雅努斯和厄庇墨透斯的旋转理论
Theory of the rotation of Janus and Epimetheus
摘要：
土星的同轨卫星土卫十和土卫八在太阳系中呈现出独特的动力学构型，这是因为它们的质量比为1阶，轨道的振幅很大。因此，它们每4年交换一次轨道，而它们的轨道周期约为0.695天。最近，Tiscareno et al.（2009）获得了关于这些卫星的形状和旋转状态的观测信息。特别是，他们发现了雅努斯预期平衡位置的偏移，以及厄庇墨透斯的大天平动。在这里，我们建议使用这些观测数据给出这些卫星的旋转的三维理论，并将其与观测到的旋转进行比较。我们认为这两个卫星作为三轴刚体，我们进行数值积分的系统假设的自由振动阻尼。我们得到了与三维空间有关的三个自由振动的周期，Janus的周期分别为1.267、2.179和2.098天，Epimetheus的周期分别为0.747、1.804和5.542天。轨道周期接近0.747天，这使得厄庇墨透斯的天平动对惯性矩的敏感度很高。我们的理论解释了Janus的振动幅度和Epimetheus的振动误差条，但没有观察到Janus方向的偏移。
英文摘要：
The Saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al.(2009) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus. We here propose to give a 3-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped. The periods of the three free librations we get, associated with the 3 dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus.
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