-03-10 15:57 · Score: 1

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.
2-body problem by Anonymous Coward · 2013-03-10 21:19 · Score: 0

http://bash.org/?818078
Re:Oh, you're talking about THAT three-body proble by Anonymous Coward · 2013-03-11 01:14 · Score: 0

YM "how can I get my girlfriend and her cute roommate into bed with each other, so I can get some work done?"
Re:Never thought it would be so hard to have a 3so by RivenAleem · 2013-03-12 04:50 · Score: 1

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.
Re:Oh, you're talking about THAT three-body proble by Dabido · 2013-03-13 02:11 · Score: 1

Sorry, how did the scientist get a girlfriend? You lost me there.

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Sure enough, the cow costume was hanging up next to the superhero outfit and sailors uniform. (S,Spud)