Birth of periodic and artificial halo orbits in the restricted three-body problem

Abstract

We investigate the bifurcation of artificial halo orbits from the Lyapunov planar family of periodic orbits around the collinear libration points of the circular, spatial, restricted three-body problem. Beside the gravitational forces, our model includes also the effect of the Solar Radiation Pressure (SRP) and this motivates the use of the term ‘artificial’ halo orbits. Indeed, as a typical problem, one may think of a solar sail, which is characterized by a performance parameter measuring the strength of the effect of the SRP on the spacecraft.To settle the model, we determine the position of the collinear points as a function of the mass and performance parameters and the energy values at which Hill׳s surfaces allow for transit orbits between the primaries. To analyze the dynamics we use a consolidated procedure which consists in the computation of a resonant normal form, allowing the reduction to the center manifold and providing an integrable approximation of the Hamiltonian dynamical system. Finally, we compute the bifurcation thresholds of the 1:1 resonant periodic orbit families (which have the standard ‘halo’ orbits as their first member) as a function of the performance and mass parameters.The results show that SRP is indeed a relevant ingredient for new dynamical features and must definitely be considered when planning a mission of a solar sail with trajectories in the neighborhoods of collinear points.