Solving the Three Body Problem
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The three body problem is famous for being impossible to solve. But actually it's been solved many times, and in ingenious ways. Some of those solutions are incredibly useful, and some are incredibly bizarre.
Hosted by Matt O'Dowd
Written by Matt O'Dowd
Graphics by Leonardo Scholzer & Adriano Leal
Post Production: Yago Ballarini, Max Willians, Pedro Osinski
Directed by: Andrew Kornhaber
Executive Producers: Eric Brown & Andrew Kornhaber
End Credits Music by J.R.S. Schattenberg: / @jrsschattenberg
Physics - and arguably all of science changed forever in 1687 when Isaac Newton published his Principia. Within it were equations of motion and gravity that transformed our erratic-seeming cosmos into a perfectly tuned machine of clockwork predictability. Given the current positions and velocities of the bodies of the solar system, Newton’s equations could be used in principle be used to calculate their locations at any distant time, future or past. I say “in principle” because the reality isn’t so simple. Despite the beauty of Newton’s equations, they lead to a simple solution for planetary motion in only one case - when two and only two bodies orbit each other sans any other gravitational influence in the universe. Add just one more body and in most cases all motion becomes fundamentally chaotic - there exists no simple solution. This is the three-body problem, and we’ve been trying to solve it for over 300 years.
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Bet this video has had its best viewership numbers yet this past week
You're the only comment less than 3 years old, so probably not :)
Show isn’t popular enough IMO
Oh 100% I'm not even embarassed to admit that series is the only reason I clicked on this 😂
Haha yeah
@@MrGencyExit64 Views != Coments
"We are not impressed, and you're still worms" - Trisolaris
But I'm not afraid of you... Just the sun
the lord does not care
You are bugs!
I’m going to destroy the earth if you try anything. You know that, right?.
"you're bugs!"
"The first to do so was Euler" because of course he was
Job van der Zwan ahaha I thought the exact same thing, whats the adage ‘In mathematics, theory’s are named after the second person who discovers them, otherwise everything would be named after Euler’
Old good Lenny, always good for a theorem!
@@justgame5508 or Gauss. But certainly more often Euler.
Someone could make a KZhead account with Euler's icon and just post "First" on all the math videos
@@alansmithee419 Who publishes ton of material and can compute really well? Euler. Who publishes ton of material and can't really compute? Cauchy. Who doesn't publish and criticize everybody else who does publish? Gauss!
The universe's preferred solution for the Three Body Problem is to eject one of the bodies from the system.
Every time the simulation runs low on RAM, a body is ejected from a trinary system.
Not if one of the bodies is heavy compared to the others.
@@sverkere: That is one of the special scenarios that has been solved.
@@deusexaethera There is also symmetry. If the initial conditions are setup up in a symmetrical way then that symmetry will be respected. Then again ejections will not happen. In a computer simulations one could see an ejection but it is only about chaos and the limited numerical precision or/and poor integration algorithm. These stable zones are well known in electrodynamics for example.
@@sverkere: That is also considered a special scenario because it requires intentional preconfiguration -- or astoundingly good luck -- for such a scenario to exist in the real world.
PBS space time have an amazing effect on me: They both make me feel bad for not pursuing studies in Astronomy (my true passion) and also make me feel good for not having pursued studies in Astronomy
me either
This is exactly how I feel. I study computer science but I find myself picking astronomy and astrophysics related courses as optionals and enjoying them far more than the mandatory computer science courses for my degree. I wonder if I chose right, or if I can still salvage something from my decision
a superposition if you will
I regret not becoming the James Webb Space Telescope :-(
Daniel Medveď if you have a degree you can join in on astrophysics research group. I’m a PhD student right now and my astrophysics friends essentially do stuff like ML on galaxy clusters. Which is just CS stuff. If you’re willing to put in effort to learning the astrophysics lingo and equations you can easily join in on astrophysics research
Pre-modern-day-computer-space-travel is so impressive to me. To calculate that stuff out by hand sounds like hell
fuuuuuuun for some ... 🤔🤪
The spice extends life. The spice expands consciousness. The spice is vital to space travel.
Gotta use all four holes
(1) When planning, for instance, the Pioneer or Voyager or Mariner missions, they would simplify the trajectories to pieces of conic sections. It wasn't perfect, but then it couldn't be perfect anyhow, and the calculations could be done with a slide rule. (2) Also, digital electronic computers -- though weak by modern standards -- already existed before Sputnik.
@@damienmcmurray9786 Wait... whaaaat?
Do not answer. Do not answer. DO NOT ANSWER.
Horrible book and Netflix series with no logic behind it.
@@mabaker have you ever thought that by claiming to author anthropomorphised plot elements that you yourself are anthropomorphising as you still think of and see reality though your biohuman lense. It's honestly a silly criticism if you consider it properly
@@mabakerDepends... cause I loved the series, concept and all.
@@mabaker "Horrible book without logic" said someone who didn't even know the existence of the "rememberance of earth's past" series just one month ago. Netflix's series was horrible and illogical though.
Well, it was done by D&D, so was not unexpected.
It is absolutely amazing to me to learn that Lagrange points were first discovered not necessarily because of their utility or for any reason we find them interesting today, but simply because they represented points in a 3-body system for which it was actually possible to calculate solutions to the problem. I just love how much the branches of human discovery and knowledge feed off of one another - "Here's an interesting way to have a comprehensible 3-body problem! Oh, we can also park space craft in these places, too!"
Euler discovered the 3 collinear points and Lagrange discovered the 2 equilateral points. The 5 equilibria are NOT collectively called the Lagrange points. The media gets this wrong...as per usual. These equilibria are solutions to the equations of motion (written in a rotating frame of reference) when the infinitesimal 3rd body has no motion and stays in place.
well, the L4 and L5 points (the equilateral ones) aren't primarily used for spacecraft but contain "trojan" asteroids, especially for the sun-jupiter system. These were discovered after the Lagrange prediction, but quite a bit before mankind thought about spacecraft. Even earth is now known to have two of these "trojans", and there's an accumulation of space dust there in the Earth-Moon-system. They are only somewhat stable due to coriolis effects. L1, L2 and L3 (the Euler ones) aren't stable, because there's a force away from them if you are the slightest bit offset from them. There are quasi-stable orbits *around* them, though, but for long-term stability you need to put in some effort for station keeping, i.e. course corrections. There appears to be one known L3 asteroid, Crantor, in the Sun-Uranus system, but with large orbit around it and a stability of maybe a few ten thousand years.
@@Engy_Wuck All good points. Interestingly, I would add, the James Webb Space Telescope is located ( purposely ) at L2 . As you say, station keeping, ( using say hydrazine gas jets ), is still necessary, but minimized because of the cancellation of the Earth-Sun gravitational forces at L2 . As well, L2 is an excellent spot for the telescope because it can remain always pointed directly away from the Sun and the Earth, allowing the sensitive instruments to have the darkest possible field of view.
@@GWaters-xr1fv The JW telescope is not located AT the Euler collinear point L2, it is in a 3D HALO ORBIT around L2. The orbit is unstable dynamically (as shown by the mathematics that describe it). Thus, some stationkeeping is required to keep in on the "nominal" (mission) halo orbit. If there is no stationkeeping, the JW will leave the vicinity of its halo orbit and (more or less) take a straight path toward the earth paralleling the earth-sun line. Fortunately, very little propellant is required for this orbit control. Vernier thruster bursts are used to keep JW "near" its nominal orbit. Only several bursts per orbit are needed.
@@walshrd Excellent clarification. Thanks !
6:37 The people who did those calculations by hand _were_ computers. The word computer used to be a job title.
Primarily by women on large scales as it was deemed as menial as typing
Was that because they were.. computing..?
Thank goodness the movie Hidden Figures finally made that fact common knowledge.
And that's why he explicitely says "artificial computers" at 6:35
I think "counter" would have been better.
Just as I was reading The Three-Body Problem by Cixin Liu. Absolute masterpiece! Welcome to the world of Three-Body!
He's a bit weak in characters but man, the science! Absolutely blown away. Infact, the sun radio resonance was so convincing that I had to actually look it up to make sure it wasn't a real thing.
I just looked for that comment.
Now, can PBS Space Time solve the Dark Forest Problem?
@@nitrox5915 please tell me what's the sun radio resonance you're talking about and find it epic Curious child here
The countdown scenes made me genuinely terrified.
"....with Newton's other great invention, calculus." Leibniz grumbles in the corner.
They both did it independently, so Newton is also it's inventor
He's a lawyer, he'll sue
I can't believe the Brits don't have the maturity to admit that Leibniz did a lot of important work in that field. No wonder I'm not subscribed. I guess I'm just envious because Newton invented the universe.
@@dannygjk just ask an american. According to US internet consensus Tesla invented everything from the wheel to nuclear fusion. Probably including sliced bread.
In a video about how approximating the answer can be useful, he is just approximating the inventor of calculus for time.
As many commenters also pointed out, The three body problem is also the title of an amazing sci-fi novel by Liu Cixin... I would definitely recommend it to anyone enjoying this channel. The author mentions some pretty weird and imaginative "applications" of particle physics by advanced alien civilizations. He also mentions a very interesting hypothesis on why we haven't made any contact yet with any alien civilization. Perhaps you would like to comment on this imaginative trilogy?
I need to read this series. Thanks for the suggestion!!
There is a book called “the killing star” in which humanity advances to the point of post scarcity and all is well. Only to be wiped out by a civilization dominated by their own machine intelligence. It is, to my knowledge the first book on the dark forest hypothesis by Stephen hawking iirc.
@@KleptomaniacJames The first book to cover the dark forest is maybe The Forge of God by Greg Bear. The dark forest hypothesis does not come from Hawking though. He expressed fears about aliens, but so have many other people before him. Despite this fear, he still supported efforts to make contact with extraterrestrial intelligence so he clearly didn't believe it.
@@cthulhuwu_ woops
I'm on the 2nd book right now. I think the premise is great and the initial ways that was presented in the first book were really good, but I just dislike Liu Cixin as a writer, and is on multiple occasions saying things that are just scientifically incorrect. He especially has a lot of subconscious biases about people/human nature/society that doesn't make his depictions of those very believable.
[Trisolaris wants to know your location]
I'm in 8 minutes too late
Trisolaris has already sent sophons headed Matt's way
Eeek! A Sophon!
@@fireheadmx I started listening to an audiobook version recently. I am in chapter 7 and still no idea what this book is about. I frequently hear the occasional science buzzwords like "quantum physics", "nanotechnology", etc. that intrigue me and keep me interested but I listen to it when I go to bed at which point I am too tired to listen more than 10 minutes at once and I usually fall asleep.
so close..
Actually, you don't have to handle them separately. Whenever I have a three body problem I just dump them in the same grave.
Yeah me too, it's just easier. Sometimes you need a second grave if they're all fat and you've got up to 5 of them.
The same grave.. .. in a'Dark Forest' maybe?
*FBI WANTS TO KNOW YOUR LOCATION*
Adam Rasmussen Except Luca Brazii - he sleeps with the fishes...
Hol' up!
When 3 bodies eject one of them, it's called a friend zone.
As good a name as any other scientific term. 🤣
story of my life
And the third planet was third wheeling 😝😂
After watching this, it seems like the Trisolarans could have guesstimated their planet's position fairly well.
Especially if they are competent enough to build a planet-sized supercomputer in 10 dimensions and fold it up to the size of proton in 3 dimensions. That math seems like it'd be infinitely harder than figuring out gravitational interactions of three stars in a system.
After years of watching this series, I can actually understand all the mathematical and technical jargon being used. This makes me super happeh! Thanks guys!
I'm like that too. This channel makes me able to pass as an astrophysicist at parties.
@@brokentombot Before or after everyone is wasted as fuck?
@@brokentombot You say it as if it were a virtue. Believe me, being considered a science guy is a huge buzz kill.
@@zwz.zdenek You must hang out with Zoolander.
Congrats - knowledge rocks. :-)
Just seeing the title is giving me PTSD. flashbacks to reading cixin lui's masterwork series. Cleanse well. Hide well.
Snowsnaype imo excellent series tho.
@@opheliapoppy7653 It blew my mind to find out that Obama reviewed the book.
It's a dark forest out there mate!
A well written series. No more need be said
Imagine if trisolaris are real and they found human actually has the answer to 3 body problem. Maybe mankind and trisolaris can have a harmony start.
8:23 His right hand shows that planetary bodies aren't the only masses that bounced back and forth
Most video presenters directly into the camera do ridiculous things with their hands.
I briefly thought about making it a GIF loop. But that would be stupid.
try spealing to a camera. You will feel stupid very quickly😅
“The first was Euler” Me : Of course it was.
7:50 Because Euler has enough stuff named after himself already.
That's just Stigler's law.
@@mina86 Thanks for the share. Didn't know that one.
@@mina86 Not really. We have evidence that Euler was extremely productive.
@@tuele4302 As a layman computer programmer myself, Euler rocks! All real engineers should have a poster of him above the bed.
Massimo O'Kissed Leonard Euler was a truly remarkable mathematician.
Anybody else get super excited that he was talking about the Cixin Liu sci-fi series? If you haven't read it yet you're missing out on one of the greatest pieces of literature, not just sci-fi, but some of the greatest writing I've encountered in modern times. And the plot is positively mind blowing.
Yup. He doesn't write good characters, but culturally that's to be expected in a way. But the ideas, the plot. Whoah, that was something else. Easily one of the best reads of the last decade in my book. In the meantime I've discovered Alastair Reynolds (if you don't know him, but seen Love, Death & Robots on Netflix: he's the author of "Beyond the Aquila Rift" and "Zima Blue"). Started with his House of Suns because I wanted something standalone in case it wasn't my kind of thing. When I was about halfway through the book, I bought the Revelation Space novels as well. If you haven't read him already, look him up, it might tickle you in the same way it did me. ;)
@Auspicious Dog Fur Pattern THANK YOU! I'm on the last book in the series and not looking forward to being done! Are his short stories part of a larger collection?
@Auspicious Dog Fur Pattern Wait whaaaat? Another Three Body Problem book by someone other than Cixin Liu? Isn't that blasphemy? Will check out The Wanering Earth stories, thank you!
I watched this video because of the title lol
Wow - I'm going to have to check this out. The fictional series that has most impressed me to date is "The Dresden Files," by Jim Butcher. Urban fantasy, so if you're not into that maybe it's not for you, but if you are, don't miss out - it is AMAZING. Books 16 and 17 dropped earlier this year - 17 just a few days ago. One word of warning, though - generally speaking each book is a full stand-alone story, but 16 is not. 16 and 17 really tell one complete story, so just go in prepared for that. I found it really good from book #1, but some people don't care that much for #1 and #2. So if you aren't totally impressed by those - don't give up. Try to get at least to book 5 or 6 before you throw in the towel.
Netflix has landed me here
Lol me too
What show?
Haha me also
@@JustSomeGuy-xe2mf3 Body Problem
Me too
I've been watching PBS Spacetime for YEARS and this is the first episode that I was able to follow and understand all the way through to the end.
Quick, someone notify Listener 1379, there may yet be time to stop the fleet...
Shut up sophon
I don't want to live in Australia
Matt O'Dowd is a wallfacer!
@@kevinware3268 Hes already 2D!
Your comment has been deemed highly reactionary! Due to this I can no longer adress you as _Comrade_ And a cadre will show up shortly to take you to a reeducation camp Please do not resist
Matt, you do such a good job, man. Thanks so much for these videos.
This is why I love this channel so much. One episode, I'm exploring the boundaries of what current science can teach us, the next I'm learning the truth about principles I thought I knew from grade school. One question I have: would Sundman's convergent series solution potentially be practically solvable using quantum computing?
Yer smart. I'm so stupid I don't even know how stupid I am.
Almost surely not, but I would have to brush up my complex analysis to be slightly more sure and even then, quantum computing is so new there might be no one in the world with the understanding required to answer your question with certainty, yet.
Well, the PRINCIPLE is pretty straightforward. It's just the numerical complexity that comes in with three significant masses that makes it crazy involved.
Thanks for helping me overcome the Dunning-Kruger effect: I now know much more about what I don't have a clue about.
:-) It is humbling, isn't it? I consider myself a smart person, and it's fair to say that "learning is my hobby." I'm 57 and have been pouring over KZhead and other net material for years, pushing the limits of my physics knowledge and so on. But it's clear that the finish line will forever elude me. Good thing I enjoy it. Maybe it will at least hold Alzheimer's at bay.
0:05 I thought he was gonna said: "Actually, super easy, barely an inconvenience" LOL... Love this channel too...
Easy solutions to the three-body problem are TIGHT!
@@feynstein1004 Wow, wow, wow!
WOWOWOWOWOW
@Carlos So, you have a math for me?
@@feynstein1004 Yes Sir I do...
The double pendulum springs to mind here as a similar chaotic system.
In fact I think this channel used that as an analogy in a related video
In many ways that system is directly comparable to the three body problem. Excellent comparison!
I think it's closely related mathematically as the top fulcrum point forms the third 'body' in a double pendulum?
@@VastinI think so too. Just lock the view to one of the bodies and I assume the rest have exactly the same behaviour as a double pendulum Edit: I just came up with a reason why what I said above is actually wrong. Pendulums are rigid in that they have fixed distances from each other, so they are not exactly the same. My assumption must have been wrong.
Came here from a TED vid on the same topic. Y'all's is way, way better. Thanks for your always-excellent material!
I love the way the ellipse was precessing in the example of the analytic solutions
Before this video, I had only heard of statistical mechanics from the following textbook quote that was being shared as a meme: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."
oh yeah I love these, I am currently studying the subject of differential equations, if you were to make more videos about the interesting uses of them in physics that would make me very happy :)
Right on! I watch both of you guys. More collaborations please!!!
I'm a proud subscriber to both channels. Thank you for all your work.
I like Dr. Lincoln from Fermilab. He's a cool dude
I like his friendly and collegial description of how the two presenters are kindred spirits even though they hadn't met before the collab.
Yeah, I know this one. But I thought it was called "threesome". When you add a third body to a system, the system becomes chaotic and almost always over time one body would get ejected.
that’s why everything changes if you add a black hole to the equation 😂
👁️👄👁️
Yup, just like a love triangle lol
Nicely done. Perfect solutions for conditions that are useless in the normal experience. Except your experiences are way beyond normal.
That's amzing. I have seen already the figuere 8 shaped one and i love it
the best way to survive a three body problem is to dehydrate for an age or two.
I just finished reading The Dark Forest today! This cant be a coincidence Edit: Please don't spoil the novels in the comments
It can. And it is...
@@mina86 and it must.
I have basically accepted Dark Forest as being the truthful answer to the Fermi Paradox. Far as I'm concerned, it's the logical conclusion, however distasteful. Enjoy Death's End!!
Dark Forest is completely useless as a filter, for the reason being that hiding a civilization in space is nearly impossible with decent sensors.
@@sankhyohalder97 hide well. Cleanse well.
you guys are doing really great things for the internet.
I think he answered all those questions in one take. Nicely done.
This. This is what I love about PBSST. Taking a seemingly simple concept and showing how it just isn't while making it's complexity understandable.
Even in nature it's just like Human Love triangle. Two stick together and 3rd one gets ejected.
Lmao u right
Yeah it's the 3 buddy problem.
You just have to stay in the stable Lagrange Points, also known as the Friendzone.
V is for Void Or the figure eight known as a threesome
Fuck, I'm a human rogue planet.
Enjoyed the collaboration and topic. Ty
KZhead algorithm knows me well , suggesting Matt’s videos only if i’m going to sleep
Finally they collaborate! Great things will come of this
Can't wait for more. They are really inspiring each other.
Love the fermilab videos also!
Netflix brought me here
They did well then.
😂 bro I bought the books
Life brought me here
Me too
I personally have not done the three body problem, but I have done the two body and many body (classical and quantum, I do research on quantum many body).. I imagine having a very large object may stabilize the problem.. And now I'm hearing about this as I type it. Great video!
So cool to see cross over videos of space time and fermilab. I watch these videos tirelessly and go to bed at night trying to imagine the true nature of a hydrogen atom
How to solve: 1. Gather a crowd of people 2. Teach them how to roughly simulate how a computer works. 3. Use them for calculations. 4. Success.
It would be a shame if they were forced to dehydrate....
*step 5: profit
You're a slave driver!
Shut von Nuemann
Ok, gonna need like 6 million flags, 3 million people, some horses, maybe some watchtowers? Whatever makes the big guy happy.
8:55 I imagined something like this as I tried a way to figure out a solution; I even put my fingers in a triangle to visualise it. I imagined the three bodies as vertices of a triangle, each side representing its gravitational interaction, with their respective centres of mass being the midpoints of the edges, and the overall centre of mass being the barycentre. I guess the solution would take an integration of the gravitational forces at infinitesimally small time intervals.
i don't know why i keep coming back to this channel; i don't understand a thing! sometimes i leave it on when i go to sleep cause the videos are quite soothing, or perhaps i'm hoping i'll be able to sleep-learn something. like the mozart effect or something or other.
Very informative! Some basics I alrdy knew but with the drawcalls and such really good to know. Just wondering: what are some 2D games that really inspire you artwise and gameplay wise? Just finished Islets and loved how simple yet effective it was drawn.
Matt!!! great episode! It would be awesome if you do a science fact check on the Earth´s Remembrance Trilogy. For example, the Unfolding of the proton on 'The Three Body Problem', the 'Dark Forest' Theory as a solution to the Fermi Paradox, as well as the concept of the Black Domain (from Death's End). Anyway, I also think you'd make a great wallfacer...
None of that is known to possible. "Unfolding a proton" was based off the idea of having many extra dimensions, which are theorized in string theory, but afaik would not be at all similar to Three Body. Their method of instantaneous communication using entangled particles is also incorrect. The Dark Forest theory is possible, and is legit if we assume the axioms to be true. Finally, the black domain would be true if we could slow down the speed of light in a certain area, which is not remotely possible by human standards. Obviously collapsing dimensions is also not based off of known physics. I don't think he would be a good wallfacer. Even the wallfacers that failed were insane geniuses.
@@ultearmilkojohn1145 There's a lot of science in the Earth's Remembrance trilogy that is either wildly speculative or just outright unlikely given our current knowledge of our universe - but its such an incredibly imaginative story, and the way its concepts aggressively play off of the far edges of our current science in such thought provoking ways earns it a welcome seat at the table of sci-fi greats.
@@Vastin Yeah of course, I thought it was insanely well written (and translated), was just responding to that guy's question. I would be interested in seeing a refutation of The Dark Forest theory that doesn't rely on another Fermi paradox solution though
@@ultearmilkojohn1145 There are a number of likely refutations. One is the simple amount of energy and effort that is likely to be required given the physics we DO know, to engage in this kind of silent-killer warfare. The other is that if sublight travel is never trivialized, then the competition for 'space' in the universe is likely to be minimal. DF also assumes that intelligent life is VERY common, which is probably not likely.
In short, if life were to only arise in, say, 1 out of 10,000 star systems, and both FTL and lightspeed travel is essentially impossible, then its unlikely that any species would feel the survival need to colonize more than a handful of systems (due to cost, difficulty, lack of necessity), meaning the need to take an aggressively competitive/paranoid stance is not present. If life were to be so common as to appear in 1 out of 10 systems though, that could get ugly.
"Physics is everything, in Spacetime."
Yea the COMBO !
Actually it's not
@@quicksilver3431 I agree. It's self-evidently obvious that we have free will, and science is not equipped to deal with "uncaused effects." Somewhere in the operation of it all is the place our free will first touches the material world, and science can't quantify the "cause" part of that causal event. The only way science could deal with that would be to consider those effects "random." Oh - wait a minute... ;-)
Strong force and representation of entrophy at stellar scales
Thank you PBS. The answers I was looking for.
Do the three body patterns mapped on a shape sphere have anything in common? Is there any sort of underlying "rule" that they all follow, that if known, would be able to produce any possible orbital pattern?
"… in fact, by many hands." - ahaha I died
@@brokentombot RIP
Interesting! I remember studying the mathematician who thought he discovered a solution to the three body problem, only to find himself wrong, leading to the discovery of chaos theory. Interesting to find a solution is possible and practical approximate solutions too. Good answers with Fermilab!!!
Me reading The Three Body Problem and this popping up on my recommended videos
The sweeping orbits in the graphics remind me of the star orbits we have tracked around our super massive black hole.
My thoughts exactly.
I remember working with the 3rd body problem in college, using my own code & old fortran code. However I limited it to only three bodies...
You should take a look at p5.js and Processing (processing.org). Using that, you can write middle level graphics code and you can programmatically create n-bodies and also make them behave like planets. The simulation will run at
@@SahilP2648 Post this somewhere if you do. I do a lot of coding, but non-scientific.. Would be interesting to see. Except the js part, ..|., js. C++ or C#/.NET or gtfo.
@@mashrien I have coded in Java, python and C#. I don't get why you don't like Java though. C# and Java are pretty similar. I am never gonna touch C++ though. That is the stuff of nightmares.
@@mashrien ok so I did some digging around and I found a project where this guy has implemented a processing n-body simulation, I took the code, ran it and outputted in video format: kzhead.info/sun/fbR_lMt7p3uLlas/bejne.html Processing actually has a tool to convert images to video which I had forgotten about. Full credit goes to him: github.com/mcnuttandrew/n-body-simulator
I remember trying to write a simulator for this in python in high schoold I couldn't figure out an answer for just two bodies that respected conservation of energy.
This is great stuff! Congrats!
I once found myself in a three body problem 😮 as you stated at the end. As I followed the dynamics, I also tried to find solutions. But it came to the same end, as one body evenually got ejected.
1:35 "his other great invention, calculus" ut oh, here we go. 😬 🤣
*Gottfried Wilhelm Leibniz* is typing... *Eudoxus of Cnidus* has joined the chat. *Zu Gengzhi* has joined the chat.
@@nibblrrr7124 *Archimedes has entered the chat*
If i am not mistaken we also have written evidence ancient egyptians had some idea about calculus,so yeah, not really newton's invention. He was a freaking genius nonetheless
@@nibblrrr7124 Gottfried always gets triggered. Isaac already set up a committee consisting of himself, Isaac Newton and Sir Newton and that committee decided that Sir Isaac Newton has priority over GFL!
Just because someone else did it better, doesn't mean that Newton didn't invent calculus.
This reminds me of the book on my bedside, "三體" by Cixin Liu, in English, The Three Body Problem
I keep Death's End in my bedside lmao
This book is amazing.
Love the guest speaker. You should do this more often.
Thank you for this explanation.
Trisolaris fought on the solution for millions of years. Someone gets's solution in 16 minutes.
One win for the bugs, zero for the seething xenos.
My wife pointed out lots of problems when i tried to introduce a third body
Was one of them a dwarf? 🤣
Let me guess, you got ejected.
lol
Was it as dead as this topic?
Have you tried numerical erection? 😂
Great topic , wonderful presentation. Now tell me that all this knowledge is put to good use in particle physics !
Love this channel. Great great stuff
Nice, we should tell the trisolarans
Could a 2-body system be run backwards to determine if there was a third body ejected at some time in the past and, if so, could it's current location/speed/heading be determined?
idk man probably
@@jbonemastaflash6852I second that wholeheartedly
Thank you for your work Matt I love you
Exceptional, thank you!
8:39 Imagine that we discover 3 stars orbiting each other in one of these configurations
It's unstable.
@@u.v.s.5583 why?
@@NoOne-qi4tb Star systems are not isolated, they get perturbed all the time, and many perturbations are significant. So it is not sufficient for an orbit to be asymptotically stable in mathematical sense for it to exist for any prolonged time period in astronomical sense. We might find such a configuration, but then it would be a short lived result of some amazing and very recent coincidence.
@@u.v.s.5583 does like a 1 cm pull every year seriously ruin that?
@@NoOne-qi4tb That not. But where will you find a region in the space in which you don't ever ever get significantly more pull during hundreds of millions of years / billions of years?
thats the best fact about physics xD "we discovered solutions for a big problem : useless solutions, but solutions nonetheless" generations later: "it IS useful afterall"!
Great! One more thing to worry about before I go to sleep!
I had a three body problem once, and I can confirm that moving all of them is is really difficult.
Hey are names are very similar. I am assuming you are a fan of the theories of relativity special or otherwise?
@@relatvity Well, not particularly. Also that's an old name I haven't used for quite some time. (My handle is supposed to be Fervidor.) Though, apparently some people can still see it. I _think_ it has to do with what sort of device you're using.
"The Three Body Problem is perfectly solved, Uselessly, or for seemingly Useless and bizarre orbits." Nice.
8:39 it would be cool if a sci-fi show had solar systems with these kind of configurations.
I would love to read a scifi book based in a figure-8 system. I'd love to see the other systems too, but they look really difficult to easily describe as part of the setting for your novel.
Check out the sci-fi book Three-Body Problem, by Cixin Liu
@@Well_Earned_Siesta That one features the general, chaotic, analytically unsolvable case, which is the main plot point.
Niven's Fleet of Worlds involved a stable 5 body case.
@@normalmighty My first thought on seeing the figure eight system was to imagine what sort of crazy planetary systems are possible. Unfortunately, stars are invariably much larger than planets, so most of the really interesting 3-body solutions are probably impossible. Also, most planets are formed from the same accretion disk as their parent star, ruling out most of the more exotic solutions. _[Edit]_ In case it wasn't clear, the three bodies in the figure eight configuration had precisely the same mass and moved in exactly the same plane. It was stable in the sense of it being periodic and perpetual, but not at all stable in the sense of it being resistant to perturbation, so not really physically possible per se.
Good to see some collaboration with PBS Spacetime and Fermilab
Amazing show Matt/Pbs. And Hi Dr. Lincoln!
Luo Ji save us!
Hmm wow, interesting! Definitely cool to learn about the three body problem, after reading the book "The Three Body Problem." :) Cool that many solutions exist.
I seem to remember a solution to the 3 body problem that involved slowing down time in case a collision occurs (basically the closer the planets are the slower time moves, so the collision only happens in infinity).
This is a much better video than the 5 minute Ted Talk I just watched yesterday on the same topic.
This one kzhead.info/sun/d5xynsuKqWarjZ8/bejne.html
someone send this video to the trisolarins
There’s awesome Matlab simulations you can look up for chaotic systems, for example double or triple pendulums. Comparing two pendulums side by side and slightly changing initial conditions of one of them winds up leading to totally different results just after a few seconds. Pretty cool to visualize it.
This is called Entrainment and they must share a relative mass.
What the hell, Dr. Lincoln?! I wasn't expecting to see you on this channel. :) It was a great surprise, and I'm glad to see two of my happy favorite channels did a "co-lab". >:)
I just solved this the other day with the Runge Kutta method for my computing project in my astrophysics class. It was pretty cool.
Useless trivia: PRINCIPIA ...pre-renaissance pronunciation would be PRINKIPIA. (It means 'beginnings') There I contributed something now i feel less inadequate
No, you're absolutely right. It's bad enough that most contemporary physicists can't pronounce supernovae (hint: it ends with a long E, or even a short a (like tap) if you absolutely must submit to the modern revisionist international phonetics), not a long A, see the _ae_ grapheme for details), and there's no reason to let the Principia slip on top of that. This is what happens when Latin and Greek are removed from the general curricula.
Came here to look for this comment. Glad someone noticed.
What did you contribute?
Isn't it PRINCHIPIA?
@@marius4iasi _Talk:Principia Mathematica - Wikipedia_ en.m.wikipedia.org/wiki/Talk:Principia_Mathematica#Pronunciation
Hi Matt, how come you said that 3 body stable solutions rarely appear in nature? Some of the sphere examples you showed in the video (9:50) look suspiciously like electron orbitals, no? And thank you for all the excellent videos, have been learning a lot from you!
I'm not the OP but I'll try to answer these questions in case you're still interested! Because the three-body system is chaotic, the evolution of the behaviour of the system is very sensitive to initial conditions. Therefore, for a lot of the stable solutions, you need exactly the right initial conditions in order for the system to evolve into this stable orbit. These initial conditions can be replicated exactly in a simulation, but it's rare that they would occur naturally. Regarding the space-sphere example, the orbits within the sphere only show a representation of the system's configuration (in this case, two of the internal angles of the triangle of bodies), rather than the actual physical orientation of the system. The bodies themselves are not actually following those orbits. Hope this is helpful!
The three body problem is not impossible to solve. We speak of an ode (or a system of odes) as either having a closed form solution or not. The 3-body problem does not have a closed form solution. But it does have a solution that can be numerically approximated. Here's a simple example of an ode that doesn't have a closed form solution: u'=e^x².
Glad to see PBS made the transition from TV to KZhead