Approximate Analytical Solutions of Motion near the Collinear Libration-Points in Restricted Three-Body Problem

Abstract

With deep space exploration becoming a research focus in aerospace, corresponding fundamental research on three-body problem is of increasingly significant, especially the motion analysis near the collinear libration-points, which play a leading role in deep space mission design The approximate analytical solutions of motion near the collinear libration-points in circular restricted three-body problem has been obtained, however, there are relatively fewer studies about the solutions in elliptic restricted three-body problem, although it is more realistic and general than circular restricted three-body problem. Based on it, the approximate analytical solutions of motion near the collinear libration-points in elliptic restricted three-body problem are deduced by referencing the method used in circular restricted three-body problem, the positions of libration-points are obtained according to its characteristic, then the nonlinear dynamic model is linearized at the collinear libration-points, and the approximate analytical solutions are finally obtained using the linear system theory and compared with the solutions of the circular restricted three-body problem. Simulation results indicated the method is valid and the deduced analytical solutions have higher precision than that of the circular restricted three-body problem.

Keywords

circular restricted three-body problem / elliptic restricted three-body problem / nonlinear system / collinear libration-points / analytical solutions