Tides of the Moon and the Orbital Evolution

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In previous works, we had studied the tidal effects on the lunar orbit and the Earth's rotation by using simple ocean models. These results helped us to understand the evolution of the Earth-Moon system, such as changes of the orbital radius and inclination and thes pin rates etc.The spin axis of the present Moon satisfies the second status of Cassini's law and the orbital period agrees with the rotational period. This could be caused by the tidal friction which reduced the spin rate of the Moon during the early 1 or 2 billion years.This research aims at improving the tidal models of the Earth's oceans and the Moon and at studying the orbital evolution more precisely to investigate the origin of the Earth-Moon system and to clarify the variation of the spin motion of the Moon. The process of research and obtained results are as follows.1) We computed the tidal models of the oceans at Permian age (200Ma b.p.) and at Cambrian age (500 Ma b.p.) and found that the tidal torque is lager in … More the case that the continents of the Earth distribute along the equator than in the case that the continents distribute along the meridian or concentrate to the polar region.2) The tidal Love numbers of the Moon were computed taking the internal construction into consideration and we succeeded to estimate the tidal deformation of the Moon due to the Earth's rotation.3) The effect of the tidal friction which works to change the lunar eccentricity was studied. A new method of computation was developed to simulate the variation of the eccentricity due to the tides.4) We estimated the effects of the Sun to the tidal evolution of the Earth-Moon system and confirmed that the fluctuation of the Earth's rotation during the past 600Ma presented by paleontological studies is well explained by the variation of the tidal friction due to the continental drift.5) We have succeeded to set bounds to the orbital evolution of the Moon during the past 4 to 5 billion years.6) VLBI observations of the Moon using the artificial radio sources were studied to make observations of the tides and the libration of the Moon Less