The Planck numbers and the essence of gravitation: phenomenology

We introduce phenomenological understanding of the electromagnetic component of the physical vacuum, the EM vacuum, as a basic medium for all masses of the expanding Universe, and "Casimir polarization" of this medium arising in the vicinity of any material object in the Universe as a result of conjugation of the electric field components of the EM vacuum on both sides ("external" and "internal") of atomic nucleus boundary of the each mass with vacuum. It is shown that the gravitational attraction of two material objects in accordance with Newton's law of gravity arises as a result of overlapping of the domains of the EM vacuum Casimir polarization created by atomic nuclei of the objects, taking into account the long-range gravitational influence of all masses of the Universe on each nucleus of these objects (Mach's idea). Newton's law of gravitational attraction between two bodies is generalized to the case of gravitational interaction of a system of bodies when the center of mass of the pair of bodies shifted relative to the center of mass of the system. The unique smallness of gravitational interactions as compared with the fundamental nuclear (strong and weak) and electromagnetic ones is determined by the ratio of the characteristic size of the domain of EM vacuum Casimir polarization in the vicinity of atomic nuclei to the Hubble radius of the Universe.