Earlier quoted context omitted.
Was the orbit of Mercury (or any other astronomical observations) important for the discover of Relativity. My understanding was that experimental impetus for relativity was the Michelson–Morley experiment, which was an in-lab experiment, not an astronomical observation. General relativity was then developed on a purely theoretical basis. That it was able to explain Mercury's orbit was a nice bit of empirical confirm…
> Was the orbit of Mercury (or any other astronomical observations) important for the discover of Relativity. For general relativity, yes. > My understanding was that experimental impetus for relativity was the Michelson–Morley experiment This was one of the results that pointed the way to special relativity. It had nothing to do with general relativity. > General relativity was then developed on a purely theoretical…
Yes. I assumed that reproducing Newtonian gravity in the classical limit would be considered theoretical, as we had a solid theoretical understanding of Newtonian physics. Implicit in that would be a bunch of empirical evidence; but Einstein wouldn't need to explicitly think about the details of what evidence supported Newtonian mechanics (beyond the general understanding that it was all in the classical limit).
> Not if the differences between its predictions and the predictions of the previous theory (in this case Newtonian gravity) are only measurable in astronomical observations at the time the new theory is proposed.
Such a theory is not "useful", for many definitions of useful. Astronomical observations allowed us to verify Relativity earlier than we otherwise would be able to; but eventually technology advanced to the point where we could conduct satellite based experiments to directly confirm it. The theory was not practically useful until we had this technology.
> Technology can of course be developed on a purely empirical basis, if you're prepared to make a lot of mistakes along the way that you wouldn't make without a good theoretical foundation. If it hadn't been for the knowledge of relativity on the part of the scientists involved, the GPS satellites probably would have been launched without any capability for adjusting their clock rates.
Its not like we launched the entire GPS constellation then just hoped it would work. Before launching the GPS constellation, we launched the experimental Timation satellites to act as a proof of concept. Difficulties with maintaining accurate clocks in orbit would have been noticed then (if not sooner).