# Overview

The initial goal of Celestial Mechanics was to explain the motion of the Sun, the Moon and planets. Nowadays the mathematical methods of Celestial Mechanics find several different applications, including the determination of the dynamics of planets, asteroids, comets, artificial satellites, and the design of orbits for interplanetary travels. The discovery in the '90s of the Kuiper belt and of extrasolar planetary systems gave a new impulse to Celestial Mechanics as a mean to understand the birth, evolution and the future of the planetary system around the Sun as well as of those around other stars. Also, the observational campaigns of small bodies of the solar system and the increase of the number of artificial satellites around our planet led to a new field of application of Celestial Mechanics: the safeguard of planet Earth. Dismissed satellites and space rockets constitute dangerous space debris around the Earth, which must be carefully monitored and eventually removed.

Both the study of the dynamics of artificial objects and of celestial bodies (i.e., planets, satellites, small bodies, etc.) makes use of the geometric theory of dynamical systems introduced by Henri Poincaré. However the numerical challenges differ. In the case of the motion of natural celestial bodies, the chaotic character of the trajectories prevents the direct use of numerical simulations over periods of time of the order of billions years, which is the remaining time before the sun becomes a red Giant. On the other hand, trying to avoid a collision with an asteroid does not require integrating the system for very long periods and may require tools from control theory. Chaos theory is used to devise interplanetary trajectories, which make use of the invariant manifolds associated to the unstable relative equilibria (collinear Lagrangian points) and unstable periodic trajectories of small bodies for interplanetary transport. This allows designing low-energy trajectories connecting the larger bodies.

The goal of this workshop is to bring together experts from the different communities in Celestial Mechanics and its applications and, in particular, to provide a bridge between the researchers working on numerical and analytical aspects.

The main themes of interest are: invariant manifolds of the $N-body problem, rotational dynamics, resonances, numerical integrations, symplectic integration techniques, chaos indicators, low-thrust orbits, low-energy orbits.