该文以小行星2867 Steins为例，研究了质量瘤的变化对小天体平衡点的位置、拓扑类型和稳定性的影响。考虑了单层相似质量瘤、单层球形质量瘤、多层相似质量瘤和多层球形质量瘤等4种质量瘤的情形。发现质量瘤的存在可能会引起平衡点稳定性和拓扑类型的变化。对于小行星2867 Steins来说，无质量瘤和有质量瘤情形的体外平衡点E4的拓扑类型和稳定性不同，前者对应的该平衡点是不稳定的，拓扑类型为Case 5；而后者对应的该平衡点是稳定的，拓扑类型为Case 1。相比无质量瘤情形，有质量瘤情形的体外平衡点的质心距更大，而体内平衡点的质心距更小。如果质量瘤位置、密度和体积基本相同，则质量瘤的形状变化对平衡点位置的影响可以忽略不计，同时质量瘤的形状变化对平衡点的拓扑类型和稳定性没有影响。该结果有助于理解内部结构的变化对小行星引力场环境的影响，可为小行星探测任务的引力场重构、轨道设计与任务可靠性分析提供参考。
This paper investigates the influence of a variety of mascon properties on the positions, topological conditions, and stability of the equilibria of minor bodies with application to asteroid 2867 Steins. Four types of mascon models are considered, the single-layer similar mascon, single-layer spherical mascon, multi-layer similar mascon, and multi-layer spherical mascon. The results show that the mascon may change the stability and topological conditions of the equilibrium points. For asteroid 2867 Steins, the topological condition and stability of external equilibrium point E4 differ between the mascon and the non-mascon cases. If the asteroid has no mascon, E4 is unstable and the topological condition is Case 5. If the asteroid has a mascon with the assumed density, E4 is stable and the topological condition becomes Case 1. The mascon case has larger distances between the external equilibrium point and the center-of-mass than the non-mascon case and smaller distances between the inner equilibrium point and the center-of-mass. If the position, density, and volume of two mascons are essentially the same, the shape has little effect on the equilibrium point position and no influence on the topological condition and stability of the equilibrium point. This study provides further understanding of the influence of the internal asteroid structure on the gravitational field around asteroids and provides a reference for gravitational field reconstruction, orbit design, and reliability analyses of asteroid exploration missions.
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