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摘要:
针对发射场射向范围和低温入轨级在停泊轨道上最长允许滑行时间严格受限下，工程设计火星探测任务发射轨道时，优化保障2~3周发射日期窗口的困难，以及精确设计拼接探测器分离点时刻轨道6根数耗时周期长等问题，提出了加入滑行时间限制再精确双向微分修正的设计算法（有别于传统B平面矢量法）。由地球影响球边界速度直接解出长征运载火箭入轨点轨道根数，将火箭飞行星下点弧段表示成滑行时间的分析式，快速找到满足诸多设计约束的初始发射轨道；并解决了考虑探测器小幅深空机动后火箭发射轨道的深入优化问题。精确力学模型下数值微分改进后，获得高精度计算结果，同等可比条件下运算精度不低于STK软件。实现了从地面起飞到抵达近火点的飞行轨道整体优化，确保了首次探火工程的顺利实施。
Abstract:In order to solve the problem of searching for optimized launch period lasting 2-3 weeks for an engineering-oriented Earth-to-Mars transfer trajectory, with constraints from the launch azimuth scope and the longest coast time on parking orbit of the cryogenic final stage, adding coast constraint into models firstly, a forward-backward bi-directional differential correction scheme which is different from the B plane vector method is proposed. It also greatly reduces the required time to accurately design and match all the six orbital elements at the separation point with probe. The hyperbolic orbital elements at the injection point of launch vehicle are directly solved from the boundary velocity at the sphere of influence of the Earth. Meanwhile the flight arc of the ground track is given analytically as a function of the coast time. Initial launch trajectory satisfying the constraints are quickly found. The problem of launch trajectory optimization is solved when considering a small deep space maneuver of Mars probe. High-precision results are obtained using this bi-directional differential correction scheme in the high-precision mechanical model. The analysis shows that the accuracy is matched with the commercial software STK under the same condition. The transfer trajectory starting from liftoff to the nominal periapsis of Mars probe is optimized as a whole, which ensures that our first Mars exploration mission implements successfully.
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图 3 射向AL、飞行航程角θ与δo关系
Figure 3. Contour map of δo with respect to launch azimuth AL and flight range angle θ
图 4 长征运载火箭设计探测火星轨道示意图
Figure 4. Schematic diagram of Long March launch vehicle for Earth-to-Mars trajectory design
表 1 发射轨道Th=1 849 s, 探测器05 : 25释放, 地球升交出发
Table 1. Trajectory Th=1 849 s, probe released on 05 : 25, ascending from the Earth
轨道根数 EJ2000 SJ2000 ME a -21 424.437 km 1.321 527 5 AU -3 816.831 km e 1.307 039 0 0.241 839 5 2.020 742 1 i/(°) 25.405 23.424 93.000 Ω/(°) 316.214 356.094 156.275 ω/(°) 293.745 293.291 118.136 M/(°) 2.781 57.042 0 Hp 200.0 km 1.001 930 0 AU 500.0 km ΔV/(m·s-1) 4 039.207 0 2 446.974 注:Hp为轨道的近拱点高度(分别相对近地、椭圆近日、近火), M为平近点角。 
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表 2 发射轨道Th=2 312 s, 探测器03 : 15释放, 地球降交出发
Table 2. Trajectory Th=2 312 s, probe released on 03 : 15, descending from the Earth
轨道根数 EJ2000 SJ2000 ME a -21 373.589 km 1.321 389 5 AU -3 815.267 km e 1.307 769 4 0.241 822 3 2.021 160 4 i/(°) 25.372 23.420 93.000 Ω/(°) 281.242 356.067 156.217 ω/(°) 325.518 293.283 118.191 M/(°) 2.790 57.077 0 Hp 200.0 km 1.001 848 1 AU 500.0 km ΔV/(m·s-1) 4 041.078 0 2 447.373
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