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This doesn't necessarily have to be a newton's cradle, but the important point is that the length of the chain of spheres is exceptionally large (on the order of light years).

Ignoring the effects of gravity, energy lost through friction or conversion to heat or anything like that, and assume that the chain of spheres are both perfectly spherical and their center of masses are all in a perfectly straight line.

Question, if the first sphere is nudged forward perfectly straight along the line going through the center of masses of the chain, how long would it take before the final sphere in the chain is pushed off the end?

Am I correct in thinking that it should be the length of the chain divided by the speed of light?

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No.
You divide by the speed of sound in the solid spheres, as it is this speed that propagates the information about the push from one end of a sphere to the other end and then to the next sphere. Probably this speed of sound gets modified somewhat by the fact that the spheres are not one single solid body, but have small interfaces.

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