The Sun-Earth heteroclinics in restricted four-body non-autonomous models

This paper presents a combination of analytical and numerical techniques for computing natural heteroclinic connections between Sun–Earth quasi-periodic libration point orbits in non-autonomous restricted four-body models. Focusing on the QBCP problem, we address several computational challenges arising from the system’s periodic time-dependence and close encounters with the primaries. We introduce the concept of mean curve to approximate quasi-Lyapunov orbits and their associated invariant manifolds, providing effective initial guesses for refinement and continuation procedures. This approach remains robust despite difficulties caused by phasing conditions and Moon perturbations. The resulting analysis characterizes the topology and families of planar connections using two physical parameters.