This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

Provides a review of recent results in the field of Celestial Mechanics, with special emphasis on theoretical aspects

2) The contribution by Gabriella Pinzari presents a review of some results of their research group, regarding the relation between some particular motions of the Three-Body problem (3BP) and the motions of the so-called Euler (or two-centre) problem, which is integrable. For the analysis of such relation, the authors make use of two novel results: on one hand, the two-centre problem (2CP) bears a remarkable property, here called renormalizable integrability, which states that the simple averaged potential of the 2CP and the Euler integral are one function of the other; on the other hand, the motions of the Euler integral are at least qualitatively explicit, and the averaged Newtonian potential is a prominent part of the 3BP Hamiltonian.