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The Michelson-Morley* experiment from the 1880's also showed there were problems with classical Newtonian dynamic (and there was the problem of the incompatibility between Maxwell's equations and Newton's paradigm on the theoretical side).

This would have been enough for at least special relativity but once you get special relativity, general relativity is the logical next step in your investigations. I don't think the "no Mercury anomaly timeline changes by much.

*Michelson-Morley experiment wanted to measure the speed of light using one of the coolest measuring tool ever, an interferometer. They got a problem because the speed of light did not change when the interferometer was moving.

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In order to rotate their interferometer, they floated their experiment on a vat of mercury. Which makes it even cooler.

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