The virial-based theory of the Earth global dynamics

Abstract

A novel dynamical approach to solve the problem of global dynamics of the Earth is put forward. The goal of the theory is to obtain the time dependant solution of the moment of inertia or the potential (kinetic) energy of the Earth as a self-gravitating celestial body. The solution must describe unperturbed virial oscillation and rotation of the Earth caused by the own internal force field, which are affected by the Sun, the Moon and the planets’ perturbations. In general case the last ones can be an arbitrary given function of time, function of the moment of inertia and their first derivatives. In order to obtain solution of the Earth motion in the own internal force field the planet’s motion is separated from the relative motion about the Sun. The fields of the internal gravitational and inertial (reaction) forces are reduced to the resultant spheroid (ellipsoid) of the gravity and inertia. The normal, tangential and dissipative components of the potential and kinetic energies are derived by their expansion. The dynamical equilibrium condition of the body mass motion by means of the virial theorem is introduced. Finally, two Jacobi’s virial equations for oscillation and for rotation of the Earth are written. Their solution gives periodic change in value of the moment of inertia or the potential (kinetic) energy of the Earth’s shells, which determine the planet’s oscillation, rotation and precession. The outer force field of the Sun and the Moon, which is by three orders of magnitude lower of the Earth’s on the surface, only perturbs the above effects by the same order of smallness. The nature of wobbling (nutation)of the planet’s crust, being in suspended state on the upper shell of the mantel, is explained by the crust inertial effects under action of the tidal interaction of the Earth and the Moon. The Chandler’s wobble becomes understandable in the light of the same phenomenon.