The vicinity of the Earth–Moon $$L_1$$ point in the bicircular problem

Abstract

The bicircular model is a periodic time-dependent perturbation of the Earth–Moon restricted three-body problem that includes the direct gravitational effect of the Sun on the infinitesimal particle. In this paper, we focus on the dynamics in the neighbourhood of the $$L_1$$ point of the Earth–Moon system. By means of a periodic time-dependent reduction to the centre manifold, we show the existence of two families of quasi-periodic Lyapunov orbits, one planar and one vertical. The planar Lyapunov family undergoes a (quasi-periodic) pitchfork bifurcation giving rise to two families of quasi-periodic halo orbits. Between them, there is a family of Lissajous quasi-periodic orbits, with three basic frequencies.