Abstract
The dynamics of the orbital motion in the planar elliptic restricted three-body problem are investigated, by using the method of grid classification. In this system, the secondary body is an exoplanet, while the corresponding primary body is its parent star. We numerically investigate how several dynamical quantities of the system, such as the orbital energy, the eccentricity, the true anomaly, and the mass parameter, influence several aspects of the motion of the test particle, such as the final state as well as the time of escape/collision of the orbits. Color-coded basin diagrams are utilized for displaying all the different types of basins, using two-dimensional maps. The results of this analysis are then compared to similar ones from the classical version of the circular problem of three bodies.