VIII. The determination of the secular effects of tidal friction by a graphical method
VIII. The determination of the secular effects of tidal friction by a graphical method
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DOI：
10.1098/rspl.1879.0028
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通讯作者：
G. Darwin
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作者：
G. Darwin
假设一个质量为m的引力粒子或卫星以角速度Ω绕质量为M的行星作圆形轨道运动，并假设该行星以角速度n绕垂直于轨道平面的轴旋转;还假设该行星的质量部分或全部是不完全弹性或粘性的，或者该行星表面有海洋;那么，卫星的引力必然会在行星的各个部分产生相对运动，而这种运动必然会受到摩擦力的影响，或者换句话说，必然会有某种摩擦潮汐。因此，系统必然会因摩擦而损失能量，其结构必然会以这样一种方式变化，即它的全部能量会减少。这样一个系统与实际的行星和卫星的系统差别不大，因此，在这种假设情况下推导出的结果必须与实际的进化过程非常接近：只要已经并将给予足够的时间来进行这种变化。
Suppose an attractive particle or satellite of mass m to be moving in a circular orbit, with an angular velocity Ω, round a planet of mass M, and suppose the planet to be rotating about an axis perpendicular to the plane of the orbit, with an angular velocity n; suppose, also, the mass of the planet to be partially or wholly imperfectly elastic or viscous, or that there are oceans on the surface of the planet; then the attraction of the satellite must produce a relative motion in the parts of the planet, and that motion must be subject to friction, or, in other words, there must be frictional tides of some sort or other. The system must accordingly be losing energy by friction, and its configuration must change in such a way that its whole energy: diminishes. Such a system does not differ much from those of actual planets and satellites, and, therefore, the results deduced in this hypothetical case must agree pretty closely with the actual course of evolution,: provided that time enough has been and will be given for such changes.