High-order solutions around the stable libration points in the low-thrust restricted three-body system

Abstract

Non-equilibrium point in the circular restricted three-body system can be changed into an artificial equilibrium point by means of low-thrust acceleration, and an spacecraft located at the artificial equilibrium point remains static relative to the primaries in the synodic coordinate system. In the classical restricted three-body system, the libration point orbit resource is limited, and the existence of artificial equilibrium point could overcome the shortage. The richness of artificial equilibrium points leads to the flexibility of mission design in deep space exploration. Due to the stability of stable artificial equilibrium points, for a spacecraft moving around them, less propellant is required for station keeping. In this paper, we expand the general motion around stable artificial equilibrium points as formal series of long-period, short-period and vertical periodic amplitudes. Then Lindstedt-Poincare method is adopted to construct the series solutions up to an arbitrary order. By taking advantage of the series expansions constructed, the motions around artificial equilibrium points can be parameterized, and these parameters are beneficial to the optimization process of libration point mission design. At last, in order to provide the available range of series expansions constructed, the practical convergence is considered.