Could someone explain to me what specifically distinguishes Einsteins more advanced treatment of gravity over Newtons? Here’s what I (think I) know. Newton described gravity as a “force” of attraction between two bodies or masses. That force was given by the G constant times the two masses divided by the square of the radius between the two masses. The force of gravity was then modeled as a corresponding acceleration vector between the bodies. The classical Lagrangian using the principal of least action reproduces newtons same equations of motion, but instead of assuming a” force of attraction” between the two bodies, models the relation between the two masses as a minimized “path.” Now we get to Einstein. Einstein eschewed the idea of attraction and instead saw gravity as a process whereby object-masses moved along a physically ill-defined but mathematically compelling “geodesic” which traced out a complex curved space-time in the vicinity of massive bodies. Mathematically the curving of this spacetime and the geodesics that arise from it are found through the continuous redefinition of the local coordinate axis due to the local mass energy density of the system in question. This value is given by the stress-energy tensor. The particular “shape,” then, of the local coordinate axis is given by the Einstein tensor. The value of each of these tensors rely on each other in real time so as to make the equations non-linear. Do I have this right? Anyway, my question is what is it about the Reimenian geometric approach of GR that gives it it’s advantage over the classical model, which works well enough for everyday modeling that we can use it solely to send people to the moon and back? Is the answer in the nonlinearity of the solutions, that the motions of the bodies are continuously updated in real time. Is it that GR incorporates energy and pressure into the stress-energy tensor whereas Newtons equations just include mass? Does it have something to do with the geometrical approach over a force of attraction approach? Also, I’ve read that it has something to do with the Taylor series expansion, where the higher order terms give you something that the lower terms don’t, which is where you get Newton’s equations? Finally, where does one want to go through the ordeal of using GR to model a system where Newton won’t work. The places I’m familiar with are black holes, GPS, the eclipse thing, and the precession of Mercury. But why and how does this give us a better solution here. Thanks.