Physicists Discover a Whopping 13 New Solutions to Three-Body Problem | Hacker News Reader

Physicists Discover a Whopping 13 New Solutions to Three-Body Problem

news.sciencemag.org

207 pointssoofy30 comments

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.

If you want to go directly to a visualization of the solutions: http://suki.ipb.ac.rs/3body/

Beautiful mathematics, but... wow that website could use some antialiasing.

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

I have added all the solutions to my html5 gravity simulation project here: http://jbochi.github.com/planets/

PS: Some of the configurations are not stable with my code. I'll try Runge-Kutta.

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.

That's some awesome work!

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.

Thanks! I did not know Stormer-Cowell, but googling it, I've found a comparision to DROMO, suggesting that it's even more stable: http://www.congrex.nl/11c01proceedings/Papers/2225317%20Pela...

I'll try both if I find the time :)

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!

Good times.

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 don't know much about this domain, but I wonder if these close approaches make it less likely that the associated orbit is stable over long times?

Nice work. Have you seen the n-body configurations in this AMS article from a few years ago? http://www.ams.org/samplings/feature-column/fcarc-orbits1

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 really like you simulation.

Consider Bulirsch-Stoer.

https://en.wikipedia.org/wiki/Bulirsch%E2%80%93Stoer_algorit...

Unfortunately, that page only reveals its text through a typing animation this is much slower than my reading speed, so I bounced.

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. :-)

"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."

It's amazing how many things are discovered this way.

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 :)

Is there any simulation online where I can just click to add planets and watch them move around each other? It's surprisingly relaxing...

http://www.nowykurier.com/toys/gravity/gravity.html

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

Here's one a made a while back. http://horuff.me/static/content/grav/

That's /really/ fun, thanks!

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.

Don't watch butterfly one for relaxation. Any life that survived the weird gravity effects in that system would also need nerves of steel.

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?

Wow, that text scrolls slowly...

when it rains, it pours.

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