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基于偏转距离近似模型的动能撞击小行星防御任务脉冲轨道优化研究

IMPULSIVE TRAJECTORY OPTIMIZATION OF KINETIC IMPACTOR MISSIONS FOR ASTEROID DEFLECTION BASED ON AN APPROXIMATION DEFLECTION MODEL

  • 摘要: 小行星撞击对地球上的生命存在重大潜在威胁,动能撞击是目前最易实现且成熟度最高的防御方案.动能撞击任务的一种轨道优化指标为最大化偏转距离(即小行星被偏转前后近地距的改变量),若用数值积分的方法精确计算偏转距离, 会导致优化效率较低.在动能撞击任务的设计初期, 可以对动力学模型及偏转距离的计算方法进行简化,以提升优化效率. 本文首先将高精度模型简化为二体模型,分析了两种经典偏转距离解析模型的适用条件,同时提出一种基于近地点时刻预估的偏转距离近似模型; 考虑运载约束,将化学推进变轨简化为脉冲推力变轨,建立了直接转移(两脉冲及三脉冲)和行星借力飞行转移(单次及两次借力)的动能撞击轨道优化模型,利用遗传算法求解了优化问题. 以偏转小行星Apophis为例, 相比于解析模型,验证了本文提出的近似模型可以同时提升最优性、降低求解复杂性. 优化结果表明,三脉冲直接转移方案与两脉冲直接转移方案的最优偏转效果基本一致,借力飞行转移方案相比于直接转移方案对偏转距离的提升效果并不明显.在动能撞击任务的前期设计中, 可以基于二体模型进行防御效果的快速评估,虽然对计算偏转距离存在一定误差, 但对防御窗口的优化结果影响不大. 进一步,数值求解偏转距离时, 可通过引入主要引力摄动项(金星、地球、木星)修正二体模型,使其与高精度模型之间的求解误差在1%以下.

     

    Abstract: Asteroid impacts pose a major threat to all life on Earth. The kinetic impactor remains a promising strategy for asteroid deflection. One objective function of a kinetic impactor mission is to maximize the deflection distance (the change of the closest-approach distance before and after the asteroid is deflected). If the deflection distance is accurately calculated by a numerical integration, the efficiency of the optimization problem will be reduced. The dynamical model and the deflection distance calculation method can be simplified in the preliminary design of a kinetic impactor mission. This paper first simplifies the high-precision N-body dynamic model to the two-body dynamic model. Two classic deflection distance analytical models are introduced, at the same time, an approximate model of deflection distance based on closest-approach epoch estimation. Considering the launch performance and simplifying the chemical propulsion to the impulsive maneuver, the direct transfer trajectory optimization model and the planetary gravity assist trajectory optimization model are established. The Genetic Algorithm is used to solve the optimization problem. Taking deflecting Apophis as an example, compared with the analytical model, it is verified that the approximate model proposed in this paper can simultaneously improve the optimality and reduce the complexity of the solution. The simulation results show that the optimal deflection effect of the three-impulse direct transfer trajectory and the two-impulse direct transfer trajectory is almost the same, and the improvement of the planetary gravity assist transfer trajectory on the deflection distance is not obvious compared with the direct transfer trajectory. During the preliminary design stage of a kinetic impactor mission, the deflection distance can be quickly evaluated based on the two-body model. Although there is a certain error in the deflection distance, it does not affect the deflection window. The main gravitational perturbation terms (Venus, Earth, Jupiter) can be introduced to further modify the two-body dynamic model, so that the deflection distance error between modified two-body and the high-precision dynamic model is below 1%.

     

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