A Numerical Contribution to the Hierarchical Three-Body Problem

The aim of this thesis is to provide a numerical investigation of the motions of the planar hierarchical three body problem, that we will regard as a perturbation of the planar two centre problem. After a presentation of the system we find the second order normal from for a general degenerate system, next we perform two perturbation steps on the Hamiltonian of the two-centre problem, and we find phase portraits for both the first and the second order normal form. We will also find a phase potrait for the non-averaged Hamiltonian of the two-centre problem, providing a detailed numerical analysis of a couple of particular orbits, too. Finally, we treat the planar hierarchical three body problem, and we provide a detailed numerical analysis of some particular remarkable cases.