Abstract
In the present paper, we investigate the dynamical behavior and motion of an infinitesimal body in the Hill problem under some perturbations. As it has been commonly noticed, this problem can be seen as a particular case of the classical restricted three-body problem. For numerical investigations, we first set the equations of motion of the infinitesimal body that we suppose having a variable mass according to Jeans' law. We get an effective and perceptible variation due to parameters in both the locations of lagrangian points, regions of motion, and basins of attraction. Finally, we examine the stability for the lagrangian points using Meshcherskii's space-time inverse transformations.