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One of my favorite webcomics, Saturday Morning Breakfast Cereal, once made a joke about Xia's five-body configuration (comic here). I went looking for what it was talking about and found our article on the Painlevé conjecture, to which I added a redirect-with-possibilities. As an aside, the article could use some TLC; the most glaring problem is that it introduces variables without saying what they represent.
Anyway I was trying to figure out where this infinite energy was supposed to be coming from. My best guess so far is that the five bodies are idealized as point masses, which means that the gravitational energy released as you let two of them approach one another grows without bound. This of course would make them black holes in our actual universe, so that energy wouldn't be available, but in the universe of the comic, I guess this wouldn't be a problem (I've never thought very deeply about what happens to general relativity as c approaches ∞, so I'm not sure about that). But in any case there's no new energy appearing that wasn't there before, so the comic's claim that "the universe collapses" seems wrong.
No, really, I actually do have a sense of humor. I just want to know if I've understood this correctly. Does anyone have a different understanding? --Trovatore (talk) 19:50, 20 April 2024 (UTC)
While we now know that noncollision singularities exist, several mysteries remain. Any partial listing has to include whether n = 5 is the cut-off for this surprising behavior, or whether the four-body problem can propel particles to infinity in a finite time. Can, for instance, Anosov’s suggestion be carried out? Are there planar examples with small n values?" This implies IMO that Xia's construction is non-planar. I think the sketch of the construction also implies this: the orbits of the pair of point masses m1 and m2 are said to be parallel to the x-y plane and highly elliptical, while m3 moves along the z-axis. The orbits of the pair m4 and m5 are also orthogonal to the z-axis, with their major axes shown at an angle to those of m1 and m2 in the accompanying figure. --Lambiam 12:52, 23 April 2024 (UTC)
How hard would it be to construct it from satelitees? Zarnivop (talk) 22:41, 25 April 2024 (UTC)