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双小行星探测轨道动力学研究进展

王悦 伏韬 张瑞康

王悦, 伏韬, 张瑞康. 双小行星探测轨道动力学研究进展. 力学学报, 2022, 54(5): 1155-1185 doi: 10.6052/0459-1879-21-637
引用本文: 王悦, 伏韬, 张瑞康. 双小行星探测轨道动力学研究进展. 力学学报, 2022, 54(5): 1155-1185 doi: 10.6052/0459-1879-21-637
Wang Yue, Fu Tao, Zhang Ruikang. Research progress on orbital dynamics about the binary asteroid system exploration. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1155-1185 doi: 10.6052/0459-1879-21-637
Citation: Wang Yue, Fu Tao, Zhang Ruikang. Research progress on orbital dynamics about the binary asteroid system exploration. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1155-1185 doi: 10.6052/0459-1879-21-637

双小行星探测轨道动力学研究进展

doi: 10.6052/0459-1879-21-637
基金项目: 国家自然科学基金资助项目(11872007)
详细信息
    作者简介:

    王悦, 副教授, 主要研究方向: 航天动力学与控制、小天体探测与防御. E-mail: ywang@buaa.edu.cn

  • 中图分类号: V412.4+1

RESEARCH PROGRESS ON ORBITAL DYNAMICS ABOUT THE BINARY ASTEROID SYSTEM EXPLORATION

  • 摘要: 双小行星系统由在万有引力作用下彼此环绕的两颗小行星组成, 对研究太阳系起源、行星系统演化和行星防御都具有重要的价值, 近年来成为行星科学和航天动力学研究的热门对象, 对双小行星系统的原位探测也即将迎来热潮. 双小行星系统的独特构型和附近的复杂动力学环境为探测器轨道动力学和任务设计带来了全新的挑战, 为应对这些挑战所进行的研究也推动了轨道动力学基础理论的发展. 本文对双小行星探测轨道动力学的研究进展进行综述, 首先介绍了双小行星研究和探测的背景及意义, 简要阐述了双小行星系统形成理论及其附近轨道动力学的研究概况. 其次, 介绍了双小行星系统不规则引力场和相互引力势的建模方法, 进而展示了双星的姿态轨道耦合动力学, 即完全二体问题, 包括双星相对运动的平衡构型和稳定性. 接着, 介绍了描述双星附近探测器轨道运动的限制性完全三体问题的动力学模型, 以及该模型下的平动点、平动点周期轨道、大范围周期轨道、转移轨道和轨道维持等方面的研究进展. 第四部分综述了环绕双小行星系统单颗星的受摄二体问题, 以轨道摄动理论和行星系统中受摄二体问题的研究现状为背景, 介绍了环绕双小行星系统主星的半解析轨道动力学建模与轨道稳定性分析. 之后, 介绍了目前面向探测任务需求和考虑实际约束的轨道动力学研究和轨道设计. 最后, 基于目前研究进展, 分析了面临的若干问题, 对未来双小行星探测轨道动力学及相关技术的发展进行了讨论和展望.

     

  • 图  1  本文结构安排及各部分之间的关系

    Figure  1.  Organization of this paper and connections between different parts

    图  2  质点群法对椭球的不同离散方式[14]

    Figure  2.  The different way of filling the ellipsoid with point masses[14]

    图  3  火卫一复合球谐函数模型分区示意图[51]

    Figure  3.  Regionalization of the compound gravity harmonic approach of Phobos[51]

    图  4  小行星4769 Castalia的球谐(左)和椭球谐(右)引力场模型的收敛域[14]

    Figure  4.  The convergence domain of spherical harmonics (left) and ellipsoidal harmonics (right) gravity models of the asteroid 4769[14]

    图  5  小行星433 Eros多面体模型

    Figure  5.  The polyhedron model of the asteroid 433 Eros

    图  6  小行星216 Kleopatra两质点链接模型(上)与243 Ida三质点链接模型(下)[62]

    Figure  6.  The double-particle-linkage model of 216 Kleopatra (up) and the triple-particle-linkage model of 243 Ida (down)[62]

    图  7  两刚体相互引力势的几何构型

    Figure  7.  Geometrical representation of mutual gravitational interaction

    图  8  球与椭球二体系统相对运动平衡构型[21]

    Figure  8.  Relative equilibrium configuration of the sphere-ellipsoid two-body problem[21]

    图  9  球与椭球二体系统长轴平衡构型的稳定[22]

    Figure  9.  Stable parameter space of the sphere-ellipsoid long-axis equilibrium configuration[22]

    图  10  航天器(质点)在双小行星系统附近的轨道运动

    Figure  10.  A massless particle moving in the gravity field of a binary asteroid system

    图  11  双多面体模型下双星系统1999 KW4附近的零速度面与平动点[32]

    Figure  11.  Zero velocity curves and libration points of the binary asteroid system 1999 KW4[32]

    图  12  双椭球模型中的平动点轨道族[28]

    Figure  12.  Libration point orbits (LPO) in the ellipsoid-ellipsoid model[28]

    图  13  不同模型下平动点周期轨道族连接方式[32]

    Figure  13.  Connections of libration point orbits in different dynamical model[32]

    图  14  不同次星形状时平动点轨道族连接情况[107]

    Figure  14.  Connections of libration point orbit families with different shapes of the secondary[107]

    图  15  单同步双星系统L1点和L2点附近的周期轨道[32]

    Figure  15.  Periodic orbits near L1 and L2 about the single synchronous binary asteroid system[32]

    图  16  双小行星系统1999 KW4中部分围绕主星和次星的周期轨道[33]

    Figure  16.  Periodic orbits about the primary and the secondary in the binary asteroid system 1999 KW4[33]

    图  17  双小行星双椭球模型下的平面共振轨道[28]

    Figure  17.  Planar resonant orbits in the ellipsoid-ellipsoid model[28]

    图  18  围绕双小行星系统1999 KW4的大范围周期轨道[33]

    Figure  18.  Period orbits with wide range around the binary asteroid system 1999 KW4[33]

    图  19  球-椭球模型下的全局探测路径[119]

    Figure  19.  Exploration trajectories in the sphere-ellipsoid model[119]

    图  20  名义轨道在平稳态(上)与活跃态(下)系统中的轨迹[35]

    Figure  20.  Trajectories of nominal orbits in the dynamical systems with relaxed mode (up) and excited mode (down)[35]

    图  21  L1点Halo轨道在平稳态(上)与活跃态(下)系统中采用目标点法实现轨道维持[35]

    Figure  21.  The trajectories during the stationing-keeping in the dynamical systems with relaxed mode (up) and excited mode (down) by using the target point method with the L1 Halo orbit as nominal orbits[35]

    图  22  轨道平面法向量在单位球面上的进动轨迹[132]

    Figure  22.  Trajectories of the orbit pole on the unit sphere[132]

    图  23  系统在参数空间$(\kappa ,h_z^2)$中的分岔

    Figure  23.  Bifurcation lines in the parameter space$(\kappa ,h_z^2)$

    图  24  二次平均化模型下的两个轨道积分常量[160]

    Figure  24.  The two orbit integral constants under the doubly-averaged model[160]

    图  25  偏心Lidov-Kozai机制下的轨道翻转[170]

    Figure  25.  Orbit flip of the eccentric Lidov-Kozai mechanism[170]

    图  26  层级三体问题中的内问题与外问题

    Figure  26.  The inner and outer problem in the hierarchy three-body system

    图  27  双小行星的二体构型和环绕主星的轨道[41]

    Figure  27.  The two-body configuration of the binary asteroid system and orbits around the primary[41]

    图  28  ${J_2}$临界倾角附近的$\omega {{ - }}e$相空间轨迹[41]

    Figure  28.  $\omega {{ - }}e$ phase trajectories around the ${J_2}$ critical inclination[41]

    图  29  不稳定轨道的轨道寿命[41]

    Figure  29.  The orbital lifetime of unstable orbits[41]

    图  30  J2摄动的层级椭圆型限制性三体问题下的轨道翻转

    Figure  30.  Orbit flip in the hierarchical elliptical restricted three-body problem with the J2 perturbation

    图  31  绕双星65803 Didymos晨昏轨道(从太阳方向看)[31]

    Figure  31.  Terminator orbits around the binary asteroid system 65803 Didymos seen from the Sun direction[31]

    图  32  双小行星系统65803 Didymos附近的周期轨道族[30]

    Figure  32.  Periodic orbits in the binary asteroid system 65803 Didymos[30]

    图  33  Hera探测器的双曲线飞掠轨迹设计

    Figure  33.  The hyperbolic fly-by trajectories design of Hera mission

    图  34  双小行星系统90 Antiope成员之间的转移轨道[192]

    Figure  34.  The spatial transfer orbits between the two bodies of the binary asteroid system 90 Antiope[192]

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  • 收稿日期:  2021-12-01
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