Abstract: In order to solve the problem of low-thrust orbit transfers between periodic orbits around  libration points in the three-body system, a novel shape function was constructed and a method based on Gauss pseudospectral method (GPM) was proposed. Firstly, the dynamics model of low-thrust transfers was built, a novel shape function was constructed to approximate the lowthrust transfer trajectory according to the type of initial orbit and target orbit. The approximate analytic solution for the transfer trajectory was deduced under the assumption that amplitude and phases change in the form of a polynomial to satisfy different constraints. Secondly, the optimal control problem of lowthrust transfer was discretized into a nonlinear programming problem based on the GPM, and the effective initial value of control variables of the nonlinear programming problem was obtained by solving and processing the approximate analytic solution. At last, the numerical simulation of transfers between Halo orbits around the L1 libration point of the Earth-Moon three-body system was conducted. The simulation result shows that the approximate analytic solution for low-thrust orbit transfers based on the new shape function is valid and general. The efficiency of GPM can be improved by 55%. Besides, the GPM can effectively solve the problem of lowthrust orbit transfers between periodic orbits around libration points in the three-body problem. 

Key words: libration-point, periodic orbit, orbit transfer, low-thrust, Gauss pseudospectral method, shape method