8 ms·
New periodic orbits of the three-body problem
- sp332 9y agoThe site hosting the videos is down. Are there only 6 families (as in the caption at the top) or 600? Are all of the orbits discussed in the article in 2D or are some of them 3D? At the end it says the new CNS technique found only 243 new families, so how were the hundreds of other new ones found?
- sova 9y agoCNS from the article, " clean numerical simulation" enabled them to find 243 more than what the computational power was capable of finding with a lossy representation of periodicity. In other words, the strength of the machine using old-style algorithms for detection would have gotten 357+ solutions, and their use of CNS which cleans up the math a lot for the supercomputer helped them find an additional 243 that would have slipped through the cracks.
- davesque 9y agoFrom a complete layman's point of view, I wonder if it's appropriate to think of a three-body system as somehow irreducible. In other words, maybe a "closed-form" representation of three-body motion can be defined in terms of a finite combination of stable periodic configurations. Anyway, just some musings.
- sova 9y agoIrreducible is a good way to describe the equally-balanced constraint in a 3-body situation.
- trhway 9y agoas we know it is too late, trisolaris fleet is already under way, and the problem with the human science progress is so apparent that it even became a subject of the recent Big Bang Theory episode.
- hellcow 9y agoFor those downvoting, the above comment is a reference to a terrific sci-fi novel, "The Three-Body Problem," which focuses on the same problem discussed in the article.
- lnanek2 9y agofortunately, we live in a dark forest, and need only threaten to shine a light to make the invasion fleet pointless...
- mirimir 9y agoYeah, but that doesn't always turn out so well :(
- musgravepeter 9y agoThe pre-print from arxiv: https://arxiv.org/abs/1705.00527v4 https://arxiv.org/abs/1705.00527v4
- phkahler 9y agoAre any of them dynamically stable?
- Pxtl 9y agoYeah, that's what I'm curious about. Would all of them deviate if they were breathed on wrong? Could any of them occur in nature?
- phkahler 9y agoThere are hints of that concern in TFA where they state the importance of accurate simulations over a long time. On the other hand, a simple two body system is very stable but will diverge in a simulation using a simple Euler integrator.
- Lerc 9y agoSo here's an odd thing. I made a puzzle game for Android where I use Euler, and some of the puzzles require the divergance to work. It has caused a curious phenomenon where some people think the game is wrong, yet the game at no stage mentions what the rules of motion are. I have seen people talk about the puzzles in terms of planets, gravity, massless bodies etc. when in-fact they are just circles that move towards or away from other circles. Theoretically people who can identifiy the Euler intergrator should be able to go "aha! I know what to do now" but so many get hung up on the idea that it is wrong.
- mnw21cam 9y agoAre you allowed to tell us the name of the game, so we can have a look?
- musgravepeter 9y agoThe close encounters will cause issues even in integrators more sophisticated than Euler. One body of research used regularizing integrators to change variables when the bodies get close, to avoid numerical instabilities. This integrator is used in my three body app, to remove the issues due to close encounters. An old blog post of mine has the details: http://nbodyphysics.com/blog/2015/12/08/threebody-2-0/ http://nbodyphysics.com/blog/2015/12/08/threebody-2-0/
- sizzzzlerz 9y agoSo if the problem was first proposed by Newton in the 17th century, how did early investigators simulate the interactions between the bodies up until the electronic computer became available. There are no closed form solutions A.F.A.I.K. so they must have calculated the body's state by hand, I guess. How tedious.
- musgravepeter 9y agoWith some symmetry you can find a couple of solutions, which is what Laplace and Lagrange did. e.g. http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/ThreeBodyProblem.pdf http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/T... The scholarpedia article is a good meta-reference:http://www.scholarpedia.org/article/Three_body_problem http://www.scholarpedia.org/article/Three_body_problem
- tr1ck5t3r 9y agoIt was probably an early form of spirograph that helped solve some of the trajectories.
- rwmj 9y agoMy probably naive intuition says that if you had a system with two "suns" in the centre rotating around each other very closely, and one distant planet rotating about the centre of mass of the two suns, that would be stable surely?
- musgravepeter 9y agoYes, that does work. In the literature this is called a "heirarchical system" The very simplest version is called the Euler problem. Two fixed masses and a third moving in the "dipole field". All the solutions can be explicitly determined (although only in terms of e.g. Jacobi elliptic functions and other elliptics). There's a book "Integrable Systems in Celestial Mechanics" by Mathuna. I recently added the Euler problem to my iOS app ThreeBody: https://appadvice.com/app/threebody-lite/951920756 https://appadvice.com/app/threebody-lite/951920756 Some day I'll get around to adding these 600 solutions...
- fdej 9y agoThe "CNS" is as far as I can tell just the use of a high order Taylor series together with multiple precision arithmetic for solving ODEs. This is a well known method for long term simulation of dynamical systems that has been around for decades. The authors basically imply that they invented this method and were the first to be able to study long term evolution of dynamical systems reliably because of it. Fair enough if they just weren't aware of previous work (which happens all the time), but it's an oversight that shouldn't have passed peer review. That said, using this method to discover new periodic solutions of the three-body system is a very neat application, which deserves applause!
- spuz 9y agoAre you sure that their numerical method isn't new? The abstract says that the author created it in 2009 and this paper further develops it to apply to the three body problem. If it already existed, can you say why it had not already been applied to the three body problem?
- fdej 9y agoIn fact the more general N-body problem is perhaps one of the most classical uses of high order Taylor methods, in particular for studying the long term stability of the solar system. Here is a paper from 1993: http://adsabs.harvard.edu/full/1993A%26A...272..687L http://adsabs.harvard.edu/full/1993A%26A...272..687L. Rigorous error analysis of Taylor methods for ODEs goes all the way back to Moore's original work on interval arithmetic in the 1960s; in the early 2000s Makino and Berz developed so-called Taylor models which combine rigorous error bounds with accurate long-term propagation of changes due to perturbations in the initial values (see http://bt.pa.msu.edu/index_TaylorModels.htm); http://bt.pa.msu.edu/index_TaylorModels.htm); they used it to study the dynamics of the solar system among other things. R. Barrio and others have published several papers about reliable solution of ODEs using Taylor methods; leading to the development of the TIDES software. See several references listed on http://cody.unizar.es/tides.html http://cody.unizar.es/tides.html. In particular the paper https://doi.org/10.1016/j.amc.2004.02.015 https://doi.org/10.1016/j.amc.2004.02.015 from 2005 investigates using variable order Taylor series with extended precision for the solutions of dynamical systems. The paper http://dx.doi.org/10.1155/2012/716024 http://dx.doi.org/10.1155/2012/716024 from 2012 is specifically about obtaining periodic solutions of dynamical systems using a high order Taylor method with multiple precision arithmetic. Actually, I made the first comment after I checked the second author's earlier paper https://arxiv.org/abs/1109.0130 https://arxiv.org/abs/1109.0130 where they essentially made the claim about inventing "CNS" as the first-ever reliable technique for long-term solutions of dynamical systems, without referencing any of the earlier work I mentioned above. However, I just checked the actual text of this new article on the three-body problem (through sci-hub) and there the authors do cite the earlier work I mentioned above, giving proper attribution to others for the basic ideas behind what they call "CNS"! So all is actually well, and the peer review presumably did work (or the authors found out about the earlier work even before writing the new paper). It is just the press release that is misleading, as usual. To answer your question, I'm not really familiar with the research on the N-body problem, so I can't say why or whether no one tried looking for periodic solutions in this way before. Perhaps no one actually thought of it, or they didn't try since they didn't expect to find anything, or they didn't have the computational resources, or they just couldn't figure out the details of how to do it (which the present authors did, and deserve credit for). Again, I was not trying to downplay the significance of this work, and finding new applications of existing methods (and making even tiny improvements along the way) is how science progresses. It also happens all the time that methods get rediscovered/reinvented independently.
- ccleve 9y agoI'm halfway through The Three Body Problem, a science fiction novel by Chinese author Cixin Liu. The apparent irrationality of three-body orbits is central to the story. So far, it's excellent, both as science fiction and as social commentary on contemporary China.
- zem 9y agoamazing series! book 2 is probably the most mindblowing sf novel i've read since brin's "startide rising"
- sova 9y agoHave you read Nexus yet?
- ChuckMcM 9y agoThat would be more literally mind blowing :-) but I can heartily recommend it.
- westoncb 9y agoI'd second this recommendation: Nexus is one of the most interesting and entertaining sci-fi novels I've read in recent years. I'd heard the sequel was not so good—anyone have an opinion?
- photojosh 9y agoI loved the whole trilogy, but that may very well be because I just love the concepts in the story.
- zem 9y agoyes, and i liked it, but it wasn't nearly as stunning as the three body trilogy was.
- shpx 9y ago(minor spoiler) in my opinion, any book that violates the theory of relativity is not science fiction, it's a fantasy novel set in "space". You can't transmit information faster than light using quantum entanglement. https://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics https://en.wikipedia.org/wiki/Faster-than-light#Quantum_mech...
- powertower 9y agoIs there an upper limit on how many different periodic orbitals a 3-body system may have?
- ChuckMcM 9y agoGenerally if you could prove that there was, or that their wasn't, you would probably win the Fields Medal at least.
- forkandwait 9y ago> Today, chaotic dynamics are widely regarded as the third great scientific revolution in physics in 20th century, comparable to relativity and quantum mechanics. Really??
- alanbernstein 9y agoI've never heard such a thing, but if you think of "chaotic dynamics" as responsible for the dramatic improvement in weather prediction, it might start to make sense.
- deleted 9y ago[deleted]
- twic 9y agoI wonder if that tells you something about the author's age. Chaos theory was the next big thing in the '80s and '90s - recall that Jeff Goldblum played a chaos theorist in Jurassic Park in 1993! It seems much less exciting today. I think it gave way to string theory, and now we have AI (yet again).
- woodandsteel 9y agoString theory is unproven, and AI is a technology, not a scientific theory.
- weerd 9y agoHere is an article that shares the opinion and gives an overview of key ideas. https://arxiv.org/abs/1306.5777 https://arxiv.org/abs/1306.5777 It seems like in the late 80s and early 90s this topic was very hot, then became a fad. You can find many books and papers that all have basically the same content (Lorenz/Henon attractors, logistic map, Mandelbrot set). I think it underwent a name change to "complexity science" during the 90s and 00s. I'm not in academia, but I do try to follow the topic because it is truly fascinating and IMO more accessible than quantum or relativity physics because many of the systems involved can be easily programmed/visualized with basic computers.
- est 9y agoThe result videos from the authors is located at http://numericaltank.sjtu.edu.cn/three-body/three-body.htm http://numericaltank.sjtu.edu.cn/three-body/three-body.htm Funny thing is, it can not be opened, because of the 19th national congress. All .edu.cn second-level domain were shutdown for "security reasons"
- yorwba 9y agoHuh. This is the first time I can access a website from China, but not when using a VPN. Here's a random GIF of orbital dynamics for you: https://imgur.com/kzPcL4h https://imgur.com/kzPcL4h (Mirror of http://numericaltank.sjtu.edu.cn/three-body/unequal-mass-data/I.A-0.5-4.gif http://numericaltank.sjtu.edu.cn/three-body/unequal-mass-dat...)
- da-bacon 9y agoYou can find a bunch of n-body solutions, some of which like those in this article are pretty amazing, on Cris Moore's gallery page http://tuvalu.santafe.edu/~moore/gallery.html http://tuvalu.santafe.edu/~moore/gallery.html