We all know that Einsteins GTR accounts for observations that Newtonian gravitation cannot account for. I have "created" a theory of gravity (I put created in quotes becase it feels more like I found it) that makes corrections to Newtonian gravity in the same extreme relativistic cases. (this theory is compatible with STR) . For the purposes of math, I am talking about a force that is a function of radial distance: F(r). The point of bothering you all with this, is that I would like to test my theory of gravity against experimental observations. I have thought about the classic test: the precession of the perihelion of mercury, but I have no idea how to undertake this calculation (I have studied the classical two body problem, but I don't know how to account for the perturbations caused by the other planets that cause the precession in the first place). I have tried looking for books, but I cannot find any that treat this problem in detail. If anyone can suggest another test of GTR (besides gravitational lensing) that I could test my theory with, I would be very grateful. If anyone can tell me anything about the precession of the perihelion of mercury, I would be very grateful. I have heard that every testable prediction of GTR is based on the Schwarschild metric, is this true?