研究修正圆型限制性三体问题的平衡点：以太阳-妊神星系统为例
Studying the Equilibrium Points of the Modified Circular Restricted Three-Body Problem: the Case of Sun-Haumea System
AI总结：
本文研究引入多摄动参数的修正圆型限制性三体问题，建立数学模型发现五个平衡点，将其应用于太阳-妊神星系统，发现摄动导致平衡点偏移，且共线点不稳定、非共线点稳定性取决于质量参数$μ$。
摘要：
我们旨在通过引入多个摄动参数来研究平面圆型限制性三体问题（CRTBP）的修正版本。我们将较大主天体视为扁球体且具有辐射，而较小主天体具有细长体形状。我们还考虑了环绕该三体系统的盘状结构带来的摄动。首先，我们建立了该修正CRTBP的数学模型。我们发现该修正CRTBP模型中存在五个平衡点，其中三个为共线平衡点，另外两个为非共线平衡点。其次，我们通过设定各摄动参数的多个值，将修正CRTBP模型应用于太阳-妊神星系统。通过数值研究，我们发现引入摄动参数导致太阳-妊神星系统的平衡点位置相比经典CRTBP发生了偏移。我们研究了平衡点的稳定性。结果表明，共线平衡点是不稳定的，而非共线平衡点的稳定性取决于系统的质量参数$μ$。与经典情况不同，非共线平衡点要实现稳定具有$μ$的最大和最小极限。我们指出，非共线平衡点$μ$的稳定范围取决于摄动参数。在太阳-妊神星系统的背景下，我们发现非共线平衡点是稳定的。
英文摘要：
We intend to study a modified version of the planar Circular Restricted Three-Body Problem (CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP. We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun-Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun-Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter $μ$ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of $μ$ for achieving stability. We remark that the stability range of $μ$ in non-collinear equilibrium points depends on the perturbing parameters. In context of the Sun-Haumea system, we have found that the non-collinear equilibrium points are stable.
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