This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts - order, chaos, invariant curves and cantori - followed by the investigation of dynamical systems with numerical methods.

The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di?erent directions. The stability theory of nearly integrable systems (a class of problems which includes many models of - lestial Mechanics) pro?ted from the breakthrough represented by the Kolmogorov Arnold Moser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con?nement of the actions for exponential times was guaranteed by Nekhoroshev s theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies. Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics.

Provides a comprehensive survey of the tools of celestial mechanics from classical theories to modern methods Presents a variety of useful computer assisted techniques with practical examples of applications Demonstrates the interplay between classical celestial mechanics and the modern tools of dynamical systems Gives useful examples for the constructive implementation of perturbation theory Investigates the regular and chaotic behavior of the trajectories of planets, spacecraft orbits, and rotation of satellites Will be used for teaching and research in space exploration

Autorentext

Alessandra Celletti received her PhD in 1989 at the Swiss Federal Institute of Technology in Zurich (ETH) under the supervision of Professors Jurgen Moser and Jorge Waldvogel. She is a full professor of Mathematical Physics at the University of Rome Tor Vergata and since 2020, she has been a member of the governing board and the Vice President of ANVUR. Her research interests include Celestial Mechanics and Dynamical Systems with reference to perturbative methods and applications to Solar system dynamics. She is a founding member of the Italian Society of Celestial Mechanics and Astrodynamics that chaired from 2001 to 2013. Since 2010, she has been an honorary member of the "Celestial Mechanics Institute". In 2018, she became the President of the Scientific Committee in Celestial Mechanics of the IAU and in 2019–2020, she was in the Governing Board of the Italian Space Agency. In 2023, she was awarded the "Dirk Brouwer Career Award" from the American Astronomical Society. In addition, the asteroid 117539 bears her name.

Inhalt
Order and chaos.- Numerical dynamical methods.- Kepler's problem.- The three-body problem and the Lagrangian solutions.- Rotational dynamics.- Perturbation theory.- Invariant tori.- Long-time stability.- Determination of periodic orbits.- Regularization theory.