双二体几何切面法及天梯地月转移轨道分析

双二体模型是求解地月转移轨道的重要基础。与传统的采用月球影响球入口点经纬度的描述方式不同,本文提出一种基于飞行轨道面参数来描述地月转移轨道的双二体模型几何表达方式,结合一维非线性方程求根算法Brent算法和Lambert原理,将原始三维球面搜索算法降维成为二维圆上的搜索算法,可以高效求解地月转移轨道的形状参数。为避免重复计算,将转移轨道窗口计算的轨道多变量搜索问题解耦分解成两个子问题——转移轨道形状参数求解问题和转移轨道面空间定向问题,降低了问题的求解维度。形成两级并行计算算法,充分发挥多核计算机算力,加速计算过程。仿真结果表明,基于提出的并行圆锥曲线几何切面法,可以成功应用于计算天梯地月转移轨道分析。

Double two-body model using geometrical section method and the analysis of Earth-Moon transfer orbit from space elevator

Double two-body model is the fundamental conception model for solving Earth-Moon transfer orbit. The traditional approaches use the latitude and longitude of entry point on the sphere of influence to describe double two-body model, while in this paper a geometrical representation method of double two-body model by using parameters in orbital plane of flight trajectory was proposed. The search space on three-dimensional sphere was reduced to be a two-dimensional circle formed by tangent of the orbital plane and the sphere of influence, the shape parameter of Earth-Moon transfer orbit can be efficiently solved by one-parameter Brent root-finding algorithm and Lambert theory. In order to avoid double calculation, the orbital multivariate search problem calculated by the transfer orbit window was decoupled into two sub-problems, the transfer orbit shape parameter solution problem and the transfer orbital plane space orientation problem, which reduce the solution dimension of the problem, The two-stage method with parallel computing was approached in order to make full use of the nowadays computational power of multi-core computer. The simulation results show that the new parallel double two-body model with the use of geometrical section of orbital plane can be successfully applied to the analysis of the Earth-Moon transfer orbit from space elevator.