  We consider the planar circular restricted three-body problem (PCRTBP), as a
model for the motion of a spacecraft relative to the Earth-Moon system. We
focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of
Lyapunov periodic orbits around either $L_1$ or $L_2$, forming Lyapunov
manifolds. There also exist homoclinic orbits to the Lyapunov manifolds around
either $L_1$ or $L_2$, as well as heteroclinic orbits between the Lyapunov
manifold around $L_1$ and the one around $L_2$. The motion along the
homoclinic/heteroclinic orbits can be described via the scattering map, which
gives the future asymptotic of a homoclinic orbit as a function of the past
asymptotic. In contrast with the more customary Melnikov theory, we do not need
to assume that the asymptotic orbits have a special nature (periodic,
quasi-periodic, etc.).
  We add a non-conservative, time-dependent perturbation, as a model for a
thrust applied to the spacecraft for some duration of time, or for some other
effect, such as solar radiation pressure. We compute the first order
approximation of the perturbed scattering map, in terms of fast convergent
integrals of the perturbation along homoclinic/heteroclinic orbits of the
unperturbed system. As a possible application, this result can be used to
determine the trajectory of the spacecraft upon using the thrust.
