  There exist cislunar and trans-lunar libration points near the Moon, which
are referred as the LL1 and LL2 points respectively and can generate the
different types of low-energy trajectories transferring from Earth to Moon. The
time-dependent analytic model including the gravitational forces from the Sun,
Earth and Moon is employed to investigate the energy-minimal and practical
transfer trajectories. However, different from the circular restricted
three-body problem, the equivalent gravitational equilibria are defined
according to the geometry of instantaneous Hill's boundary due to the
gravitational perturbation from the Sun. The relationship between the altitudes
of periapsis and eccentricities is achieved from the Poincar\'e mapping for all
the lunar captured trajectories, which presents the statistical feature of the
fuel cost and captured orbital elements rather than generating a specified
Moon-captured segment. The minimum energy required by the captured trajectory
on a lunar circular orbit is deduced in the spatial bi-circular model. It is
presented that the asymptotical behaviors of invariant manifolds approaching
to/from the libration points or halo orbits are destroyed by the solar
perturbation. In fact, the energy-minimal cislunar transfer trajectory is
acquired by transiting LL1 point, while the energy-minimal trans-lunar transfer
trajectory is obtained by transiting LL2 point. Finally, the transfer
opportunities for the practical trajectories escaped from the Earth and
captured by the Moon are yielded by transiting halo orbits near LL1 and LL2
points, which can be used to generate the whole trajectories.
