And here I was thinking two points always lie in a common plane.
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Yeah but are two *moving* points in the same plane at all times? That requires conservation of angular momentum.
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Actually this comes directly from the symmetry of the problem, which is a very fundamental property. It then works not only with Newtonian gravity but also in General Relativity. The conservation laws (as angular momentum) come from the underlying symmetries.
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Both are right, angular momentum conservation is precisely a statement about symmetries (Noether’s theorem) We just view symmetries as ‘more fundamental’
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Remember, it is their own plane, try introducing a third planet? And...?
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n-body problem.
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