An atlas of periodic solutions to the three-body problem

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!

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!

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?

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?

Quick, someone tell the Trisolarans!

So proud to see the prof. who oversaw my masters thesis has their paper (and solutions) featured here. :D

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.

I assume some of the solutions are stable against small perturbations, while others are not. That would be interesting to see.

Very nicely animated. Also didn’t know there can be so many stable solutions for 3 body problem

This is an amazing looking website, I like it a lot.

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.

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 name on this page.

Wow. This is really cool. Deterministic chaos is my absolute favorite in all the nerdy things there are to like in the abstract world.

This is pretty cool to be able to see all the varieties.

I'm going to spend so much time on this website, very good work

SPIROGRAPH, lowtech!

Fantastic UX, so smooth even on smartphone ! Congrats

This is beautiful. And fast!!!

Oh, this is so nice, but man is it hugely frustrating not to be able to rotate the thing in 3D.

Or did I not find the controls?

very ai but also pretty cool. wheres the data source? could I find my own periodic solution?

I assume this is at least partially vibe coded, but this is the first good vibe coded website I've seen. Amazing work.

Is this assumed to be 2D? I was going to ask if there are any observed examples of 3 body equilibrium observed in nature.

cool!