Problem 13 from Chapter 6 of Goldstein's "Classical Mechanics" reads:
Show that the relativistic motion of a particle in an attractive
inverse square law of force is a precessing ellipse. Compute the
precession of the perihelion of Mercury resulting from this
effect. ( The answer, about 7" per century, is much smaller than
the actual precession of 40" per century which can be accounted
for correctly only by general relativity.)
Can someone kickstart my brain with a hint as to what approach I should
consider to solve this problem?