Abstract:
The circular restricted three-body problem is used as an approximate model in
space mission planning. Its periodic solutions around equilibrium points, which are referred
to as the libration points, are utilized for exploration of possible spacecraft trajectories in
the preliminary stages of mission design. In this paper, a numerical methodology for periodic
libration point orbits (LPOs) computation is introduced and applied to the construction and
study of $N$-periodic (up to $N = 6$) quasi-planar orbit families in the Earth-Moon system. The
stability and the bifurcation points of these families are determined. The proposed method is
based on an iterative algorithm searching for the initial state vector of periodic LPOs, which
allows computing unstable long-periodic and large-amplitude orbits. The method is suited to
perform a straightforward switch to bifurcating branches of periodic orbits.
Keywords:circular restricted three-body problem (CRTBP), libration point orbits (LPOs), periodic orbits, bifurcation analysis, unstable trajectories, numerical methods
References