Celestial Mechanics: Classical and Modern Methods

Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.

Antonio Giorgilli is a Member of the Istituto Lombardo Accademia di Scienze e Lettere and a former Professor of Mathematics at the Università degli Studi di Milano, now retired. His research in dynamical systems focuses on the characterization of chaos, KAM theory and Nekhoroshev's theory on exponential stability. In addition to being an Invited Speaker of the 1998 International Congress of Mathematicians, Giorgilli's other notable honours include the international Gili Agostinelli Prize for Pure or Applied Mechanics or Classical Mathematical Physics by the Accademia delle Scienze di Torino in 2007. The minor planet 27855 Giorgilli is named in his honour.

Ugo Locatelli is Full Professor of Mathematical Physics at the Università degli Studi di Roma 'Tor Vergata'. Since 2023, he has been President of SIMCA (Italian Society of Celestial Mechanics and Astrodynamics). From 1996 to 1999 he was supported by a Marie Curie Fellowship awarding his research project 'Stability in Celestial Mechanics problems into the light of KAM and Nekhoroshev's theory'. He is author of more than forty articles appearing in scientific journals, most in the field of dynamical systems.

Marco Sansottera is a mathematician with a Ph.D. in Mathematics from the Università degli Studi di Milano. He held postdoctoral and research positions at the Università degli Studi di Roma 'Tor Vergata', the Université de Namur, and the Università degli Studi di Milano, where he has also taught courses in celestial mechanics, Hamiltonian systems and mathematical physics. His research interests lie in the long-term stability of dynamical systems, with particular emphasis on perturbation theory, KAM theory and Nekhoroshev estimates. He is author of more than twenty-five scientific publications.