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Leigh, I don't quite know what you're up to with your particular
version of this orbital precession problem and its seemingly
manually inserted counter-terms in the potential function, but I
thought I would point out that it is possible to map the exact
*general* relativistic version of the problem's orbit (in standard
Schwarzschild coordinates) onto a corresponding *Newtonian* problem
with a particularly chosen attractive 1/r^3 potential (1/r^4 force)
counter-term in addition to the actual 1/r^2 potential present.