论文标题
自旋轨重力锁定 - 有效的潜在方法
Spin-orbit gravitational locking -- an effective potential approach
论文作者
论文摘要
本文的目的是研究潮汐锁定的3：2旋转轨道共振在太阳周围。为了实现这一目标，考虑了确定椭圆形行星轴周围旋转运动的有效势能。通过研究具有固定偏心率和半高轴的椭圆形轨道上绕球体旋转的椭圆形行星的旋转势能，结果表明该系统显示了无限数量的亚固函数平衡构型。这些状态对应于在轨道上平均的旋转势能的局部最小值，在轨道上，该行星围绕其轴的旋转周期与恒星周围的革命周期之间的比率是固定的。该比率是整数或半整数的配置特别感兴趣。在这些配置中，平均势能中最深的最小值对应于行星旋转和轨道运动同步的情况，并且系统被潮汐锁定。最深的最低限度对应于行星在需要在太阳周围完成两个轨道的时间周围旋转三倍的情况。后者确实是描述了水星动议的情况。这项工作中讨论的方法使人们可以识别与旋转轨道共振相对应的整数和半数比例，并描述行星在共振轨道中的运动。
The objective of this paper is to study the tidally locked 3:2 spin-orbit resonance of Mercury around the Sun. In order to achieve this goal, the effective potential energy that determines the spinning motion of an ellipsoidal planet around its axis is considered. By studying the rotational potential energy of an ellipsoidal planet orbiting a spherical star on an elliptic orbit with fixed eccentricity and semi-major axis, it is shown that the system presents an infinite number of metastable equilibrium configurations. These states correspond to local minima of the rotational potential energy averaged over an orbit, where the ratio between the rotational period of the planet around its axis and the revolution period around the star is fixed. The configurations in which this ratio is an integer or an half integer are of particular interest. Among these configurations, the deepest minimum in the average potential energy corresponds to a situation where the rotational and orbital motion of the planet are synchronous, and the system is tidally locked. The next-to-the deepest minimum corresponds to the case in which the planet rotates three times around its axis in the time that it needs to complete two orbits around the Sun. The latter is indeed the case that describes Mercury's motion. The method discussed in this work allows one to identify the integer and half-integer ratios that correspond to spin-orbit resonances and to describe the motion of the planet in the resonant orbit.
