Esther Barrabés is currently visiting the Department of Mathematics and Statistics of Boston University from the 1st of July until de 23rd of December. She is working on a project in collaboration with Glenn R. Hall. The project is framed in the field of Celestial Mechanics and it is twofold. The first problem consists in to look at exo-planetary systems where large planets have been discovered to see if there are likely places for smaller plantes. The second problem consists in detecting among the population of NEO (Near Earth Objects) in the Solar System, those that can be more hazardous. Both problems, although very different, are addressed from a similar perspective: the use of variational methods consideting two-body dynamics plus perturbations.