  The motion of a satellite around a planet can be studied by the Hill model,
which is a modification of the restricted three body problem pertaining to
motion of a satellite around a planet. Although the dynamics of the circular
Hill model have been extensively studied in the literature, only few results
about the dynamics of the elliptic model were known up to now, namely the
equations of motion and few unstable families of periodic orbits. In the
present study we extend these results by computing a large set of families of
periodic orbits and their linear stability and classify them according to their
resonance condition. Although most of them are unstable, we were able to find a
considerable number of stable ones. By computing appropriate maps of dynamical
stability, we study the effect of the planetary eccentricity on the stability
of satellite orbits. We see that, even for large values of the planetary
eccentricity, regular orbits can be found in the vicinity of stable periodic
orbits. The majority of irregular orbits are escape orbits.
