  We consider the planar Hill's lunar problem with a homogeneous gravitational
potential. The investigation of the system is twofold. First, the starting
conditions of the trajectories are classified into three classes, that is
bounded, escaping, and collisional. Second, we study the no-return property of
the Lagrange point $L_2$ and we observe that the escaping trajectories are
scattered exponentially. Moreover, it is seen that in the supercritical case,
with $\alpha \geq 2$, the basin boundaries are smooth. On the other hand, in
the subcritical case, with $\alpha < 2$ the boundaries between the different
types of basins exhibit fractal properties.
