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摘要:
围绕火卫一的准卫星轨道（QSOs）因其具有良好的稳定性，是火卫一探测任务最为实用的轨道。在平面圆型限制性三体问题模型下，利用庞加莱截面和KAM环迭代方法探究了准卫星轨道的周期轨道族，并给出不同能量准卫星周期轨道的初始条件。针对火卫一周期准卫星轨道入轨，提出一种转移轨道设计方法：对准卫星周期轨道调整速度后进行反向积分，直至离开火卫一邻近区域，从而得到由火星环绕轨道向火卫一周期准卫星轨道的转移轨道，并调整转移轨道参数对燃料与时间消耗进行优化。研究结果表明，当周期准卫星轨道能量处于特定区间时，存在特定速度脉冲区间，可利用火卫一引力实现较少燃料消耗的轨道转移；在该速度脉冲区间中，通过选取较小的速度脉冲，可缩短转移时间。
Abstract:The Quasi-Satellite Orbits (QSOs) around Phobos are the most practical orbits in Phobos exploration missions due to their stability. With the planar circular restricted three-body problem model, Poincaré's surface of section and KAM tori iterations are employed to investigate the periodic QSOs. Initial conditions of periodic QSOs with different energy are determined. A method to design transfer orbits from orbits around the Mars to periodic QSOs is proposed, which propagates orbits backward from injection points on QSOs with a Δ
V to somewhere away from Phobos to complete a transfer. The fuel consumption and transfer time are optimized by changing transfer parameters. It is found that when the energy of the periodic quasi-satellite orbit is in a specific interval, a specific interval of impulsive velocity exists, in which the Phobos' gravity can be used for fuel saving, and a shorter transfer time can be achieved with a small impulsive velocity. -
图 1 原点位于火星火卫一系统质心的旋转坐标系
Figure 1. Synodic coordinate system with origin at the barycenter of Mars and Phobos
图 4 不同Jacobi常数下的庞加莱映射边界
Figure 4. Poincaré's maps' borders with different Jacobi constants
图 8 不同速度脉冲ΔV时回溯轨道与火卫一的最远距离(C=2.999890，x=98.3209km)
Figure 8. Maximum distance from backward orbits to the Phobos with different impulsive velocity ΔV (C=2.999890, x=98.3209km)
图 10 不同Jacobi常数下的T区窗口分布
Figure 10. T window distribution with different Jacobi constants
图 11 不同Jacobi常数下，轨道转移时间与T区速度脉冲ΔV的关系
Figure 11. Relationship between orbit transfer time and impulsive velocity ΔV with different Jacobi constants
表 1 不同Jacobi常数下周期准卫星轨道初始条件
Table 1. Initial conditions of periodic QSOs with different Jacobi constants
C x/km ẏ/(m·s －1) 2.999890 98.3209 -44.8851 2.999895 96.0619 -43.8670 2.999900 93.7446 -42.8242 2.999905 91.3702 -41.7557 2.999910 88.9317 -40.6591 2.999915 86.4245 -39.5325 2.999920 83.8423 -38.3731 2.999925 81.1778 -37.1777 2.999930 78.4230 -35.9433 2.999935 75.5678 -34.6659 2.999940 72.6002 -33.3401 2.999945 69.5060 -31.9607 2.999950 66.2674 -30.5208 2.999955 62.8619 -29.0120 2.999960 59.2610 -27.4234 2.999965 55.4265 -25.7418 2.999970 51.3062 -23.9504 2.999975 46.8255 -22.0263 2.999980 41.8731 -19.9418 2.999985 36.2733 -17.6650 
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表 2 入轨区P4点入轨停泊轨道要素(相对火星)
Table 2. Orbital elements of parking orbit for injection point P4 (with respect to the Mars)
参数 数值 半长轴a/km 9248.87 偏心率e 0.016906 升交点赤经Ω/(°) 0 近火点辐角ω/(°) 221.99 倾角i/(°) 0
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