Tides of the Moon and the Orbital Evolution

在以前的工作中，我们已经使用简单的海洋模型来研究潮汐对月球轨道和地球自转的影响。这些结果帮助我们了解了地月系统的演化，如轨道半径、倾角和自转速率等的变化。目前月球的自旋轴满足卡西尼定律的第二状态，轨道周期与自转周期一致。这可能是由潮汐摩擦引起的，在最初的10或20亿年里，潮汐摩擦降低了月球的自转速度。这项研究的目的是改进地球海洋和月球的潮汐模型，更精确地研究轨道演化，探索地月系统的起源，并阐明月球自转运动的变化。研究过程和取得的成果如下：1)计算了二叠纪(200 Ma B.P.)的海洋潮汐模型。寒武纪(500 Ma B.P.)发现…的潮汐扭矩较大地球大陆沿赤道分布的情况多于大陆沿子午线分布或向极地集中的情况。2)考虑内部结构，计算了月球的潮汐勒夫数，并成功地估计了地球自转引起的月球潮汐形变。3)研究了潮汐摩擦对月球偏心率的影响。4)我们估计了太阳对地月系统潮汐演化的影响，证实了古生物学研究提出的过去600 mA期间地球自转的波动可以很好地解释为大陆漂移引起的潮汐摩擦的变化。5)我们成功地确定了过去40到50亿年间月球的轨道演化的界限。6)研究了利用人工射电源对月球的VLBI观测，以实现对潮汐和月球振动的观测

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