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Denoting their mean motions by nI, nE, and nG, respectively, we have nI nG ,

nE nE 2

Hence, to a remarkable degree of accuracy, and certainly within the limits of observational error, nI - 3nE + 2nG = 0, a relation first noted by Laplace. The physical cause of resonances such as this is still a subject of debate, but some of its consequences are clear. One effect is that triple conjunctions of the three satellites are impossible, since whenever two of them are in conjunction the third is always at least 60° away.

Another example, though one that has been understood fully only recently, is the 3 : 2 resonance between Neptune and Pluto, discovered in 1965. The

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