The construction of periodic orbits close to triangular libration points for the three-body problem in a resistive medium

Abstract

A circular, restricted three-body problem is considered when a passively gravitating point also experiences the action of small resistive forces, acting in the opposite direction to the absolute velocity vector. The nature of the loss of stability of the triangular libration points is studied using the Poincaré method in whcih the ratio of the magnitude of the resistive force to the force of gravitational attraction serves as the small parameter. Asymptotically stable periodic orbits are constructed. Two Lyapunov families of periodic orbits, which exists in the neighbourhood of the libration points of the classical theory, are the generating families. Calculations were carried out for mass ratios corresponding to the Earth-Jupiter and Earth-Moon systems, with different values of the parameters characterizing the law of resistance.