Dynamic evolution of the Earth Moon system

Abstract

In this work, it was developed a semi-empirical model by describing the dynamic evolution of the Earth-Moon system from data on the Earth rotation supplied by IERS (International Earth Rotation and Reference System Service) combined with Celestial Mechanics equations. Focusing the interest on secular terms, an equation that supplies the Earth angular velocity was gotten, which, combined with the equation that relates the loss of the Earth rotation angular momentum due to the tide friction of the Moon and the Sun with the change in the lunar orbital angular momentum culminated in the expression that yields the major semi-axis of the Moon’s orbit. In addition, an expression for the tidal time lag response to the force of gravitational attraction suffered by the Earth as a function of the orbital parameters of the Moon and the time was found, which was applied to the differential equations system integrated to the past. Equations expressing the
Earth’s rotation velocity, Earth-Moon distance, eccentricity and inclination of the lunar orbit were obtained. The results were compared to those found by methods that analyze records derived from research based on sedimentary cyclic rhithmites sedimentation and an excellent agreement between them was gotten.