On the tidal time delay of the Earth

Abstract

We present an expression for the tidal time delay of the Earth, that takes into account paleonthological observations. A semi-empirical model of the dynamics of the Earth-Moon system is obtained considering that the energy dissipation and the time delay are not constant in time. In a previous work, we established a similar model by taking into account only the dynamics of a circular orbit radius for the Moon. In the present paper, three differential equations describe the dynamics of three variables, namely, the Moon's orbital mean radius, the eccentricity of the orbit, and the inclination of the Moon's orbital plane with respect to the inertial plane which is orthogonal to the total angular momentum of the Earth-Moon system. In this sense, the Earth-Moon system is considered isolated. We compare our picture with that one which considers the tidal time delay as constant in time and show that our approach is consistent with the modern theories concerning the Earth-Moon system formation.