The effective inertial acceleration due to oscillations of the gravitational potential: footprints in the solar system

The conjecture is considered that every body induces the wave field which imposes oscillations on the gravitational potential of a body. The function for oscillations is chosen to prevent the gravitational collapse of the matter at the nucleus energy density. The conjecture leads to modification of the Newtonian gravity. The effect is too small to be seen in observations in the solar system. Oscillations of the gravitational potential of a body produce effective inertial outward acceleration for a particle orbiting around the body. Footprints of the effective inertial acceleration due to oscillations of the gravitational potentials of the Sun and Earth are investigated. The conjecture allows to explain the anomalous shift of the perihelion of Mercury and Icarus, the anomalous shift of the perigee of LAGEOS II, the anomalous acceleration acting on Pioneer 10, 11, the anomalous increase in the lunar semi-major axis. The advance of the Keplerian orbit for Earth, Jupiter, Neptune, Uranus caused by the effective inertial acceleration due to oscillations of the gravitational potential of the Sun is in agreement with the observational bounds from the planetary ephemeris. The theory of gravity [1] faces the problem of singularities. In particular, singularities may arise as a result of the gravitational collapse of massive stars. A body contracted to the nucleus energy density resembles the neutron star [2]. There is a maximum mass for the neutron star of order of the mass of the Sun mmax ∼ m⊙. For the neutron star with the mass less than the maximum mass, the pressure due to the degenerated neutron Fermi gas balances the gravity of the star. For the neutron star with the mass more than the maximum mass, the gravity of the star overcomes the pressure due to the degenerated neutron Fermi gas, and the star goes to the singularity. The radius of the first Bohr’s orbit of the Hydrogen atom a0 and the classical radius of electron re are related as re a0 = α (1) where α is the fine structure constant. The velocity of the electron at the first Bohr’s orbit is given by ve = αc (2) where c is the velocity of light. The radius of the nucleus of the Hydrogen atom rn is of order of the classical radius of electron