  This paper investigates the motion of a small particle moving near the
triangular points of the Earth-Moon system. The dynamics are modeled in the
Hill restricted 4-body problem (HR4BP), which includes the effect of the Earth
and Moon as in the circular restricted 3-body problem (CR3BP), as well as the
direct and indirect effect of the Sun as a periodic time-dependent perturbation
of the CR3BP. Due to the periodic perturbation, the triangular points of the
CR3BP are no longer equilibrium solutions; rather, the triangular points are
replaced by periodic orbits with the same period as the perturbation.
Additionally, there is a 2:1 resonant periodic orbit that persists from the
CR3BP into the HR4BP. In this work, we investigate the dynamics around these
invariant objects by computing families of 2-dimensional invariant tori and
their linear normal behavior. We identify bifurcations and relationships
between families. Mechanisms for transport between Earth, L4, and Moon are
discussed. Comparisons are made between the results presented here and in the
bicircular problem (BCP).
