3,915 Periodic Orbits Solved for the Three-Body Problem
An atlas of periodic solutions to the three-body problem
The three-body problem has no general solution, but it does have thousands of periodic orbits—three masses that return exactly to their starting positions and velocities after one period. This interactive atlas maps 3,915 such orbits, grouping similar ones into families and letting you zoom, drag, and click to explore each orbit live.
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.
- pixelpoet
I have something similar at https://gravitoy.xyz
With 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=sIfff10hYZA
Example rendered output from Gravitoy (not of a choreography though): https://www.youtube.com/watch?v=N3BwCoiwsGk
Looks like I need to update my catalogue to take into account the many different 2D choreographies from the references on this site!
- cobbzilla
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?
- mr_mitm
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!
- deskamess
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?
- jrflo
Quick, someone tell the Trisolarans!