Greg Neil wrote:
No amount of fiddling around with classical mechanics can
produce the correct result.

Now that's for sure at least an exaggeration, as I know for fact that
in 1898 Paul Gerber derived from Newtonian mechanics the same equation
as Einstein for the perihelion, and that he calculated c from it with
high accuracy. But I don't have his paper so I don't know the details
of how he did it. I only have a copy of the original end part as
printed in the book Einstein plus two, and Gerber found c = 305500
km/sec.

Harald