In the present paper, we investigate the dynamical behavior and motion of an infinitesimal body in the Hill problem under some perturbations. As it has been commonly noticed, this problem can be seen as a particular case of the classical restricted three-body problem. For numerical investigations, we first set the equations of motion of the infinitesimal body that we suppose having a variable mass according to Jeans' law. We get an effective and perceptible variation due to parameters in both the locations of lagrangian points, regions of motion, and basins of attraction. Finally, we examine the stability for the lagrangian points using Meshcherskii's space–time inverse transformations.

中文翻译：

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具有可变质量的扰动希尔问题

在本文中，我们研究了希尔问题中无穷小体在某些扰动下的动力学行为和运动。正如人们普遍注意到的那样，这个问题可以看作是经典受限三体问题的一个特例。对于数值研究，我们首先设置根据金斯定律假设具有可变质量的无穷小物体的运动方程。由于拉格朗日点的位置、运动区域和吸引力盆地的参数，我们得到了有效且可感知的变化。最后，我们使用 Meshcherskii 的时空逆变换来检查拉格朗日点的稳定性。