基于DRO的小行星往返飞越探测轨道设计优化方法
doi: 10.11728/cjss2023.05.2023-0011 cstr: 32142.14.cjss2023.05.2023-0011
Orbit Design Optimization Method for an Asteroid Flyby Mission from DRO
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摘要: 远距离逆行轨道（Distant Retrograde Orbits，DRO）是地月系统内一类稳定的周期性轨道，本文研究航天器从DRO轨道站出发，通过月球和地球引力辅助实现飞越探测近地小行星的往返转移轨道设计方法。通过地月引力辅助作用和中途杠杆机动等技术手段减少调整倾角所需的速度增量，扩大在相同速度增量约束下飞越探测小行星的可达范围。同时，通过引入DRO调相轨道，减少DRO逃逸和俘获时的相位约束，将转移轨道段与DRO轨道站的相位解耦，从而降低了该问题的计算复杂度。仿真结果表明，在2 km·s–1的速度增量等约束条件下，通过此研究方法可以实现从DRO轨道站出发飞越探测近地小行星并返回的轨道设计。Abstract: Distant Retrograde Orbit (DRO) is a kind of stable periodic orbit in Earth-Moon system. In this paper, a design method of distant retrograde orbit for spacecraft to fly by and explore near-Earth asteroids by means of the moon and Earth’s gravity assistance starting from DRO orbital station is studied. By means of earth-moon gravity assistance and mid-course lever maneuver, the velocity increment required for adjusting the inclination angle is reduced, and the reachable range of the asteroid flying by exploration under the same velocity increment constraint is expanded. At the same time, the calculation complexity of the problem is reduced by introducing DRO phasing, with reducing the phase constraints of escape and capture in DRO, and decoupling the phase of the transfer track from the DRO orbital station. The simulation results show that under the velocity increment of 2 km·s–1, the method can realize the orbit design of flyby exploration of near-Earth asteroids from DRO orbital station and return.
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Key words:
- DRO /
- Near-Earth asteroid /
- B plane parameters /
- Lunar gravity assist /
- Orbital phasing
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图 2 远距离逆行轨道 （a）地球惯性系 （b） 地月旋转坐标系
Figure 2. DRO track diagram. (a) Earth’s inertial system, (b) Earth-Moon rotating coordinate system
图 3 飞越小行星时黄道面与各天体的关系
Figure 3. Relationship between ecliptic plane and celestial bodies during asteroid flyby
图 4 DRO直接转移轨道整体设计（I表示DRO直接往返的小行星飞越探测轨道）
Figure 4. DRO direct transfer orbit overall diagram (I expresses DRO direct return asteroid flyby orbit)
图 5 借力转移轨道整体设计（I：地球往返的小行星飞越探测轨道。II：地球与DRO间转移轨道。III：DRO调相轨道）
Figure 5. Overall schematic diagram of transfer orbit by force (I: asteroid flyby detection orbit of Earth round trip. II: Earth DRO transfer orbit. III: DRO phase orbit)
图 6 地球往返的小行星飞越探测轨道（ECI，左侧点为小行星位置，右侧点为地球位置）
Figure 6. Earth round-trip asteroid flyby orbit（ECI. The left point is the location of the asteroid and the right point is the location of the Earth）
图 7 遍历与黄金分割方法结合的轨道初值搜索方法DRO往返地球轨道设计流程
Figure 7. Ergodic search method combined with the Golden section method schematic diagram of the DRO_Earth round trip orbit design flow
图 10 DRO直接往返的小行星飞越探测轨道（ECI）
Figure 10. DRO direct round trip asteroid flyby detection orbit（ECI）
表 2 常数取值与约束条件
Table 2. Constant values and constraints
名称 参数 地球引力常数/（km3·s–2） 398600 太阳引力常数/（km3·s–2） 132712440018 月球引力常数/（km3·s–2） 4902.8 地球半径/km 6378 月球半径/km 1738 初始时刻 MJD 60676 最大地球距离/km $ 2\times {10}^{7} $ 最小近地点高度/km 200 最小近月点高度/km 50 两机动间最小间隔时间/d 1 最大总速度增量/（km·s–1） 2 最大总飞行时间/a 4 
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表 1 虚拟目标小行星轨道参数
Table 1. Target asteroid orbit parameters
参数名称 初始历元（MJD） 半长轴（AU） 偏心率 倾角/（°） 升交点赤经/（°） 近地点幅角/（°） 真近地点角/（°） 数值 59600 1.129 0.366 2.68 163.67 188.14 182.30
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表 3 飞越探测轨道近地点参数
Table 3. Perigee parameters of flyby detection orbit
参数名称 近地点出发参数 返回近地点参数 初始历元（MJD） 63882.99 64243.01 ECI x/km –3278.43 3251.21 ECI y/km –4306.81 1011.57 ECI z/km 3739.86 –5628.97 ECI vx/（km·s–1） 0.971 1.070 ECI vy/（km·s–1） –7.688 10.790 ECI vz/（km·s–1） –8.002 2.557 白道面倾角/（o） 59.99 59.88 C3 /（km2·s–2） 2.9068 2.9238
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表 4 地球与DRO间转移轨道各项参数
Table 4. Perigee parameters of flyby detection orbit
参数名称 近地点机
动量
/（km·s–1）中途机
动量
/（km·s–1）中途机
动与近地
点间时长
/ d近月点机
动量
/（km·s–1）总速度
增量
/（km·s–1）DRO出发轨道 0.169 0.206 10.693 0.313 0.688 返回DRO轨道 0.166 0.234 15.701 0.271 0.671
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表 5 DRO调相轨道各项参数
Table 5. Elements of DRO phasing orbit
参数名称 调相起始
点机动量
/（km·s–1）调相滑行
时间/dDRO轨道站
会和机动
/（km·s–1）总速度增量
/（km·s–1）DRO出发调相轨道 0.132 43.542 0.096 0.228 返回DRO轨道 0.159 47.967 0.142 0.301
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