  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. 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.
