Comment by raincole
9 hours ago
Why would the plane keep changing? If there are only these three objects, won't the vectors of their gravitational pull to each other all be on this plane too?
9 hours ago
Why would the plane keep changing? If there are only these three objects, won't the vectors of their gravitational pull to each other all be on this plane too?
If you define the initial conditions such that their relative velocity is zero or parallel to the plane, yes. But that's not the case in general.
Each orbit is a spinning top. You pull on a top from the side, it's spin axis precesses.
It’s an arbitrary plane, chosen at each moment just so you can flatten it
Not from an external point of view, as you might have a momentum component perpendicular to that plane
(but yes I think you might be right if we're centered on the CG)
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.
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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