About Mercury perihelion again Sorry to bother you, but I did not get anywhere answer what exactly moves Mercury periapsis. "Sun gravity" or "GR" or "warp of spacetime" are very broad answers, I want to know how they affect this guy. As far as I learn, at first it seems that root of such behavior is speed of gravity, so when Mercury goes away from the Sun, gravity needs more time to travel and thus trajectory somewhat changes. But if so, there must be the reversed effect when Mercury moves closer. If these effects are not equal by absolute value, why?
My second thought was the "descending" path along gravity curvature is not symmetrical to "ascending". Then question is "Why?" again.
If shorter, if there is a difference in Newton's and Einstein's formulas, what's this difference means if said with common words?
 A: A simple explanation comes from Bertrand's theorem. It states that the only types of central forces that result in bounded orbits that repeat their tracks (i.e., "closed") are forces that are either proportional to distance ($F=-kr$) or are inversely proportional to the square of distance ($F=-k/r^2$). While other forms of a central force can produce bounded orbits, they cannot produce closed orbits.
The simple explanation then is that general relativity is not of either of the two forms that result in closed orbits. Non-circular orbits in general relativity cannot be closed orbits.
In the case of the solar system, where velocities are small compared to the speed of light and distances are large compared to the  Schwarzschild radius, general relativity can be viewed as being of the form of small perturbations on top of Newtonian gravitation. Because the perturbations are small, the result is orbits that are close to but not quite Newtonian. The orbits are close to being ellipses, but those ellipses rotate. 
A: The reason for GR's contribution to Mercury's perihelion precession is nonlinearity of GR. Nonlinearity is absent in Newtonian gravity: to describe the effect of gravity on the motion of an object (say Mercury), you calculate the gravitational potential that the said object experiences as sourced by other objects in its surrounding (say the sun and other planets). Whichever way you position these objects, or add more or remove some of them, you just need to algebraically add the gravitational potentials to calculate the final effect of gravity on Mercury. This has been done for Mercury where the effect of other planets are taken into account, but the numerical value of perihelion precession doesn't match observations. This is because we missed new contributions coming from the nonlinear nature of GR: in a loose sense, the effect of gravity on Mercury is not just a plain sum of effects of gravity of each object around it. GR is a nonlinear theory which explains this missing piece. In field theory language, nonlinearity (in GR) means that gravitons self-interact. Also see my answer here on a related question.
