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Orbital mechanics (also called astrodynamics) is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft on an orbital or escape trajectory. For the movements of celestial bodies, use [celestial-mechanics], not this.
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Are the Jupiter-Io Lagrange points stable?
Lagrange points are solutions to the three-body problem. Moving among Jupiter's Galilean moons seems likely to be at least a six-body problem, so there is no reason to assume the three-body solutions …