Role of general relativity and quantum mechanics in dynamics of Solar System

Abstract: Let m(i) be the mass of i-th planet and M be the Solar mass. From astronomical data it is known that ratios r(i)=m(i)/(m(i)+M) are of order 10^-3-10^-6 for all planets. The same is true for all satellites of heavy planets. These results suggest that Einstein's treatment of Mercury dynamics can be extended to almost any object in the Solar System. This fact does not explain the existing order in the Solar System. Indeed, all planets lie in the same (Sun's equatorial) plane and move in the same direction coinciding with that for the rotating Sun.The same is true for regular satellites of heavy planets and for planetary rings associated with these satellites.In addition to regular satellites, there are irregular satellites (and at least one irregular (Saturn) ring associated with such a satellite (Phoebe)) grouped in respective planes (other than equatorial) in which they all move in "wrong" directions on stable orbits. These are located strictly outside of those for regular satellites. This filling pattern is reminiscent to that in atomic mechanics. Based on the original Heisenberg's ideas, we develop quantum celestial mechanics explaining this filling pattern and that for rings of heavy planets. The formalism takes essentially into account that planets and satellites are moving on geodesics.