TITLE:
Dynamics Around the Earth-Moon Triangular Points
in the Hill Restricted 4-Body Problem

AUTHORS:
Luke T. Peterson^(1), Gavin Brown^(1) , Angel Jorba^(2,3),
Daniel Scheeres^(1)

(1) Ann and H.J. Smead Aerospace Engineering Sciences,
    University of Colorado Boulder, CO, USA.
(2) Department de Matemàtiques i Informàtica,
    Universitat de Barcelona (UB), Barcelona, Spain.
(3) Centre de Recerca Matemàtica, Edifici C,
    Campus Bellaterra, 08193 Bellaterra, Spain.

ABSTRACT:
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 performing a center
manifold reduction and computing families of 2-dimensional invariant
tori and their linear normal behavior. We identify bifurcations and
relationships between families. Mechanisms for transport between the
Earth, L4 , and the Moon are discussed. Comparisons are made between
the results presented here and in the bicircular problem (BCP).