Seconded. Amusing terminal effects, but really poor visualization of the thing I actually care about, which is these new orbits. They should look into CDF or three.js
awesome work! If you get all configurations to be stable (maybe decrease the dt in addition to RK?) you can thank the scientists by sending a link to your work, I'll bet they'll be very happy with such pretty renderings.
Hah, my high school memories - a graphical gravity simulator project for my CS class, leaking energy due to the use of a very naive integrator (the Euler method for ODEs).
You might want to try Stormer-Cowell, it's sort of a gold standard in orbit simulation.
UPDATED: Hmm, now that I think of it, this would probably profit more from a variable step method. Some of the close approaches seem to be really close for a fixed-step integrator.
Heh, that's exactly what I made with a friend for a physics project in high school. We didn't even consider different methods--we used the Euler method because it's the most intuitive. I didn't even know it had a name!
This is very helpful, thanks! It's interesting to see how many 'near misses' there are in the new solutions (e.g. butterfly_1) -- a point that wasn't clear to me from the original plots.
I find it surprising that some configurations are as stable as they are with the simple integration method. At least (if I'm reading this correctly) you calculate positions and velocities at different times.
I know! We're so spoiled. I wanted to see WebGL animations of the real space orbits. Some nicely textured planets or something. All I got was an animated gif and the cheesey typewriter text thing. :-)
As someone with an undergraduate level education in physics I find this stuff pretty cool. Having a number of homework exercises for my graduate level classical mechanics courses end with the fact that the solution degenerates into a three-body problem, and therefore an unsurmountable task, this kind of news gives me hope :)
thanks. watching that is strangely satisfying. it's like the path of the planets has been predestined, yet it still feels somehow random. kind of like life
It doesn't work, though. On firefox 19.0.2 (archlinux), it seems to detect clicks shifted a good bit to the right (maybe 100 pixels?), and a little bit down. It looks like it's using whole-screen coordinates without correcting for the position of the canvas.
It would also be cool if you could give some quantitative data below - the total amount of kinetic/potential energy would be fun to watch, for instance. (And graph it.)
You also seem to be using an inverse-square law, which is "incorrect" in a 2D universe, but I suppose it makes it seem more natural.
"What we did was the most simple-minded thing that you could do," Dmitrašinović says. "We were shocked when we discovered all these things, and we were even more shocked when we discovered that they had not been discovered before us."
After seeing the animations and reading the article, I am somewhat skeptical about the stability of these orbits. They are rather long and have plenty of near-misses. Even if they are stable in the sense of a pure 3 body problem, at close distances stars don't behave as point objects anymore. Instead, you have things like tidal forces and matter around stars.
Additionally, all the near misses makes it difficult to calculate the orbits, even with variable step size.
You've been downvoted, and I don't know why, because you raise a worthwhile point ("will these be observed in real systems?"). In addition to the non-ideal factors you mention, there may also be the possibility of mass exchange in the close approaches.
Those are some awesome orbits. There don't seem to be any solutions where all three bodies are in the ecliptic? If so does that mean we would only see these in the wild in a planet/star "capture" situation?
31 comments
[ 2.8 ms ] story [ 71.5 ms ] threadPS: Some of the configurations are not stable with my code. I'll try Runge-Kutta.
You might want to try Stormer-Cowell, it's sort of a gold standard in orbit simulation.
UPDATED: Hmm, now that I think of it, this would probably profit more from a variable step method. Some of the close approaches seem to be really close for a fixed-step integrator.
I'll try both if I find the time :)
Good times.
I really like you simulation.
https://en.wikipedia.org/wiki/Bulirsch%E2%80%93Stoer_algorit...
It doesn't work, though. On firefox 19.0.2 (archlinux), it seems to detect clicks shifted a good bit to the right (maybe 100 pixels?), and a little bit down. It looks like it's using whole-screen coordinates without correcting for the position of the canvas.
It would also be cool if you could give some quantitative data below - the total amount of kinetic/potential energy would be fun to watch, for instance. (And graph it.)
You also seem to be using an inverse-square law, which is "incorrect" in a 2D universe, but I suppose it makes it seem more natural.
Additionally, all the near misses makes it difficult to calculate the orbits, even with variable step size.