The efficient computation of transfer trajectories between earth orbit and L_1 halo orbit within the framework of the sun-earth restricted circular three body problem

摘要

The method of regularization is applied to the singular differnetial equations of the restricted circular three body model in rotating corrdinates centered at the L_1 Lagrange libration point of the sun-earth system. It is later used to construct robust computer codes that produce, through an iterative process, converged transfer trajectories from a low circular parking orbit around the earth to the vicinity of the L_1 point where a small velocity change inserts the spacecraft into a desired periodic halo orbit. These computer codes, which use backwards numerical integration to provide a transfer solution that meets the end or boundary conditions with one meter accuracy, are built around double precision integrators with built-in interpolators as well as an unconstrianed optimization algorithm that minimizes the summed squares of the differences between certain achieved parameters and their desired target values. The existence of optimal values of certain target parameters tht lead to the minimization of the velocity change needed to insert into the halo orbit of interest is also shown, as well as the range of its feasible values at least in the case of the perigee location of the departure hyperbola.