I have been reading about Lagrange points and Lagrange regions and how we can apply Laplace's equation for these regions however which are the boundary conditions of the Laplace equation at these points/regions?
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$\begingroup$ Welcome to Astronomy SE! Could you add to your question where you've been reading about "how we can apply Laplace's equation for these regions"? If it's in a book, title, author, edition, chapter/page, if published scientific papers then just add links. Also, by Laplace's equation do you mean $\nabla^2 \phi=0$, or perhaps some other equation related to dynamical system behavior in a rotating frame? Laplace was pretty active and probably has a lot of equations out there! The more information you add to your question, the better. Thanks! $\endgroup$– uhohMay 18 at 22:10
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$\begingroup$ See for example Laplace–Runge–Lenz vector $\endgroup$– uhohMay 18 at 22:14
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1$\begingroup$ The vagueness of the question makes it a bit hard to determine what you are asking about. Have you read about the Jacobi integral, which is a constant of motion in the three body problem? $\endgroup$– David HammenMay 19 at 11:00
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$\begingroup$ I think that unless you respond to comments and clarify your question significantly, there's a good chance that close votes for "needs details or clarity" will begin to appear. $\endgroup$– uhohMay 21 at 4:09
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$\begingroup$ @DavidHammen Quanta Magazine's May 16, 2023 New Proof Finds the ‘Ultimate Instability’ in a Solar System Model links to three new papers, the third being A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes which makes for some interesting reading (not that the others don't) $\endgroup$– uhohMay 21 at 4:59
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