Deformed state of viscoelastic bodies in one problem of tidal interaction

Abstract

In our previous articles we considered the motion of two viscoelastic bodies in the gravitational field of a massive material point. We studied the evolution of the bodies, stationary solutions and their stability. We solved the equations of translational-rotational motion of the bodies together with the equations of their deformed state, using the method proposed by V G Vil’ke for the systems with infinite numbers of degrees of freedom. In our manuscript we continue our research and our aim is to get the global characteristics of the bodies, deformed by tidal forces: their shape, moments of inertia, the tidal lag angle, the relationship between the viscosity coefficient and the lag angle, tidal torques, internal material properties, depending on elastic constant and viscosity coefficient. It is very important for study of an evolutional motion of the celestial bodies, since tides affect this. In order to achieve this goal we use the tidal potential perturbation and displacements of each point of the bodies. The formulation of the problem, goal set and used methods are the novelty of our research. We applied our theory to the Earth, and it was found that the Earth’s substance (in global) behaves like an auxetic.