Tidal Friction

The tides in the oceans occur primarily because of the gravitational force of the Moon and secondarily the Sun's tidal force. Tidal forces stretch the Earth in the direction of the tide producing body because of the inverse square law, i.e., the force on the near side is greater than the force on the far side, giving a net stretching force. While more noticeable in the oceans, there is also tidal stretching of the land masses.

海洋中的潮汐现象主要由于月球的引力作用，次之是太阳的潮汐力。由于反平方定律，潮汐力会使地球在潮汐作用体方向拉伸，因为近侧的力大于远侧的力，产生一个净拉伸力。虽然在海洋中更为明显，陆地也会发生潮汐拉伸。

The tidal forces on an orbiting body slowly change the character of the orbit. For example, assume an orbiting moon which is also rotating about an axis perpendicular to the orbital plane. The tidal force stretches the moon along the line joining it with the planet, and then that stretching relaxes as that diameter rotates away from the line. There is frictional resistance to the stretching, and energy is dissipated to heat in the stretching and in the relaxing of the deformation, gradually taking energy away from the rotating system.

天体轨道上的潮汐力逐渐改变了轨道的特性。例如，假设一个绕行的月球也绕着垂直于轨道平面的轴旋转。潮汐力会将月球沿着它与行星的连线方向拉伸，然后这种拉伸在该直径远离连线时逐渐松弛。拉伸过程中存在摩擦阻力，能量在拉伸和松弛变形的过程中被转化为热量，逐渐从旋转系统中消耗掉能量。

As the deformed moon rotates away from the connecting line, gravity exerts a torque which acts to diminish the rotational angular momentum of the moon, gradually slowing its rotation rate. This braking effect over a long time period brings the moon's rotation rate relative to the connecting line to zero, so that its rotation period approaches the orbital period and the same face is toward the planet at all times. The Earth's Moon has reached that state so that we always see the same side of the Moon.

当变形的月亮远离连接线时，重力施加了一个力矩，该力矩作用于月亮的角动量，使其逐渐减小，从而减慢其自转速率。这种制动效应在长时间内使月亮相对于连接线的自转速率降至零，因此其自转周期接近公转周期，使得同一面始终朝向行星。地球的月亮已达到这种状态，因此我们总是看到月亮的同一面。

The planet Mercury is tidally coupled to the Sun but this does not produce the 1:1 ratio of orbit period to rotation period like the Earth's Moon. From the Mercury planetary data we find that the sidereal period of Mercury around the Sun is 87.969 days but the planet's period of rotation about its axis is 58.646 days. The planet makes an accurate 3/2 rotations in one orbital period of the planet. This is called a "tidal resonance" or a "spin-orbit resonance".

The Moon's tidal force on the Earth likewise influences it so that energy is being dissipated by tidal friction. As the tidal deformation of the Earth rotates away from the connecting line, the asymmetry produced by the slightly elongated shape provides a lever arm for a braking torque that slows the Earth's rotation, currently increasing the length of the day by about 2.3 milliseconds per century. A million years from now the day will be about an hour longer.

月球对地球的潮汐力同样影响着它，使得能量通过潮汐摩擦而耗散。当地球的潮汐形变远离连接线时，由略微拉长的形状所产生的不对称性提供了一个力臂，产生一个制动力矩，使地球自转减慢，目前使每天的时间长度增加约2.3毫秒每世纪。一百万年后，一天将大约长一小时。

水星与太阳潮汐耦合，但这种耦合并不像地球的月球那样产生轨道周期与自转周期1:1的比例。从水星的行星数据可知，水星绕太阳的恒星日为87.969天，但水星绕其轴自转的周期为58.646天。水星在一个轨道周期内精确地完成3/2次自转。这种现象称为“潮汐共振”或“自转轨道共振”。