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.

Autorentext

Giulio Baù is a Associate Professor at the Department of Mathematics of the University of Pisa. His research activity deals with the development of new orbit propagation and determination methods for small celestial bodies (in particular asteroids and space debris), the study of their dynamics, and regularizations techniques in the $N$-body problem.

Sara Di Ruzza is a researcher of Mathematical Physics at the Department of Mathematics at the University of Palermo. Her main field of interest is celestial mechanics. She worked on the spin-orbit problem, on some particular cases of the three-body problem both from an analytical and numerical point of view. She applied theory to real scenarios such as asteroid motion and space missions. The latest works are focused on the occurrence of chaos in the planar three-body problem.

Rocío Isabel Páez is a senior postdoctoral researcher at the University College Cork in Ireland. She received her Ph.D. in Mathematics from the University of Rome "Tor Vergata" in 2016. Since then, she has held academic positions at the University of Rome "Tor Vergata", the Academy of Athens and the University of Padova. Her research area is in Applied Mathematics, with a focus on the application of advanced methods of perturbation theory and numerical simulations in dynamical astronomy.

Tiziano Penati is Associate Professor of Mathematical Physics at the Department of Mathematics, University of Milan. His main field of interest is Hamiltonian perturbation theory, with special attention to normal form techniques. His work focuses on the investigation of time-periodic localized structures and metastability phenomena in Hamiltonian lattices, such as the Fermi-Pasta-Ulam-Tsingou, discrete Klein-Gordon or discrete Nonlinear Schroedinger models.

Marco Sansottera is a Researcher of Mathematical Physics at the Department of Mathematics, University of Milan. His research activity is mainly focused on dynamical systems and celestial mechanics. In particular, he studied the stability properties of planetary systems, investigating the dynamics in the neighborhood of some invariant objects, such as maximal dimension KAM tori, equilibrium points and lower dimensional elliptic tori.