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首页> 外文期刊>Celestial Mechanics and Dynamical Astronomy: An international journal of space dynamics >Mission design through averaging of perturbed Keplerian systems: The paradigm of an Enceladus orbiter
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Mission design through averaging of perturbed Keplerian systems: The paradigm of an Enceladus orbiter

机译：通过平均扰动的开普勒系统进行任务设计：土卫二轨道器的范例

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摘要

Preliminary mission design for planetary satellite orbiters requires a deep knowledge of the long term dynamics that is typically obtained through averaging techniques. The problem is usually formulated in the Hamiltonian setting as a sum of the principal part, which is given through the Kepler problem, plus a small perturbation that depends on the specific features of the mission. It is usually derived from a scaling procedure of the restricted three body problem, since the two main bodies are the Sun and the planet whereas the satellite is considered as a massless particle. Sometimes, instead of the restricted three body problem, the spatial Hill problem is used. In some cases the validity of the averaging is limited to prohibitively small regions, thus, depriving the analysis of significance. We find this paradigm at Enceladus, where the validity of a first order averaging based on the Hill problem lies inside the body. However, this fact does not invalidate the technique as perturbation methods are used to reach higher orders in the averaging process. Proceeding this way, we average the Hill problem up to the sixth order obtaining valuable information on the dynamics close to Enceladus. The averaging is performed through Lie transformations and two different transformations are applied. Firstly, the mean motion is normalized whereas the goal of the second transformation is to remove the appearance of the argument of the node. The resulting Hamiltonian defines a system of one degree of freedom whose dynamics is analyzed.
机译：行星卫星轨道器的初步任务设计需要对通常通过求平均值技术获得的长期动力有深刻的了解。该问题通常在汉密尔顿主义环境中公式化为主要部分的总和，这是通过开普勒问题给出的，再加上取决于任务特定特征的小扰动。它通常来自受限三体问题的缩放过程，因为两个主体是太阳和行星，而卫星被认为是无质量的粒子。有时，使用空间希尔问题代替受限的三体问题。在某些情况下，平均的有效性仅限于非常小的区域，因此无法进行有意义的分析。我们在土卫二中发现了这种范例，其中基于希尔问题的一阶平均的有效性在于人体内。但是，这一事实并没有使该技术无效，因为在平均过程中使用了摄动方法来达到更高的阶次。通过这种方式，我们可以将希尔问题平均到第六阶，从而获得有关土卫二附近动力学的有价值的信息。通过李变换执行平均，并应用两个不同的变换。首先，将平均运动归一化，而第二次变换的目标是消除节点自变量的出现。由此产生的哈密顿量定义了一个自由度的系统，对其动力学进行了分析。

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