Bury Luke, McMahon Jay
Office 422 Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO 80303 USA.
Office 461 Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO 80303 USA.
Celest Mech Dyn Astron. 2020;132(9):45. doi: 10.1007/s10569-020-09983-3. Epub 2020 Sep 25.
The circular restricted three-body model is widely used for astrodynamical studies in systems where two major bodies are present. However, this model relies on many simplifications, such as point-mass gravity and planar, circular orbits of the bodies, and limiting its accuracy. In an effort to achieve higher-fidelity results while maintaining the autonomous simplicity of the classic model, we employ zonal harmonic perturbations since they are symmetric about the -axis, thus bearing no time-dependent terms. In this study, we focus on how these perturbations affect the dynamic environment near the secondary body in real systems. Concise, easily implementable equations for gravitational potential, particle motion, and modified Jacobi constant in the perturbed model are presented. These perturbations cause a change in the normalized mean motion, and two different formulations are addressed for assigning this new value. The shifting of collinear equilibrium points in many real systems due to of each body is reported, and we study how families of common periodic orbits-Lyapunov, vertical, and southern halo-shift and distort when , , and of the primary and of the secondary body are accounted for in the Jupiter-Europa and Saturn-Enceladus systems. It is found that these families of periodic orbits change shape, position, and energy, which can lead to dramatically different dynamical behavior in some cases. The primary focus is on moons of the outer planets, many of which have very small odd zonal harmonic terms, or no measured value at all, so while the developed equations are meant for any and all zonal harmonic terms, only even terms are considered in the simulations. Early utilization of this refined CR3BP model in mission design will result in a more smooth transition to full ephemeris model.
圆形限制性三体模型在存在两个主要天体的系统的天体动力学研究中被广泛使用。然而，该模型依赖于许多简化条件，例如质点引力以及天体的平面圆形轨道，这限制了其准确性。为了在保持经典模型自主简单性的同时获得更高保真度的结果，我们采用带状调和摄动，因为它们关于z轴是对称的，因此不存在时间相关项。在本研究中，我们关注这些摄动如何影响实际系统中次天体附近的动态环境。给出了摄动模型中引力势、粒子运动和修正雅可比常数的简洁且易于实现的方程。这些摄动会导致归一化平均运动发生变化，并且针对分配这个新值提出了两种不同的公式。报告了许多实际系统中共线平衡点由于每个天体的[具体因素未明确]而发生的移动，并且我们研究在木星 - 木卫二和土星 - 土卫二系统中考虑主天体的[具体因素未明确]、[具体因素未明确]和[具体因素未明确]以及次天体的[具体因素未明确]时，常见周期轨道族——李雅普诺夫轨道、垂直轨道和南部晕轨道——是如何移动和变形的。研究发现，这些周期轨道族会改变形状、位置和能量，在某些情况下可能导致截然不同的动力学行为。主要关注点是外行星的卫星，其中许多卫星的奇数带状调和项非常小，或者根本没有测量值，所以虽然所推导的方程适用于任何和所有带状调和项，但在模拟中只考虑了偶数项。在任务设计中尽早使用这种改进的CR3BP模型将导致向完整星历模型的更平稳过渡。
