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Why is the L3 Lagrangian point not perfectly stable? In the circular restricted three-body problem (CR3BP or CRTBP) an object at any of the first Lagrange points L1, L2, L3 is unstable mathematically. Yes, a ball at the exact top of a hill will sit there, but any tiny offset in position or tiny nonzero velocity will lead to it accelerating down the hill. As ...


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L1, L2 and L3 are saddle points in the effective potential of the gravitational field in a rotating frame of reference. That is if you combine gravity (of Earth and Sun) with the centrifugal force on an object that is moving around a point at one orbit per year you find that there are three saddle points, and these are L1, L2 and L3 If an object is in orbit ...


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