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摘要:
随着天文观测的深入，发现不仅土星、木星等气态巨行星环绕有光环，某些小天体也环绕有光环。针对目前发现环的半人马型小天体女凯龙星（10199 Chariklo），研究其引力场中粒子（视为质点）的轨道动力学，分析赤道椭率和小天体自转对环中粒子轨道运动的影响，通过庞加莱截面中的KAM环迭代，得到第一类周期轨道和1∶3共振周期轨道，并通过对比和分析得到小天体光环位置与小天体自转平运动共振的关系。研究结果表明：女凯龙星内环中的粒子最可能处在满足径向振荡幅值范围的第一类周期轨道及其附近的准周期轨道上，但不能排除处在1∶3共振周期轨道及其附近的准周期轨道上；外环中的粒子不可能处在1∶3共振周期轨道上，只可能处在第一类周期轨道及其附近的准周期轨道上。
Abstract:With the development of astronomical observations, it has been found that, not only Saturn, Jupiter and other giant planets, but also some small bodies are surrounded by rings. Focussing on rings of the Centaur 10199 Chariklo, we study the orbital dynamics of particles in the gravitational field of Chariklo, and analyze the impacts of equatorial ellipticity and rotation of Chariklo on the orbital motion of particles. The first kind of periodic orbits and 1:3 resonant periodic orbits are obtained by using KAM torus iteration on the Poincaré sections. The relationship between the position of rings and the mean motion resonances are revealed by analyzing the properties of the periodic orbits. The results show that, the particles in the inner ring of Chariklo are most likely associated with the first kind of periodic orbits and their quasi-periodic orbits, but are also likely associated with the 1:3 resonant periodic orbits and their quasi-periodic orbits. The particles in the outer ring of Chariklo are not associated with the 1:3 resonant periodic orbits, but are associated with the first periodic orbits and their quasi-periodic orbits.
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图 2 粒子在固连坐标系oxy平面内的运动及庞加莱截面
Figure 2. Motion of particles in oxy plane of body-fixed frame and Poincaré section
图 4 1∶3共振周期轨道在固连坐标系中的形状
(C=7 472 m2/s2)
Figure 4. Shape of 1∶3 resonant periodic orbits in body-fixed frame (C=7 472 m2/s2)
图 5 1∶3共振周期轨道在惯性坐标系中的形状
(C=7 472 m2/s2)
Figure 5. Shape of 1∶3 resonant periodic orbits in inertial frame (C=7 472 m2/s2)
图 6 1∶3共振周期轨道在3年内的轨迹
(C=7 472 m2/s2)
Figure 6. Trajectory in 3 years of 1∶3 resonant periodic orbits (C=7 472 m2/s2)
图 7 不同C下的1∶3共振周期轨道
Figure 7. 1∶3 resonant periodic orbits with different Jacobi constants
图 8 第一类周期轨道在固连坐标系中的形状
(C=7 472 m2/s2)
Figure 8. Shape of the first kind of periodic orbits in body-fixed frame (C=7 472 m2/s2)
图 9 第一类周期轨道在惯性坐标系中的形状
(C=7 472 m2/s2)
Figure 9. Shape of the first kind of periodic orbits in inertial frame (C=7 472 m2/s2)
图 10 两类周期轨道的周期随C的变化
Figure 10. Change of period with C of two kinds of periodic orbits
图 11 两类周期轨道的轨道半径r随C的变化
Figure 11. Change of orbit radius r with C of two kinds of periodic orbits
图 13 两类周期轨道和女凯龙星环的aeq-eeq图
Figure 13. aeq-eeq map of two kinds of periodic orbits and 10199 Chariklo's rings
图 14 极限范围内2类周期轨道在惯性坐标系中的对比
Figure 14. Comparison of two kinds of periodic orbits in limit range in the inertial frame
表 1 女凯龙星及其环的参数和估算出的2∶6共振位置
Table 1. Parameters of 10199 Chariklo and its rings and estimated 2∶6 resonance position
参数 数值 a/km 157 b/km 139 c/km 86 参考半径Re/km 123.349 6 质量M/kg 6.3×1018 自转周期T/h 7.004 椭率ε 0.175 1 扁率f 0.479 4 环中心位置/km CR1:390.6±3.3, CR2:404.8±3.3 环宽/km CR1:7，CR2:3 2∶6共振位置/km 392.22 
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