A rudimentary simulation of the three-body problem

https://github.com/achristmascarl/three_body

by achristmascarl • 2 years ago

219 115 2 years ago

github.com

Gys• 2 years ago

In this simulation the bodies also collide together. Luckily that never happened in the book.

maelito• 2 years ago

Should a collision conduct to a simulation of a 4 body problem ?

achristmascarl2• 2 years ago

that might just be because of my low resolution gif ;)

SamBam• 2 years ago

I was wondering about this too, but I think they're not colliding. I think they're pulling towards each other and getting tightly pulled around each other so they end up slingshotting and flying back the way they came, in a way that looks like a bounce.

You can see this in the very beginning of the simulation, with the blue and green dot.

Can anyone say if this is actually accurate? It seems like an unintuitive motion to me, but I'm often surprised by how these things work.

achristmascarl2• 2 years ago

i believe you're correct, other (higher resolution) visualizations of periodic orbits show that "wrapping" behavior more clearly.

example from wikipedia: https://en.wikipedia.org/wiki/Three-body_problem#/media/File...

CWuestefeld• 2 years ago

The book is mis-named. Their system was not 3 bodies, but 4 (3 stars, plus a planet). And the system is so chaotic that even that little planet will make a huge difference over time. And even beyond that, the bodies themselves were transformed, having the ability to tear atmosphere away from each other.

marginalia_nu• 2 years ago

Chaotic N-body behavior appears when the bodies have similar mass. In that scenario, every solution is either chaotic or unstable.

The solar system is strictly speaking a 20+ body system. That said, the behavior of the solar system is fairly predictable because the the sun has almost all of the mass, and jupiter has almost all of what remains, everything else is a small correction term. We can to a good approximation calculate the other satellites' orbits around either the sun or the center of mass of the sun-jupiter system.

woooooo• 2 years ago

Luckily??! Could have saved everyone a lot of trouble and kept them in the proper number of dimensions.

aaronbrethorst• 2 years ago

Arguably this was all Mao Zedong's fault.

at_compile_time• 2 years ago

If you want to demonstrate why the three-body problem is chaotic, you can set it up to run a couple hundred very similar simulations in parallel. Just nudge each body by a tiny amount to simulate uncertainty in the initial conditions and watch the resulting configurations diverge as tiny differences become large differences. Rather than points, you get lines of probability that stretch out and wrap around each other. It's quite striking.

Edit: semantics

jovial_cavalier3• 2 years ago

This only demonstrates that the system is chaotic, not that there is no closed form solution.

ncallaway• 2 years ago

But the chaos is extremely critical, since we can’t ever perfectly measure the initial conditions.

So, even having a closed form solution isn’t helpful when computing real world situations.

nyrikki2• 2 years ago

This may be a bit pedantic, the nbody problem is not chaotic, it is harder, having riddled basins.

A riddled basin implies a kind of unpredictability, since exact initial data are required in order to determine whether the state of a system lies in such a basin, and hence to determine the system’s qualitative behavior as time increases without bound. (Note this is different from “chaos,” where very precise initial data are required to determine finite-time behavior.) What is more, any computation that determines the long-term behavior of a system with riddled basins must use the complete exact initial data, which generally cannot be finitely expressed. Hence such computations are intuitively impossible, even if the data are somehow available.

http://philsci-archive.pitt.edu/13175/1/parker2003.pdf

The above post is a good 'example' of sensitivity to initial conditions, and riddled basins do have a positive Lyapunov exponent which is often the only criteria in popular mathematics related to chaos. But while a positive Lyapunov exponent is required for a system to be chaotic, it is not sufficient to prove a system is chaotic.

If you look at the topologically transitive requirement, where you work with the non-empty open sets U,V ⊂ X....riddled basins have no open sets...only closed sets.

With riddled basins, no matter how small your ε, it will always contain the boundary set.

If you have 3 exit basins you can run into the Wada property, which is also dependent on initial conditions but may have a zero or even negative Lyapunov exponent and is where 3 or more basins share the same boundary set...which is hard to visualize, non-chaotic, and nondeterministic.

Add in strange non-chaotic attractors, which may be easier or harder than strange chaotic attractors, and the story gets more complicated.

Sensitivity to initial conditions is simply not sufficient to show a system is chaotic in the formal meaning.

But the 3 body problem's issues do directly relate to decidability and thus computability.

mistermann• 2 years ago

This only demonstrates that the system is chaotic, not that there is no closed form solution.

This seems a bit off, it seems like[1] an implicit assertion ("only(!) demonstrates") that it is not possible for a system that lacks a closed form solution in fact (beyond our ability to discern) to be demonstrated.

To be clear I'm in no way implying this was your intent (I see it as an interesting "quirk" of our culture)...I'm mainly interesting if you can see what I'm getting at.

As a thought experiment, stand up two instances: one is our current situation (inability to discern, indeterminate), the other where we have (somehow) proven out (or, come to believe we have, reality being Indirect but experienced as Direct, thus: "is "proven", thus: "is") that a closed form solution is not possible: would the second instance "be(!) a demonstration that the system has no closed form solution"? (Thinking more....I think maybe the choice of the word "demonstrate" may very well make a path to seeking the truth of the matter ~impossible to achieve in these sorts of cases, especially if one takes cultural forces[2] into consideration).

[1] Using "pedantry", which few people understand the technical meaning of, and tend to flip flop on depending on what is being considered (precision & accuracy in science/physics is good, precision & accuracy in philosophy/metaphysics is bad - no explanation or justification needed: a Cultural Fact).

[2] Which make the 3 body problem in the known to be deterministic physical realm seem like child's play.

constantcrying4• 2 years ago

This is irrelevant to the unsolvability.

That the three body problem is unstable and that no analytic solution exists are completely independent statements.

The upright pendulum is also an unstable ODE, yet it has an analytical solution.

7373737373• 2 years ago

There is this cool paper "Crash test for the restricted three-body problem" [0], that plots where the third body eventually ends up when dropped from any location. Looks very fractal-like [1][2]

[0] https://scholar.archive.org/work/wnwgyliq5fgtba45k535t5lb5e/...

[1] https://www.semanticscholar.org/paper/Crash-test-for-the-res...

[2] https://www.semanticscholar.org/paper/Crash-test-for-the-res...

jameshart• 2 years ago

‘Strange attractors’: https://en.wikipedia.org/wiki/Attractor

“An attractor is called strange if it has a fractal structure.”

cl3misch• 2 years ago

Thank you for reminding me of this beautiful field of mathematics.

The best textbook I've ever read: Nonlinear Dynamics and Chaos by Steven Strogatz.

mock-possum• 2 years ago

Looks like fluid dynamics / turbulence to me

DrFalkyn2• 2 years ago

E&M and gravity are both n^2 forces, but E&M has polarity, whereas gravity (at least we encounter it) does not.

antognini• 2 years ago

If anyone is interested in playing around with gravitational dynamics I highly recommend the REBOUND library [1]. It has a simple Python interface but under the hood it has a collection of research grade integrators. It came out around the time I was finishing up my PhD in gravitational dynamics, but if I were still in the field it's what I'd be using.

If you're curious what would happen to the Solar System if you made Jupiter 10 times more massive you can pip import the library and find out for yourself in about five minutes.

[1] https://github.com/hannorein/rebound

ricksunny• 2 years ago

Looks awesome. I have a question that might be pedantic but I think you could speak to. Coming from an engineering mindset, I like the use of the term 'integrator' instead of 'solver'. In MATLAB, 'solvers' are used to iterate states of ODE models. But the term 'integrator' is more intuitive to me. Can you speak to the use of one term vs another in the ephemeris community?

constantcrying4• 2 years ago

Solver is a general term, it is just an algorithm which solves a certain problem. You have solvers for linear systems, PDEs, optimization problems, graph problems, etc.

An integrator is an algorithm which allows the numerical approximation of the solution to an ODE, given that the ODE is written in a specific form where it is equivalent to calculating the integral of multiple functions.

dreamcompiler3• 2 years ago

You can solve differential equations by integrating or by differentiating. Real-world integrators were easier to build back when DEs were solved with analog computers. Although "easier" is an understatement: Differentiators have a nasty habit of trying to blow up to infinity, which means you can't really build a good, general differentiator either with analog or digital electronics.

Integrators are much better behaved pets and they don't shit on the carpet. So everybody uses integrators. Integrators have lots of issues too but those can be sufficiently mitigated for many classes of problems. Differentiators are mostly hopeless, feral beasts.

lucgommans• 2 years ago

It's a hundred times less polished than rebound (that readme looks seriously cool!), but in 2021 I also wanted to toy around with orbital mechanics / gravity and couldn't find a quick and easy simulator so I made this to run in a browser: https://lucgommans.nl/p/badgravity/

Since it's so rough on the edges (especially on mobile, initially I was surprised it works at all), here's the steps for the mentioned example of making Jupiter 10x heavier:

    1. Open the scenarios on the left and click play on the inner solar system to load that up
    2. Click the plus on the outer planets to add them in (if it looks like nothing happened: zoom out. Space is big and this is to scale)
    3. Fold out the "bodies" section and alter the mass for "J"upiter. The change is applied live.
    4. Optionally press Restart to restart with the current settings but back at their initial positions and speeds

Making Jupiter 1000× heavier (and fast-forwarding the time in the Simulator controls by 10×) makes it eject Mars from the solar system within one minute, but interestingly Mercury and Venus seem pretty stable around the sun in that configuration

The help/about page (https://lucgommans.nl/p/badgravity/about.html) contains links to all other orbit projects I could find. Seeing Rebound as well as the OP, I should probably add a "libraries" section! Or do you think that should just go with "Software to download" alongside Stellarium and such?

JKCalhoun• 2 years ago

And since A. K. Dewdney is fresh on my mind, he did a Computer Recreations article generally about this (about simulating orbital mechanics) and the clever bit that I remember: you dial the time slice way down as objects got close, you care little when the objects are far apart.

Not a "solution" of course, but certainly an optimization if you're just generally doing gravitational simulations.

PaulHoule4• 2 years ago

See https://en.wikipedia.org/wiki/Adaptive_step_size

xyst• 2 years ago

Netflix really going hard on pushing their IP. It’s like guerilla marketing on steroids.

I jest. Tbh, I didn’t know this was an actual problem. Thanks for sharing.

nonfamous• 2 years ago

This account has been posting simulations of interesting 3-body scenarios for quite a while. It used to be on Twitter but moved to Mastodon. You can check out the archives and play the videos, it’s quite neat: https://botsin.space/@ThreeBodyBot

Hugsun• 2 years ago

I love this bot, thanks for sharing!

hackernewds• 2 years ago

How is it random if the 3 body problems are chosen to have overlapping ellipses that look beautiful

pixelesque• 2 years ago

Rejection sampling? /s

itishappy• 2 years ago

The Mastodon videos have random initial conditions, the GitHub example does not. Are you checking the right link?

rsynnott• 2 years ago

Do you want ghost numbers counting down on your retinas? Because this is how you get ghost numbers counting down on your retinas.

lagadu• 2 years ago

It's ok, I'll just make sure never to measure the CMB for variations.

joe_the_user• 2 years ago

One of the first programs I ever wrote was a simulator for a planet rotating a star with a naive difference equation approximation to Newton's law. I was a bit disappointed to see the planet reliably spiral into the sun.

The main thing is that something like Euler's method (naive iterative approximation) doesn't guarantee conservation of energy. I believe that this is why planetary dynamics are usually handled with Lagrangian equations rather than the naive approximation approach.

Edit: It would be nice to see what the author's system does for two bodies as a sanity check. Three body system was indeed chaotic but still conserve energy - would this system do that?

https://en.wikipedia.org/wiki/Lagrangian_mechanics

forgotpwd163• 2 years ago

Can convert Euler's method to a symplectic integrator utilizing v_{n+1} when computing x_{n+1}. That said although such integrators are widely used (usually of higher order than Euler's) in celestial mechanics, one is not restricted to them. For example Bulirsch-Stoer is also very used even if it isn't symplectic because remains accurate (energy error very low) even on long integrations.

FredFS456• 2 years ago

I think symplectic integrators are typically used, which are derived from hamiltonian mechanics

https://en.wikipedia.org/wiki/Symplectic_integrator

zokier• 2 years ago

It's true that Euler integration is about as crude as you can get, but you don't need to reach to Lagrangians for improvement; something like Verlet integration can already bring dramatic gains with fairly small changes needed.

_0ffh• 2 years ago

Yes, I think it's probably the simplest symplectic method, which would be quite the improvement already.

dekhn5• 2 years ago

It wasn't the first program I wrote, or even a program I wrote, but in middle school a friend wrote a 3-body integrator in BASIC (sun, earth, moon). That single 20 line program shaped my entire world view for a long time (decades), implying to me that we could, if we had powerful enough computers, simulate all sorts of things... even entire universes (which was also an idea that I explored with cellular automata).

It's not a particularly helpful worldview and can often be harmful if you're working with complex systems, or systems that require more than o(n(log(n)) per step, or any number of other real-world problems scientists face.

Many years later I was impressed at how well astronomy packages work (IE, "it's time T at local L, what is the angle of the sun in the sky?") and stumbled across this paper by Sussman: https://web.mit.edu/wisdom/www/ss-chaos.pdf which shows some pretty serious work on future prediction of solar system objects.

forgotpwd163• 2 years ago

simulate all sorts of things... even entire universes

You also assumed that chaos is a measurement problem. You could simulate entire universe if you knew the initial conditions sufficiently enough. There were two nice recent papers[1][2] that showed in order to predict some orbits you'll need an accuracy less of Planck length or else some systems are fundamentally unpredictable.

[1] https://arxiv.org/abs/2002.04029 [2]: https://arxiv.org/abs/2311.07651

bufferoverflow3• 2 years ago

if we had powerful enough computers, simulate all sorts of things

In reality, we're having a hard time precisely simulating even two atoms interacting, with all the quantum effects, diffraction, gravity (however minuscule), etc.

Our universe is surprisingly detailed.

64-bit floats aren't even close enough to precisely simulate real world. What's the precision of the mass of an electron? What's the precision of its coordinates or motion vectors? Maybe plank length for coordinates, maybe not. What about acceleration? Can it be arbitrarily low? An electron's gravitational field from a billion light years away should theoretically affect us (in time).

PeterisP• 2 years ago

Would it make sense to explicitly implement conservation of energy?

I.e. do a simple method but calculate the total energy at the beginning, and at each step adjust the speeds (e.g. proportionally) so that the total energy matches the initial value - you'll still always get some difference due to numerical accuracy issues, but that difference won't be growing over time.

comicjk• 2 years ago

The method you describe would be an example of what is called a "thermostat" in molecular dynamics (because the speed of molecules forms what we call temperature). Such adjustments to the speed can definitely paper over issues with your energy conservation, but you still have to be careful: if you rescale the speeds naively you get the "flying ice cube" effect where all internal motions of the system cease and it maintains its original energy simply by zooming away at high speed.

https://en.wikipedia.org/wiki/Flying_ice_cube

danAtElodin• 2 years ago

Nicely done! We were playing with this concept as well, in case it's useful to compare notes together: https://app.elodin.systems/sandbox/hn/three-body

zakhar• 2 years ago

Hah, I did something similar at https://ari.blumenthal.dev/!/-2/-1/three-body after reading the book last year.

Source at https://github.com/zkhr/blog/blob/main/static/js/three.js

airstrike• 2 years ago

Loved your website. Thanks for sharing.

yzydserd• 2 years ago

Also see the source code for the popular ThreeBodyBot [0] as seen on mastodon etc [1]

It contains a numerics tutorial [2] that I found very useful for my use case.

[0] https://github.com/kirklong/ThreeBodyBot

[1] https://botsin.space/@ThreeBodyBot/112200106103679713

[2] https://github.com/kirklong/ThreeBodyBot/blob/master/Numeric... (ipynb)

PaulHoule4• 2 years ago

I noticed that paper they link to was the first one to find new periodic orbits in the three body problem in a long time which confirms what I’ve believed for a long time which is that nonlinear mechanics is badly underresearched.

sameoldtune• 2 years ago

There’s a saying in mathematics circles which I’ll butcher here: “everything is either a linear system, reducible to linear systems, or unapproachable.”

Think about how bad we are at analytically solving “simple looking” diff-eqs and the above statement starts to sound too true.

PaulHoule4• 2 years ago

Exactly. Finding a few hundred periodic orbits is a lot of hard work but you don’t have the glory of having “solved” something. Because of that kind of thinking there are many unanswered questions which are ignored because they don’t seem to be part of some masterstroke.

nico• 2 years ago

This is great! Thank you

In college, a long time ago, I wrote something like this, for n bodies, but in c++ and OpenGL

More recently I’ve built something similar in python

For anyone interested in this, I recommend this Wired article that goes from the 2 body problem to n, with simulations and code that run on the browser: https://www.wired.com/2016/06/way-solve-three-body-problem/

maxglute• 2 years ago

Would be neat if there's planet level visualization in Space Engine like in the show where you see the suns whizzing around and enviroment freeze/burn.

adamredwoods2• 2 years ago

This isn't planet level, but shows surface: https://universesandbox.com/

adamredwoods2• 2 years ago

Also check out: https://universesandbox.com/

https://twitter.com/UniverseSandbox/status/17709221751443007...

a_gnostic• 2 years ago

Not to forget https://www.kerbalspaceprogram.com

zamadatix• 2 years ago

KSP doesn't actually do > 2 body simulations allowing the paths to follow closed form solutions. This is why you have an abrupt orbit change between bodies instead of just a freeform path. There is a mod "Principia" which adds this functionality in but bewarned it makes the game very different to play!

wkat4242• 2 years ago

KSP even while simplified is so amazing.

I've never gotten very far but the one thing it did manage to impress extremely thoroughly on me is "space is hard". And it's like 5x easier in KSP than on earth lol.

Also it showed me that that ever recurring thought of "why don't they just..." is usually pretty misguided.

I really respect how they managed to make this fun and so incredibly educational at the same time.

fayalalebrun• 2 years ago

A few years ago a friend and I made something similar to universe sandbox, though only with the gravitational simulation part: https://github.com/fayalalebrun/Astraria

Surprisingly enough the jar still runs without issue. Something which probably would not be the case for linux binaries, but maybe for windows.

melondonkey• 2 years ago

Looks like Pokemon Jirachi

mhkeller• 2 years ago

Adding a svelte three-body animation by rich harris https://svelte-cubed.vercel.app/examples/trisolaris

QuantumG• 2 years ago

I've used the NAIF SPICE toolkit (https://naif.jpl.nasa.gov/naif/toolkit.html) which includes the Yarkovsky effect and such, important for small bodies.

MrCheeze• 2 years ago

If, like me, you are suddenly curious what would happen if you added a small fourth body: https://youtu.be/WrahPSY9pf0

asdfman123• 2 years ago

This is nothing like what I remember from the book!

jxy• 2 years ago

Probably try to implement a much better integrator. Some energy preserving higher order integrator should serve a lot better.

dreamcompiler3• 2 years ago

If you want to take the next step up in accuracy and cleverness, investigate the work of Mr. Runge and Mr. Kutta.

pizza• 2 years ago

If you want a good read that (to summarize it quite tersely) takes the idea of 3- or n-body simulations and goes very far indeed with it (i.e. why there is something rather than nothing), I highly recommend checking out Julian Barbour's The Janus Point.

mafuku• 2 years ago

I've always read about how astronomers, especially after Newton, could predict the movement of the planets with incredible precision, yet n-body problems are so infamously complex and hard to solve, even now. Why is that? Is it simply that the mass of everything except for the sun is just so negligible?

aoanla• 2 years ago

N-body problems can't be analytically solved. However, you can still compute integrals into the future (with some acceptable error), you just need to step through all the intermediate states along the way

In the case of the solar system, yes, it helps that the Sun is much more massive than everything else (and then Jupiter is 4 times more massive than Saturn, the next biggest) - you can go a long way to a "reasonable" solution by starting with the 2-body solution if only the Sun affected each planet, and then adding in the perturbation caused by Jupiter and Saturn. (In fact, that's how we predicted the existence of Neptune, by noticing that there were extra perturbations on Uranus beyond those, and hence another massive planet must exist, far enough away from the sun to only significantly affect Uranus).

DrFalkyn2• 2 years ago

IAMAP, but n-body problems result in non-linear partial differential equations, to which only a few special cases are known, and even that case its do to simplifications, e.g., treating planets as point masses and ignoring tidal forces, or ignoring the pull of the planets on the Sun, (or on each other).

One such case where a solution is known is the Lagrange point of the Earth-Moon-Sun system (and similiarly for other points) https://en.wikipedia.org/wiki/Lagrange_point But in reality, they exist only as an approximation. They aren't truly stable.

My understanding the way to calculate spacecraft, asteroid, etc. trajectories is just through a discrete simulation.

Like f you don't know how to solve the antiderivative of a given function, you can still calculate the integral since you know the value of the function.

constantcrying4• 2 years ago

For almost any differential equation there is no analytical solution for it's initial value problem. That the n-Body problem behaves that way is unsurprising and poses no inherent challenge to making predictions.

Computers can easily solve initial value problems for most ordinary differential equations. They integrate them, calculating an approximate solution after every small, but finite step.

Getting an approximate solution to the 3-Body problem can be achieved in around 20 lines of python, without having to use any libraries. It is a remarkable simple and effective technique.

piuantiderp• 2 years ago

You can solve it numerically using Finite Differences. Basically using linear approximations

rcxdude• 2 years ago

To add to the points from others: 3+-body systems are generally chaotic, so you cannot predict arbitrarily far into the future, but the solar system is reasonably well-behaved in that manner, so the timescales are long, but we don't know where the planets in the inner solar system will be in their orbit in ~5-10 million years (as in, that's the timescale where the error bars for the position in the orbit span the whole orbit). Of course, if you care about more precise predictions then the timescales are shorter: eclipse predictions more than 1000 years in the future are likely to be quite inaccurate.

octachron• 2 years ago

Predictions of the solar system state are accurate only on "short" periods. The solar system is chaotic, and predicting its state after few million years is no more possible that predicting the weather for next year. This does not preclude making very accurate on short period.

Note that n-body problems are not particularly complex or hard to solve compared to other chaotic systems. In many ways, the existence or nonexistence of closed-form solutions is mostly a distraction: it merely reflects our choice of primitive functions and there is no sets of primitive functions that is stable for addition, multiplication, composition, inversion and integration. Typically, even the simple integral ∫ eˣ/x dx cannot be decomposed into more elementary functions.

But that doesn't matter in practice, because we are already using numerical approximation to compute primitive functions that are not implemented in hardware. Using numerical solvers to compute solutions to ODE is not so different. A good illustration of that point is that there is an analytic solution for the 3-body problem (in the form of an infinite series in t^{1/3}). But this solution is useless for computing orbits because it has bad convergence properties. In other words, it is better to use a numerical solver rather than stick to the analytical solution. And a similar phenomenon exists for polynomial equation of degrees 3 and 4: the exact formula is numerically unstable, and its better to use a numerical solver when one wants a numerical solution.

huksley• 2 years ago

I was wondering why it called a three-body problem (at least as it presented in Liu Cixin novel). There is actually at least 4 bodies (3 suns and a planet), right? I suppose the planet will affect the movement of the 3 suns.

kqr• 2 years ago

No, it's just three. The reason it's a thing – as far as I understand – is that solving analytically for one body is trivial: it's stationary. Solving analytically for two bodies is possible but takes some calculus. Three bodies have chaotic behaviour and need to be simulated.

belst• 2 years ago

in the novels there are 3 suns, so it is 4 bodies.

The simulation doesn't get easier with 4 tho, so 3 body problem is still a good name. Also the planets mass is "almost" negligible compared to that of the suns, so I assume simulating (+ occasional correcting) 3 bodies is already a good approximation.

forgotpwd163• 2 years ago

Probably a misnomer. And issue isn't really about the planet affecting the movement of the 3 suns (its mass can be considered deligible compared to them) but how the suns affect the movement of the planet. Essentially they're looking for a solution to the restricted 4bp rather the 3bp.

micheljansen2• 2 years ago

I've been re-reading the trilogy lately and it also lead me to search for some three-body simulations. I noticed that a lot of them are simulating only a 2D space. Any good (animated) 3D simulations? Best I've been able to find so far are https://demonstrations.wolfram.com/ThreeBodyProblemIn3D/ and https://labs.sense-studios.com/threebody/index.html

yieldcrv• 2 years ago

isn’t that story a 4-body problem?

micheljansen2• 2 years ago

Not a physicist, but apparently the planet does not really have enough mass to matter: https://www.reddit.com/r/threebodyproblem/comments/15cgd51/i...

badrunaway• 2 years ago

What does three body problem tell us about our universe? It surprises me that universe by its nature ended up with such smart safeguards to disallow predictability via computation.

zelphirkalt• 2 years ago

Is there some way of determining, whether the orbits, given some starting parameters, _at some point_ will become stable? I probably mean periodic. And I probably mean mostly periodic, with only slight deviation from orbits. And I don't necessarily mean that we can calculate/predict what they will look like in a stable form.

This reminds me of Langtons Ant, that has very simple rules, but at first still seems very chaotic. Then after some number of iterations it just shoots away in a regular endlessly regular repeating pattern. "Order came from chaos." So it makes me think, maybe there is not a way to tell, whether the orbits "stabilize" at some point, but maybe they will, and we simply don't know when or how to tell?

alex_duf• 2 years ago

Completely selfish plug, but it's not very hard to implement, so here's my implementation using p5js: https://editor.p5js.org/alexduf/full/c-iSj_b4p

you can play around with the code. Clicking generate a new solar system. There are a few constants you can adjust at the top of the file.

A rudimentary simulation of the three-body problem

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