受限三体问题中无降级的闭式微扰理论与长期运动域
Relegation-free closed-form perturbation theory and the domain of secular motions in the Restricted 3-Body Problem
AI总结：
本研究针对受限三体问题中外侧轨道场景，提出无降级的闭式微扰理论方案，通过李级数归一化构建长期哈密顿量，经太阳-木星系统参数验证，可半解析估计长期运动的有效边界。
摘要：
我们提出了一种闭式（即无需对轨道偏心率进行展开）方案，用于受限三体问题（R3BP）中无质量粒子轨道位于主摄动体轨道外侧时的微扰理论计算。从质心（雅可比约化）哈密顿量的多极展开出发，我们利用李级数在德洛内变量中进行一系列归一化处理，无需使用降级操作即可得到长期哈密顿量模型。为此，我们引入了一种类似Cavallari与Efthymiopoulos（2022）针对主摄动体内侧测试粒子轨道提出的记账方法，但此处将其调整以适用于外侧轨道的情况。我们针对与太阳-木星系统相关的参数，给出了该方法在平面圆形和空间椭圆受限三体问题中的性能数值示例。具体而言，我们证明了该方法在重现远离平运动共振的轨道根数变化方面的准确性。作为该方法的一项基本成果，我们展示了如何以级数余项的大小为判据，准确地半解析估计边界（在轨道根数空间中），在该边界处消除粒子快自由度后得到的长期哈密顿量模型可对真实动力学提供有效近似。
英文摘要：
We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the primary perturber. Starting with a multipole expansion of the barycentric (Jacobi-reduced) Hamiltonian, we carry out a sequence of normalizations in Delaunay variables by Lie series, leading to a secular Hamiltonian model without use of relegation. To this end, we introduce a book-keeping analogous to the one proposed in Cavallari and Efthymiopoulos (2022) for test particle orbits interior to the one of the primary perturber, but here adapted, instead, to the case of exterior orbits. We give numerical examples of the performance of the method in both the planar circular and the spatial elliptic restricted three-body problem, for parameters pertinent to the Sun-Jupiter system. In particular, we demonstrate the method's accuracy in terms of reproducibility of the orbital elements' variations far from mean-motion resonances. As a basic outcome of the method, we show how, using as criterion the size of the series' remainder, we reach to obtain an accurate semi-analytical estimate of the boundary (in the space of orbital elements) where the secular Hamiltonian model arrived at after eliminating the particle's fast degree of freedom provides a valid approximation of the true dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
