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 better first question would be, "Why does Newtonian gravity predict the perihelion shift to be zero?" This is quite a special property and essentially any deviation will lead to a perihelion shift. Commented Sep 19, 2019 at 8:52
• @PM2Ring: For sake of brevity, I ignored that. There is even a measurable Newtonian correction due to the fact that the sun is not spherical. Commented Sep 20, 2019 at 7:03
• @PM2Ring The general relativistic precession of Mercury's perihelion is less than 10% of the precession caused by the other planets: 43 arc seconds per century for GR compared to 530 arc seconds per century caused by the other planets using Newtonian gravitation. Commented Oct 22, 2023 at 14:56
• @David Good point! I don't know where that figure of a half came from... Maybe there was some confusion with the early GR prediction of gravitational lensing, as observed during a solar eclipse. FWIW, here are some questions with good info on Mercury's precession, astronomy.stackexchange.com/q/49253/16685 & astronomy.stackexchange.com/q/44654/16685 Commented Oct 22, 2023 at 19:53

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.
• You want to add an $1/r^3$ or $1/r^4$ term to the Newtonian gravitational central force to get GR? You could perhaps in principle keep the Newtonian central force and describe the GR addition as an effect of slowing down accelerations the closer you get to the speed of light? Commented Oct 22, 2023 at 1:04