Mercury's orbit

Can one explain the perihelion precession of Mercury’s orbit with Newtonian gravity? What would be needed for this explanation? Please keep in mind that at the time of Einstein’s derivation (happy birthday, Prof. Einstein!) there was no real observational need for general relativity.

for bonus points: What’s the order of magnitude of the perimelasma shift (point of closest approach to the black hole) precession of the stars orbiting the black hole at the centre of the Milky Way?