TITLE:
Leveraging L3 to Transfer to L4 in the Sun-perturbed Earth-Moon System

AUTHORS:
Yuying Liang^(1), Bego\~na Nicolas^(2), Angel Jorba^(2)
(1) Department of Earth and Space Science and Engineering,
    York University, Canada.
(2) Departament de Matematiques i Informatica
    Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

E-mails: buaa_liangyuying@163.com, bego@maia.ub.es, angel@maia.ub.es

ABSTRACT:
This paper is devoted to a new approach to construct the transfers
from the Earth to the Earth-Moon (EM) L4 using stable and unstable
manifolds of quasi-periodic Lyapunov orbits (QPLOs) of the EM L3 in
the planar bicircular Sun-Earth-Moon system. Some QPLOs have stable
manifolds intersecting the Earth parking orbits and unstable manifolds
going through the EM L4 region, which gives a skeleton to build up
such transfers. Tentatively, the stable and unstable manifolds of a
QPLO are employed to construct transfer segments connecting the Earth
and L4 vicinity, respectively. The trajectories near the stable
manifolds spent some time moving around L3 before going away and
approaching the unstable manifolds towards L4 . To reduce the
multi-revolution behavior around L3 , a multiple shooting algorithm
is developed to switch from the stable to the unstable manifold, where
additional maneuvers are performed at some distance from the QPLO to
reduce the time spent in the L3 vicinity. By such construction a
spacecraft can visit and park around two high-cost far-away libration
points in a single journey.  Eliminating most of the loops around L3,
the quickest one among the example transfers needs about 175 days.
Furthermore, it is showed how to utilize the stable manifolds of the
QPLO alone to design faster transfers to the EM L4 vicinity. By this
construction, the lowest time of flight is about 61 days. The
advantages of these two constructions are discussed.