Over 150 new families of Newtonian periodic planar three-body orbits

Has anyone explored the computational nature of Newtonian gravity? That is, if you carefully setup a set of masses in some manner, and let them interact though their gravitational pull, what kinds of things can you compute? Is gravity Turing complete? Is it a push down automata? Finite state machine? Can you use choreographies like these, coupled together to create register machines, or simulate cellular automata?

This paper seems to be missing some related work, for instance Carles Simó.<p>Greg Minton created a computer-assisted proof system for showing that there must exist a choreography with parameters within a certain distance of some given approximate parameters. This isn&#x27;t just a matter of more floating point precision; it certifies that there is a critical point for action of the right kind. <a href="http:&#x2F;&#x2F;gminton.org&#x2F;#gravity" rel="nofollow">http:&#x2F;&#x2F;gminton.org&#x2F;#gravity</a> and <a href="http:&#x2F;&#x2F;gminton.org&#x2F;#cap" rel="nofollow">http:&#x2F;&#x2F;gminton.org&#x2F;#cap</a><p>Greg Minton also has a bunch of proved choreographies at <a href="http:&#x2F;&#x2F;gminton.org&#x2F;#choreo" rel="nofollow">http:&#x2F;&#x2F;gminton.org&#x2F;#choreo</a>

Here&#x27;s an older visualization for other interesting planar n-body choreographies:<p><a href="http:&#x2F;&#x2F;www.maths.manchester.ac.uk&#x2F;~jm&#x2F;Choreographies&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.maths.manchester.ac.uk&#x2F;~jm&#x2F;Choreographies&#x2F;</a><p>...plus a link to the animations for the linked paper:<p><a href="http:&#x2F;&#x2F;numericaltank.sjtu.edu.cn&#x2F;three-body&#x2F;three-body.htm" rel="nofollow">http:&#x2F;&#x2F;numericaltank.sjtu.edu.cn&#x2F;three-body&#x2F;three-body.htm</a>

How stable are these orbits? Do they tend to degenerate into simpler forms over time? If they&#x27;re stable, do we see any asteroid triplets in such configurations? Why not?

Reminds me of Cixin Liu&#x27;s &#x27;Three Body Problem&#x27;, about alien invaders that want to escape their own chaotic three-body planetary system by taking over ours... The first two books of the trilogy are just spectacular science fiction.

Guess I have some work to do to update my mobile app Three Body! (It presents galleries of solutions up to those found in 2013, and lets you explore your own initial placements)<p>iOS: <a href="https:&#x2F;&#x2F;itunes.apple.com&#x2F;us&#x2F;app&#x2F;threebody-lite&#x2F;id951920756?mt=8" rel="nofollow">https:&#x2F;&#x2F;itunes.apple.com&#x2F;us&#x2F;app&#x2F;threebody-lite&#x2F;id951920756?m...</a> Android: <a href="https:&#x2F;&#x2F;play.google.com&#x2F;store&#x2F;apps&#x2F;details?id=com.nbodyphysics.threebodylite" rel="nofollow">https:&#x2F;&#x2F;play.google.com&#x2F;store&#x2F;apps&#x2F;details?id=com.nbodyphysi...</a><p>The authors of the new solutions have published all the initial conditions - so hopefully it won&#x27;t be too hard. (Although they use an 8th order RK integrator and the one I have is a regularizing Bulirsch-Stoer integrator).

I wonder how can authors claim such great certainty in their results, after all, it is all based on number crunching. Some floating point error, and similar is bound to creep in...

What are the implications of this?<p>Until 2013, only 3 or so solutions to the 3-body problem are known. Now we have over 150 solutions. This sounds incredible, given how fundamental the problem is, but So what?<p>Will this change astrophysics - for example - in any way?

It&#x27;d be fascinating to see a harmonic analysis of these orbits. They seem (qualitatively) to exist on some edge of order and chaos.

Holy cow, some of those are complex. The equations of motion must be arcane.

I, for one, welcome our new Trisolarian overlords!