绕月轨道阴影区域建模与轨道优化

Mathematical models of lunar orbit shadow and optimization of lunar orbits

针对绕月运行轨道建立月球阴影区域与地球阴影区域的数学模型,给出了卫星是否处于阴影区域的判据;利用黄金分割法搜索出了阴影区域的边界值。将禁忌搜索算法嵌入遗传算法中并结合具体案例,搜索出了阴影时长最短的最优目标轨道。所给出的绕月轨道阴影区域模型简单且能够满足工程精度需求,可用于星上自主预报算法;所给出的嵌入式遗传算法能有效避免陷入局部最优并快速收敛。

Mathematical models of lunar and Earth shadow were established for lunar orbits. Also,the criterion was proposed to decide whether the satellite was in the shadow area. Golden section search optimization was used to search out the boundary values of the shadow area. In combination with specific cases,the optimal targeting lunar orbit was given by the genetic algorithm which was embedded in tabu search. The mathematical models of lunar orbit shadow given out in this article are simple enough to be used in on-board computer. Meanwhile,they can meet the engineering accuracy requirements. The embedded genetic algorithm has advantage of fast convergence without trapping in local optimum.