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What is the difference between Sphere of Influence and Hill sphere?

Wikipedia's definition of Hill sphere is: An astronomical body's Hill sphere is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit ...
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Maximum Amplitude of a Lissajous Orbiting Object in a L4 or L5 Position

I stumbled on The Lagrangian points during some wikipedia reading. After looking at the gravity contours, I naturally come to the conclusion that the L4 & L5 should have a wave pattern and then ...