Global Search Strategy for Periodic Orbit Near an Irregular Asteroid
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摘要: 研究不规则小行星附近的自然周期轨道，有助于更好地认识小行星附近的动力学特性。周期轨道的搜索过程需要频繁地进行轨道递推，其中绝大多数的计算时间消耗在不规则小行星附近的引力加速度计算中。为提高加速度计算效率，提出一种不规则小行星引力加速度快速估计方法；在此基础上，通过参数空间内随机化粗略搜索获得周期轨道的初值猜想；利用遗传算法在初值猜想附近区间进行精细搜索，找到周期轨道的初值。通过对不规则小行星433 Eros附近周期轨道的搜索，对其附近不同形状的周期轨道进行了分类，分析周期轨道在小行星附近的分布规律。Abstract: Natural periodic orbits around irregular asteroids can help us better understand the dynamics of asteroids. The search process of periodic orbit requires frequent orbit recursion, and most of the calculation time is consumed in the calculation of gravitational acceleration near irregular asteroids. In order to improve the efficiency of acceleration calculation, a new fast estimation method for gravitational acceleration of irregular asteroids is proposed. On this basis, the initial guess of periodic orbits is obtained by random rough search in parameter space. Finally, genetic algorithm is used to find the initial value of periodic orbit. By searching the periodic orbits of irregular asteroid 433 Eros, the periodic orbits of different shapes near the asteroid are classified, and the distribution of periodic orbits near the asteroid is analyzed.
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Key words:
- Irregular asteroid /
- Gravitational acceleration /
- Periodic orbitals /
- Random search /
- Genetic algorithm
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图 1 检验点和小行星质心与伪中心位置关系
Figure 1. Test point, asteroid centroid and pseudocenter location relationship
图 2 标准多面体模型（a）和快速估计方法采样模型（b）
Figure 2. Standard polyhedral model (a) and fast estimation method sampling model (b)
图 3 20 km（a）和30 km（b）高度快速估计方法的相对误差分布
Figure 3. Relative error distribution of fast estimation method for height at 20 km (a) and 30 km (b)
图 9 近赤道面类圆轨道各方向视图
Figure 9. All directions view of near-equatorial quasi-circular orbit
图 10 赤道投影心形轨道各方向视图
Figure 10. All directions view of Equatorial projection cardioid orbit
图 11 绕小行星大双圈轨道各方向视图
Figure 11. All directions view of the large double circle orbit around the asteroid
图 12 近赤道面三角平衡点单弯折轨道各方向视图
Figure 12. All directions view of the near-equatorial plane single-bent orbit at the triangular libration point
图 13 三角平衡点双弯折轨道各方向视图
Figure 13. All directions view of the double-bent orbit at the triangular libration point
图 14 L3点附近类8字形周期轨道分布
Figure 14. Distribution of similar to 8 shape orbits near L3 point
图 15 L4点附近类8字形周期轨道分布
Figure 15. Distribution of similar to 8 shape orbits near L4 point
图 16 L1点（a）和L2点（b）附近类8字形轨道分布
Figure 16. Distribution of similar to 8 shape orbits near L1 (a) and L2 (b) points
图 17 倾斜双翘曲面轨道在小行星附近的分布
Figure 17. Distribution of oblique double warpage orbits near asteroids
图 18 近赤道面类圆形轨道在小行星赤道面附近的分布
Figure 18. Distribution of near-equatorial quasi-circular orbits near the asteroid's equatorial plane
图 19 三角平衡点附近赤道投影心形轨道的分布
Figure 19. Distribution of Equatorial projection cardioid orbits near triangular equilibrium point
图 20 绕小行星大双圈轨道在小行星周围的分布
Figure 20. Distribution of large double-circle orbits around the asteroid
图 21 近赤道面三角平衡点单弯折轨道在小行星赤道面附近的分布
Figure 21. Distribution of near-equatorial plane single - bent orbits near the asteroid's equatorial plane
图 22 三角平衡点双弯折轨道的分布
Figure 22. Distribution of the double - bent orbit at triangular translational points
表 1 不同引力加速度计算方法的计算速度
Table 1. Calculation velocity of different gravitational acceleration calculation methods
引力加速度计算方法 1000次运算总用时/s 相对计算效率（以标准多面体模型的结果作为1） 多面体法（49152面片标准多面体模型） 69 1 多面体法（3000面片简化多面体模型） 6.9 10 10×10阶次球谐函数模型 0.64 107.8 6×6阶次球谐函数模型 0.28 246.4 快速估计方法 0.075 920 
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