The Lunar Orbit Revisited - Part Three

In this paper we present an investigation on the tidal evolution of a system of three bodies: the Earth, the Moon and the Sun. Equations are derived including dissipation in the planet caused by the tidal interaction between the planet and the satellite and between the planet and the sun. Dissipation within the Moon is included as well. The set of differential equations obtained is valid as long as the solar disturbances dominate the perturbations on the satellite's motion due to the oblateness of the planet, namelya/R _e greater than 15, and closer than that point equations derived in a preceding paper are used. The result shows the Moon was closer to the Earth in the past than now with an inclination to the ecliptic greater than today, whereas the obliquity was smaller. Toward the past, the inclination to the Earth's equator begins decreasing to 12° fora/R _e=12 and suddenly grows. During the first stage the results are weakly dependant on the magnitude of the dissipation within the satellite, whereas the distance of the closest approach and the prior history are strongly dependent on that dissipation. In particular, the crossing of the Roche limit can be avoided.