The direction of rotation of the Sun around its axis and the direction of Mercury orbital movement around the Sun are the same ones. Let us suppose the luminiferous medium (physical vacuum, aether) is entrained by rotating Sun near its surface. When Mercury moves in the area of its perihelion it can meet lesser aether resistance due to collinearity (at first approximation) of the aether movement (orbital wind) velocity and Mercury velocity. Lesser resistance lead to additional acceleration in the movement direction which causes the perihelion shift. What do you think?
The article about luminiferous medium entrainment by massive solids (by Earth at least) is here:
Article Entrainment of Luminiferous Medium with Massive Solids
The problem for Einstein theory is in inconsistency with such phylosophical criterium as falsifiability as well as with Occam's razor principle. The statements that the "vacuum" does not contain any unknown media and the light speed is the maximal possible speed in the nature look like popular "Flat Earth" theory of the present time. Don't forget about heuristic criterium also. A physical theory not only describes well-known experimental data, but correctly predicts new ones.
Dear Volodymyr,
Your explanation is mathematical, not a physical. As well as Einstein and many other theoretics you base on the mathematical ideas, not on a physical ones. This leads to breaking with physical reality.
To introduce any term mechanically it needs a number of mechanical objects (statistics). Observations of only one orbit are not enough to produce the correct theory.
The Newtonian is based on the great number of astronomical observations (thanks to Kepler and many other astronomiers). Newton's law of gravity is the good example of truly physical theory which uses mathematics only as a language for obtained experimental data.
My hypothesis above may be verified in the following way. In accordance with it all Mercury- like planets and other similar cosmic bodies should be shifted by their rotating gravity centers in the direction of rotation, closely to the centers surfaces.