Tidal Dynamics of Extended Bodies in Planetary Systems
Tidal Dynamics of Extended Bodies in Planetary Systems
复制标题
行星系统中扩展体的潮汐动力学
DOI：
10.1051/0004-6361/20079054
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
C. L. Poncin
中科院分区：
文献类型：
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作者：
S. Mathis;C. L. Poncin
上下文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接近但分离的双星的存在，潮汐相互作用必须仔细研究。目标。这种相互作用通常是用潮汐扰动的点近似来研究的。本文的目的是检查步骤，超越了传统的方法，考虑潮汐扰动作为一个扩展的机构。为了实现这一点，我们研究了两个扩展机构之间的引力相互作用，更准确地说，质量多极矩的引力场和相关的潮汐现象之间的相互作用。方法.我们使用Carnival对称的迹自由张量，它们与球谐函数和Kaula变换的关系使我们能够解析地导出潮汐势和相互作用势，以及扩展体系统中的相关扰动函数。结果导出了两个伸展体的潮汐势和相互作用势。此外，利用Love数理论，还得到了这种潮汐扰动的扩展体的外部引力势，以及相应的扰动函数。最后，给出了这种系统的动力学演化方程的更一般的形式，没有任何线性化。我们还比较，在一个简化的假设下，这种形式主义的准时的情况下。我们证明了在非常封闭的系统（a B/R B ≤ 5）中，对于强形变扰动（J2> 10 - 2），非准时项必须考虑.结论.我们展示了如何推导出引力和潮汐之间的相互作用扩展机构和相关的动力学方程。给出了应用这种形式主义的条件。
Context. With the discovery during the past decade of a large number of extrasolar planets orbiting their parent stars at distances 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 close but separated binary stars, tidal interaction has to be studied carefully. Aims. This interaction is usually studied with a punctual approximation for the tidal perturber. The purpose of this paper is to examine the step beyond this traditional approach by considering the tidal perturber as an extended body. To achieve this, we studied 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. Methods. We use cartesian symmetric trace free tensors, their relation with spherical harmonics and Kaula's transform enables us to analytically derive the tidal and mutual interaction potentials, as well as the associated disturbing functions in extended body systems. Results. The tidal and mutual interaction potentials of two extended bodies are derived. In addition, the external gravitational potential of such a tidally disturbed extended body is obtained, using the Love number theory, as well as the associated disturbing function. Finally, the dynamical evolution equations for such a system are given in their more general form without any linearization. We also compare, under a simplified assumption, this formalism to the punctual case. We show that the non-punctual terms have to be taken into account for strongly deformed perturbers (J 2 > 10 -2 ) in very close systems (a B /R B ≤ 5). Conclusions. We show how to derive the dynamical equations for the gravitational and tidal interactions between extended bodies and associated dynamics. The conditions for applying this formalism are given.