Show HN: Browser-based interactive 3D Three-Body problem simulator

[jgchaos]

Features include:

  - Several preset periodic orbits: the classic Figure-8, plus newly discovered 3D solutions from Li and Liao's recent database of 10,000+ orbits (https://arxiv.org/html/2508.08568v1)
  - Full 3D camera controls (rotate/pan/zoom) with body-following mode
  - Force and velocity vector visualization
  - Timeline scrubbing to explore the full orbital period

The 3D presets are particularly interesting. Try "O₂(1.2)" or "Piano O₆(0.6)" from the Load Presets menu to see configurations where bodies weave in and out of the orbital plane. Most browser simulators I've seen have been 2D.

Built with Three.js. Open to suggestions for additional presets or features!

[emmanueloga_]

Tried writing an electrostatic particle simulator in Turbo Pascal 7 with BGI as a teen, a handful of particles before it crawled. Then saw a galaxy collision sim on a CD-ROM magazine disc handling thousands of bodies smoothly. Thought it was assembly tricks.. now I'm sure it's algorithmic (avoiding N**2 runtime) but never dug into the specifics. Are charges vs gravity sims essentially the same n-body problem?

[physicsguy]

There's two ways of doing it, I implemented them both in my PhD and didn't have a ton of fun doing it.

(a) There's a method that works well for monopolar sources (gravitational + electrostatic particles) called the Barnes-Hut method. You effectively divide space up into a quadtree (2D) or octree (3D), and in each cell work out the center of mass / total charge. You make particles in "nearby" cells (using a distance criterion that can be adjusted to speed up/slow down the simulation in a trade off with accuracy) interact directly, and far away cells you just use the center of mass to work out the interaction between any given 'far' particle and the particles in that cell. The method is O(N log N) but in practice, this is 'good enough' for many applications.

(b) uses a more rigorous technique called the Fast Multipole Method which is O(N), where rather than just using the center of mass or sum of charges, you expand the potential from particles out into higher order components which captures the distribution of particles within each cell. This also means you can capture more complex potentials. The downside is that this is a nightmare to implement in comparison to the Barnes-Hut method. Each cell has it's own multipole expansion, and it is 'transferred' to work out the additive contribution to every 'far' cell, calculating a 'local' expansion. Typically people use the most compact representation of these potential expansions which uses Lagrange polynomials, but this is a pain.

[egorfine]

EGAVGA.BGI

Oh this brings memories. I have tried to create a little bit of 3D→2D renderer in TP 6.0 but precision was never enough for nodes to not fall apart and 80286 speed was too slow to render anything meaningful except maybe a cube.

[hermitcrab]

>Are charges vs gravity sims essentially the same n-body problem?

The force falls off as the inverse square of distance in both cases. So they are essentially the same problem. Except that charge can attract or repel and gravity (as far as we know) only attracts.

[wcrossbow]

They might have been using the fast multipole expansion method

[ralferoo]

One thing I'd never really considered before is how frequently bodies get ejected at high speed from the simulation, especially as the number of initial bodies is increased. Suddenly made me realise that the "big bang" which previously seemed a bit of a random and magical theory (obvious question is why would the universe be expanding from a single point when gravity would be immense) now seems a lot more plausible without needing any "magic" to justify it.

[hermitcrab]

Some of the high speed ejections might be due to the approximations used. You can see this with a simple time-stepper when the forces get massive when 2 bodies get very close and that force is then applied for the whole timestep.

[constantcrying]

I doubt that most (if not all) are physical. This happens since these are considered as point masses, which can not collide. Instead of a collision you get extremely high forces, which add another layer of unphysical results as the large numbers cause numerical problems.

Relating any of this to the big bang is not appropriate at all.

[layer8]

The universe didn’t expand from a single point in the Big Bang, that’s a common misconception: https://lweb.cfa.harvard.edu/seuforum/faq.htm#m9

https://lweb.cfa.harvard.edu/seuforum/questions/#:~:text=EVO...

https://ned.ipac.caltech.edu/level5/Peacock/Peacock3_3.html

[voxleone]

Yes, in real world 3-body systems tend to “decay” into a two-body system + one escaping object.

[iso1631]

The universe isn't really expanding from a single point though, not in the sense that objects were flung away from that point into a vacuum like the objects in this simulation

[oskarkk]

Looks very nice!

I think I found a bug: after pausing, moving a body and unpausing, I cannot move the camera. Changing "follow" to something and back to "none" helps.

[jgchaos]

This should be fixed!

[TMEHpodcast]

This is really lovely work! Simple to use, surprisingly solid, and just a pleasure to poke around with. The fact it runs in the browser is a bit of magic on its own.

One idea for later might be a few preset systems, such as Alpha Centauri or other known three-body systems. It would give people a quick way to drop into something real before they start making chaos of their own.

Anyway, cracking project.

[jgchaos]

Thanks so much, really appreciate it! I’ve been focusing the presets on stable or interesting solutions that aren’t tied to real systems, but adding a few real examples like Alpha Centauri would fit in nicely. I’ll keep that on the list for future updates.

[phkahler]

How about a perturb button so those special stable orbits can be nudged just enough to destabilize them.

[drsopp]

It destabilized after a few minutes on my phone.

[JKCalhoun]

Pause, choose a body, tweaks its mass, resume.

[HeliumHydride]

Suggestion: add a preset for a configuration of the Painleve conjecture. https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture

[westurner]

Will this simulate the sun and planets of the solar system?

Do these models of n-body gravity predict the perihelion in the orbit of Mercury?

Newton's does not predict perihelion, GR General Relativity does, Fedi's SQG Superfluid Quantum Gravity with Gross-Pitaevskii does, and this model of gravity fully-derived from the Standard Model also predicts perihelion in the orbit of planet Mercury.

Lagrange points like L1 and L2 are calculated without consideration for the mass of the moon.

Additional notes on n-body mechanics: https://westurner.github.io/hnlog/#comment-45928486 Ctrl-f n-body, perihelion

[westurner]

More notes on CFD, spiceypy, Navier-Stokes, quantum fluids, and SQG: https://news.ycombinator.com/item?id=44383829 :

> this model of gravity fully-derived from [~~the Standard Model~~ QFT] also predicts perihelion in the orbit of planet Mercury.

And also:

>> "Perihelion precession of planetary orbits solved from quantum field theory" (2025) https://arxiv.org/abs/2506.14447 .. https://news.ycombinator.com/item?id=45220460

Planetary orbits are an n-body problem. GR, SQG, and Gravity from QFT solve for planetary orbits

[nhatcher]

This is amazing! Nicely done!

I did something similar, mostly 2D here:

https://www.nhatcher.com/three-body-periodic/

(Mine is just unfinished)

[jgchaos]

Thank you! Your 2D version is great, I love seeing how different people approach this stuff. As for integrators, I currently only have Velocity Verlet and RK4 (can change in the advanced settings). I started with just Verlet, but to get some of the presets to behave properly I ended up needing RK4 as well. I’ve been thinking about adding adaptive methods next, but I'll take a look at the methods you've got listed too. Everything is still running in plain JS for now. I started moving some of the work into web workers but haven’t finished that part yet.

[nhatcher]

I would be very curious to compare notes on the integrators you used. How good do they perform in general?

In the avobed shared you can go to the settings a pick an integrator. I did the integrators in wasm although I suspect js is just as fast.

Color me impressed! I love the ammount of settings you can play with. I still need to understand what happens whe yu add more bodies though.

[tetris11]

what the heck? are those three orbits genuinely symmetrical in 2D or did I misinterpret

[joshdavham]

Nice work!

Were you by any chance inspired to make this because of the three body series by Cixin Liu? Or were you moreso just inspired because the simulation/math/physics are interesting?

[jgchaos]

Thanks! The Three-Body series definitely helped spark the idea, and the URL is a little nod to the books. I also took some simulation classes back in college, so the math and physics side pulled me in too. It’s crossed my mind that it could be fun to add a kind of Trisolaran mode that tracks a small planet and how habitable its position is throughout the orbits.

[notaurus]

I think the URL is telling

[thrance]

There is also this fun website: https://labs.sense-studios.com/threebody/index.html

Simulating a four-body problem from the point of view of a telluric planet being juggled around by three stars. It's supposed to emulate the evolution of trisolarans from the "Three Body Problem" novel by Liu Cixin.

[gorgoiler]

I didn’t realize something until I used this simulation: with three bodies you can eject one body in one direction and the barycentre of the remaining two in another. This means that compared to the original frame of reference you have an orbiting pair that moves.

It’s one of those things that seems so obvious and yet actually seeing it is a really important step in understanding.

[layer8]

There are animations of how the solar system as a whole moves through space. (The solar system isn’t stationary within our galaxy.) The planets therein are forming spirals around the trajectory of the sun in a similar fashion.

[lutusp]

> Open to suggestions for additional presets or features!

Anaglyphic (red/cyan) 3D rendering would be nice. I've created a lot of anaglyphic 3D apps over the years, but they're no longer very popular -- I suspect it's the goofy glasses one must acquire and wear.

But a true 3D view of an orbital simulator like this greatly increases its impact and tutorial value.

[jgchaos]

I do not currently have a set of those glasses so I can't test it, but three.js has this and it's pretty easy to add. There should be an "Anaglyph 3D" checkbox at the bottom of the configuration settings. Let me know if you are able to test it out.

[ge96]

Oh one question I have, when I messed around with ThreeJS line width was a problem, these curves look pretty nice/thick on mac, maybe that was updated recently. (lines as in orbit path)

ThreeJS is awesome btw, I exported a GDB file I think from a CAD program and imported it into ThreeJS/able to animate each part pretty cool.

[thomasikzelf]

You might be using the webgl lines (LINE_STRIP), those are always thin. The other way is to build a mesh that looks like a line (which Three.js also has functions for). select the line type here to see the difference: https://threejs.org/examples/?q=lines#webgl_lines_fat

[jgchaos]

I'm using https://threejs.org/docs/#Line2 which does support variable thickness - you can change this via the Trail Thickness slider. I think older versions did have some issues with line width.

[buf]

I spent a long time playing with the sim. Nice work.

Most of the random data sets that I ran ended up with a two body system, where the third body was flung far into space never to return. However, some of these were misleading. I had one running for 15 minutes at 5x, and the third body did eventually return.

[lutusp]

> However, some of these were misleading. I had one running for 15 minutes at 5x, and the third body did eventually return.

That's not misleading. Real three-body orbital systems show this same behavior. Consider that such a system must obey energy conservation, so only a few extreme edge cases lose one of its members permanently (not impossible, just unlikely).

Ironically, because computer simulators are based on numerical DE solvers, they sometimes show outcomes that a real orbital system wouldn't/couldn't.

[jgchaos]

It might be fun to add some kind of visualization showing when a body has enough energy to potentially escape the system.

[xnx]

By coincidence, Google demoed an example of Google Search using Gemini 3 Pro to generativity create an interactive UI for the three body problem: https://youtu.be/uYQGrK55gxQ?t=21

[grumbelbart2]

I triggered some bug by pausing the simulation, setting the mass of one of the objects to 29.1, then resuming. The lighter objects bounced into the massive objects a few times, then all three objects were suddenly ejected with a very high velocity.

[ge96]

My dumb question: I thought the whole thing with this is the instability/inability to predict. It starts off with the three bodies locked in to fixed motions? I guess it has to be for the user to start messing around with it?

[teraflop]

Not a dumb question at all!

There is no general closed-form solution to the three-body problem. There are certain specific initial conditions which give periodic, repeating orbits. But they are almost always highly "unstable", in the sense that any tiny perturbations will eventually get amplified and cause the periodic symmetry to break.

It's analogous to balancing an object on a sharp point. Mathematically, you can imagine that if the object's center of gravity was perfectly balanced over the point, then there would be zero net force and it would stay there forever. But the math will also tell you that any tiny deviation from perfect balance will cause the object to fall over. It's an equilibrium, but not a stable equilibrium.

The example at the link demonstrates this. The numerical integration can't be perfectly accurate, due to both the finite time steps and the effects of floating-point rounding. Initially the error is much too small to see, and the orbits seem to perfectly repeat. But if you wait a couple of minutes, the deviations get bigger and bigger until the system falls apart into chaos.

[pixelpoet]

Super cool!

I've been working on some n-body code too, currently native only though: https://www.youtube.com/watch?v=rmyA9AE3hzM

[Ethan312]

The 3D presets are the standout here, especially the ones that move in and out of the orbital plane. The interaction feels smooth, and it’s great to see this level of detail running in the browser.

[chombier]

Nice! It would be interesting to visualize the total momentum vector, IIRC Verlet being symplectic should be good at preserving symmetries, whereas RK4 is good at conserving energy.

[brna-2]

Starting out with the stable preset I had no idea how hard it would be to not make a object slingshot out. But it is a really fun sim, I think I will let my kid play with it.

[Mikhail_Edoshin]

I recently thought that if life supposedly happened by chance then it should be same for the three-body problem: naturally occurred solutions floating here and there somewhere.

[adastra22]

There’s a big one in the sky right now - the Earth-Moon-Sun system.

[carodgers]

Just beautiful. I love that the pattern appears stable but diverges after 5 mins or so. Is the initial state proven to be stable under exact conditions?

[hermitcrab]

Excellent work. Is this based on simple Newtonian gravity applied over a uniform time-step, or something more sophisticated?

[constantcrying]

What you describe is the Euler method, which is well known for being a comparatively bad choice in most situations. The ODE solver can be selected, the default is RK4, which is a Runge–Kutta method of 4th order, it computes the next time step by combining the values at 4 previous time steps.

[JKCalhoun]

For accuracy, time step can get smaller when bodies are closer.

[MrQianjinsi]

So beautiful, I once had a similar idea, and I'm glad to see someone bring it to life

[sbinnee]

I really enjoyed the book series. This is an amazing work! Thanks for sharing.

[deafpolygon]

nice simulator…

one issue i have always had with the n-body calculations is how can you be sure there is exactly n?

[kapitanjakc]

No physics expert but isn't this unpredictable (based on what I saw in series) ?

Amd this does seem predictable, I saw this for almost a minute

[adastra22]

No, and please don’t try to learn anything from that science-free series. The author doesn't even have a Wikipedia-level understanding of what he is writing about.

N-body problems for N>3 do not have exact, closed form solutions. For N=2 the solution is an ellipse. For N=3+ there is no equation you can write down that you can just plug in t and get any future value for the state of the system.

But that is NOT the same as saying it is unpredictable. It is perfectly predictable. You just have to use one of the many numerical solutions for integrating ODEs.

[lutusp]

> No physics expert but isn't this unpredictable (based on what I saw in series) ?

A three-body orbital problem is an example of a chaotic system, meaning a system extraordinarily sensitive to initial conditions. So no, not unpredictable in the classical sense, because you can always get the same result for the same initial conditions, but it's a system very sensitive to initial settings.

> Amd this does seem predictable, I saw this for almost a minute

The fact that it remains calculable indefinitely isn't evidence that it's predictable in advance -- consider the solar system, which technically is also a chaotic system (as is any orbital system with more than two bodies).

For example, when we spot a new asteroid, we can make calculations about its future path, but those are just estimates of future behavior. Such estimates have a time horizon, after which we can no longer offer reliable assurances about its future path.

You mentioned the TV series. The story is pretty realistic about what a civilization would face if trapped in a three-solar-body system, because the system would have a time horizon past which predictions would become less and less reliable.

I especially like the Three Body Problem series because, unlike most sci-fi, it includes accurate science -- at least in places.

[jgchaos]

The link points to one of the stable solutions, and there are actually quite a few of those. The problem is that there’s no general closed form that tells us exactly where the bodies will be in the future, so we rely on numerical methods to approximate the motion. If you hit Reset All a few times or add more bodies, you’ll start to see the chaos

[constantcrying]

The math in the 3 body problem was made up.

Computing the trajectory of a 3 body problem is a comparatively simple task.

The two grains of truth are that the solutions for most starting conditions are not analytic, roughly meaning that they can not be expressed in terms of functions. The other being that the numerical solution to an ODE diverges exponentially.

[mclau153]

Any github?

[jjmarr]

Is this with Gemini 3?

[lutusp]

> Is this with Gemini 3?

An LLM couldn't provide results for a sim like this, compared to a relatively simple numerical differential equation solver, which is how this sim works. Unless you're asking whether a sim like this could be vibe-coded, if so, the answer is yes, certainly, because the required code is relatively easy to create and test.

Apart from a handful of specific solutions, there are no general closed-form solutions for orbital problem in this class, so an LLM wouldn't be able to provide one.

[kona358]

fuck this is so cool. im currently reading deaths end from the three body trilogy and seeing the physical representation is so cool. Makes a certain moment in deaths end seem awesome.

[sim04ful]

LLM spam ? on my HN ?

[alexwebb2]

LLM spam