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A comment on An atlas of periodic solutions to the three-body problem. Parent comment

Re:An atlas of periodic solutions to the three-body problem by twnettytwo on Monday September 14, 2026 @09:04AM (#49696175)
One of the necessary conditions here is that the three objects return to their exact initial position, and so does the centre of mass. Initial conditions with non-zero momentum must trivially be ruled out. But this doesn't stop them from having velocities perpendicular to the initial plane that cancel out perfectly, so this doesn't refute the assertion that the planes keep changing.
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Re:An atlas of periodic solutions to the three-body problem by btilly on Monday September 14, 2026 @11:36AM (#49698772)
Sorry, but this is a word salad.

Most of the solutions always have non-zero momentum, including in the initial conditions. And https://numericaltank.sjtu.edu.cn/three-body/three-body.htm includes periodic solutions that move in all three dimensions.

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Re:An atlas of periodic solutions to the three-body problem by drdeca on Monday September 14, 2026 @02:13PM (#49701368)
They presumably meant non-zero total momentum. If the total momentum were non-zero, then the center of mass will be moving in a straight line, and will not return to where it began, and therefore the orbit would not be periodic.
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Re:An atlas of periodic solutions to the three-body problem by PaulHoule on Monday September 14, 2026 @02:38PM (#49701793)
Big picture the center of mass momentum is concerned and it does not matter if the system as a whole is moving up or down or to the right or the left. Like the Earth is basically orbiting the sun in an ellipse [1] so far as the sun is concerned and from the viewpoint of the solar system not care so much that it is moving around the galaxy unless we are interested that orbit being perturbed by other stars that we pass near over millions and milions of years.

[1] ignoring the parameters of that ellipse changing slightly and slowly thanks to the other planets

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Re:An atlas of periodic solutions to the three-body problem by btilly on Monday September 14, 2026 @03:02PM (#49702188)
Oh. That makes sense. Yes. The total momentum has to be zero.

All of the things in the solution can constantly have momentum.

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Re:An atlas of periodic solutions to the three-body problem by twnettytwo on Monday September 14, 2026 @03:48PM (#49702882)
Oh sorry, yeah - I wasn't fully awake yet when I wrote it. As a sibling comment mentioned, I was talking about the total momentum. Anyway, it was in response to GP's assertion that GGP may be correct if "we're centered on the CG", which doesn't make sense because the CG can't move.
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