Community shares related work and extensions
3 Sep 14 9:37 AM · 9d ago · 2 posts · 9 comments · 2 sources · development 3 of 4
Commenters begin sharing related projects, including a similar tool at gravitoy.xyz with discoveries of up to 11-dimensional choreographies, and questions emerge about which specific solutions are included or excluded.
“The three-body problem has no general solution, but it has thousands of periodic orbits: three masses falling around each other and arriving, after one period, at precisely their starting positions and velocities.”
Three Body Orbits site · hn ↗threebodyorbits Site creator
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I have something similar at https://gravitoy.xyzWith it I have discovered up to 11-dimensional choreographies, see https://lycium.github.io/hyperchoreography/ and code at https://github.com/lycium/hyperchoreography/Exposition video: https://youtube.com/watch?v=sIfff10hYZAExample rendered output from Gravitoy (not of a choreography though)…
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I took graduate orbital mechanics from Roger Broucke. He was one of my best professors. Not only did I learn from him what orbital elements were, but he also taught me the Runge-Kutta numerical integration method.I didn't learn until years later that he had discovered several of the periodic solutions to the three-body problems. You'll see his…
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It’s my understanding that most 3-body orbits are unstable; minor random perturbations will set them adrift.Are there any 3-body orbits with a natural resonance that maintains the shape of the orbits?If so, how large of a disturbance can the most-stable 3-body orbit withstand?
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I was surprised that I couldn't find any simple-looking solutions in this atlas. At first I was looking for Lagrange orbits, but maybe it makes sense to exclude them if zero-mass bodies aren't allowed. I think the equilateral triangle ought to be included though.
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I guess I misunderstood or mis-scoped the problem. Does the 3-body problem state 'the general case' has no solution, but that does not preclude some configurations from having a solution?
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It's well organized, the animations are smooth, and it looks beautiful... I'm not sure what to do with the information, but it's mesmerizing and fascinating. Great find!
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Very cool visuals and site! Could I make a suggestion: You show the masses (1,1,1), but not the starting positions, which alter the course of events too.
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I assume some of the solutions are stable against small perturbations, while others are not. That would be interesting to see.
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So proud to see the prof. who oversaw my masters thesis has their paper (and solutions) featured here. :D
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Very nicely animated. Also didn’t know there can be so many stable solutions for 3 body problem
All 4 developments of Three Body Orbits atlas catalogs 3,915 periodic solutions →
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