行星系统和多星中伸展体的潮汐动力学
Tidal dynamics of extended bodies in planetary systems and multiple stars
摘要：
随着过去十年发现大量太阳系外行星围绕其母恒星运行，距离小于0.1天文单位，（以及发射和准备专门的空间飞行任务，如CoRoT和KEPLER），随着我们太阳系中巨大行星周围的内部天然卫星的位置以及非常封闭但分离的双星的存在，潮汐相互作用必须仔细研究。特别是，出现了一个问题的有效性通常的近似用于这种相互作用的建模。本文的目的是研究潮汐摄动的超越实际近似的步骤。为了实现这一目标，我们研究了两个伸展体之间的引力相互作用，更准确地说，是它们的引力场的质量多极矩之间的相互作用以及相应的潮汐现象。使用笛卡尔对称无迹（STF）张量，它们与球谐函数和Kaula变换的关系，能够解析地导出潮汐和相互作用势以及扩展体系统中的相关干扰函数。导出了两个伸展体的潮汐势和相互作用势。其次，利用Love数论得到了这种引潮力扰动的扩展体的外引力势，以及相应的扰动函数。最后，给出了这类系统的动力学演化方程的一般形式，而无需任何线性化。推导了扩展天体和相关动力学之间引力和潮汐相互作用的动力学方程，它们可以直接用于行星系统或多恒星潮汐演化的相干数值模拟。
英文摘要：
With the discovery during the past decade of a large number of extrasolar planets orbiting their parent stars at a distance lower than 0.1 astronomical unit (and the launch and the preparation of dedicated space missions such as CoRoT and KEPLER), with the position of inner natural satellites around giant planets in our Solar System and with the existence of very closed but separated binary stars, tidal interaction has to be carefully studied. In particular, a question arises about the validity of usual approximations used in the modelling of this interaction. The purpose of this paper is to examine the step beyond the ponctual approximation for the tidal perturber. To achieve this aim, the gravitational interaction between two extended bodies and more precisely the interaction between mass multipole moments of their gravitational fields and the associated tidal phenomena are studied. Use of Cartesian Symmetric Trace Free (STF) tensors, of their relation with spherical harmonics and of the Kaula's transform enables to derive analytically the tidal and mutual interaction potentials as well as the associated disturbing functions in extended bodies systems. The tidal and mutual interaction potentials of two extended bodies are derived. Next, the external gravitational potential of such tidally disturbed extended body is obtained, using the Love's number theory, as well as the associated disturbing function. Finally, the dynamical evolution equations for such systems are given in their more general form without any linearization. The dynamical equations for the gravitational and tidal interactions between extended bodies and associated dynamics are derived in a form where they could be directly implemented to perform coherent numerical simulations of planetary systems or multiple stars tidal evolution.
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