Sadly, if Dr. Carlip told you the above example, then you are both absolutely wrong. Mercury's orbital precession was known when there was *only* Newtonian physics, long before the General Relativity Theory, much less Special Relativity came into our knowlege.
But it isn't so important that you were wrong. What's important is that Newtonian physics *did* suffice to solve that particular question (among others).
...And even more important is that Newtonian physics may still be quite viable to solve *other* vexing questions, such as where the orbital planes of our planets are centered, and why.
Again you are wrong. The phenomenon was known but Newtonian mechanics could provide no explanation of it.
If you think otherwise, please post the Newtonian explanation here. We'd all be interested to see it.
The world was in an uproar when Einstein's predictions were shown to match the actual measured precession.
And Dr. Carlip did not tell me this.
--Boris