Suggestion: add a preset for a configuration of the Painleve conjecture. https://en.wikipedia.org/wiki/Painlev%C3%A9_conjecture
Show HN: Browser-based interactive 3D Three-Body problem simulator
51–60 of 119 posts
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#52So beautiful, I once had a similar idea, and I'm glad to see someone bring it to life
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#53No 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
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
An interesting corollary to this is that even if the future trajectory of a general 3-body orbit is predictable in theory using numerical methods (and infinite precision calculations), in practice the use of finite-precision floating point means that after some time the trajectory predicted by an ODE solver will diverge from the mathematically-true trajectory. Even symplectic integrators have this problem. More details on the general case of chaos are provided by this insightful blog post:
https://www.stochasticlifestyle.com/how-chaotic-is-chaos-how...
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#54Tried 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?
They might have been using the fast multipole expansion method
[deleted]
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#55Tried 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?
>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.
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#56One 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 w…
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.
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#57Earlier quoted context omitted.
This made me irrationally annoyed, lol. But that was only the start (I've only seen the TV show though)
Seriously there was so much wrong with that book.
There was a lot right with it as well IMHO. It was very original (I've only read the first book so far).
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#58Excellent work. Is this based on simple Newtonian gravity applied over a uniform time-step, or something more sophisticated?
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#59Excellent work. Is this based on simple Newtonian gravity applied over a uniform time-step, or something more sophisticated?
For accuracy, time step can get smaller when bodies are closer.
Re: Show HN: Browser-based interactive 3D Three-Body problem simulator
#60One 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 w…
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.
I don't doubt that the math allows for escape velocities in some interactions. But I am wondering if, realistically, tidal forces might instead shred the bodies before forces were adequate for a body to achieve escape velocity.