New periodic orbits of the three-body problem

The &quot;CNS&quot; is as far as I can tell just the use of a high order Taylor series together with multiple precision arithmetic for solving ODEs. This is a well known method for long term simulation of dynamical systems that has been around for decades. The authors basically imply that they invented this method and were the first to be able to study long term evolution of dynamical systems reliably because of it. Fair enough if they just weren&#x27;t aware of previous work (which happens all the time), but it&#x27;s an oversight that shouldn&#x27;t have passed peer review.<p>That said, using this method to discover new periodic solutions of the three-body system is a very neat application, which deserves applause!

I&#x27;m halfway through The Three Body Problem, a science fiction novel by Chinese author Cixin Liu. The apparent irrationality of three-body orbits is central to the story. So far, it&#x27;s excellent, both as science fiction and as social commentary on contemporary China.

&gt; Today, chaotic dynamics are widely regarded as the third great scientific revolution in physics in 20th century, comparable to relativity and quantum mechanics.<p>Really??

The result videos from the authors is located at <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><p>Funny thing is, it can not be opened, because of the 19th national congress. All .edu.cn second-level domain were shutdown for &quot;security reasons&quot;

The site hosting the videos is down. Are there only 6 families (as in the caption at the top) or 600? Are all of the orbits discussed in the article in 2D or are some of them 3D? At the end it says the new CNS technique found only 243 new families, so how were the hundreds of other new ones found?

The pre-print from arxiv: <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1705.00527v4" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;1705.00527v4</a>

Are any of them dynamically stable?

From a complete layman&#x27;s point of view, I wonder if it&#x27;s appropriate to think of a three-body system as somehow irreducible. In other words, maybe a &quot;closed-form&quot; representation of three-body motion can be defined in terms of a finite combination of stable periodic configurations. Anyway, just some musings.

Is there an upper limit on how many different periodic orbitals a 3-body system may have?

So if the problem was first proposed by Newton in the 17th century, how did early investigators simulate the interactions between the bodies up until the electronic computer became available. There are no closed form solutions A.F.A.I.K. so they must have calculated the body&#x27;s state by hand, I guess. How tedious.

You can find a bunch of n-body solutions, some of which like those in this article are pretty amazing, on Cris Moore&#x27;s gallery page <a href="http:&#x2F;&#x2F;tuvalu.santafe.edu&#x2F;~moore&#x2F;gallery.html" rel="nofollow">http:&#x2F;&#x2F;tuvalu.santafe.edu&#x2F;~moore&#x2F;gallery.html</a>

as we know it is too late, trisolaris fleet is already under way, and the problem with the human science progress is so apparent that it even became a subject of the recent Big Bang Theory episode.