Abstract
The smallest bodies of our Solar System, such as asteroids and comets, are characterised by very irregular sizes and shapes and therefore, very irregular gravitational fields. Moreover, asteroids are also found in binary or multiple systems, which allow for complicated dynamics with coupling between translational and rotational motion. Classical problems used to study astrodynamics such as Kepler’s problem, Hill’s equations or the Restricted Three Body Problem cannot describe the dynamics near asteroids and comets as they do not take into account the non-spherical shape of the bodies. In this thesis, the non-linear dynamical environment around rotating non-spherical bodies or around binary systems when at least one of the bodies is not spherical has been studied. The study consists of the analysis of different mathematical models that can be used to describe the movement of massless particles, such as dust or a spacecraft, orbiting an elongated body, the dynamics between the components of a binary system, or a spacecraft orbiting the vicinity of a binary asteroid. In order to do this an analysis and development of gravitational potentials has been performed. A gravitational potential that takes the shape of the non-spherical bodies into account has allowed us to describe the movement of the dusty environment of an asteroid, to design trajectories to approach and observe an asteroid, and even land on it. Furthermore, the effect of the shape and rotation period of asteroids and binaries on the dynamics has been studied. The fact that asteroids and comets are not point masses but elongated irregular bodies leads to rich dynamics around them. Equilibrium points, periodic orbits and invariant manifolds exist in their vicinity. These are used in this thesis to design low cost landing missions to asteroids, understand the dynamics of binary systems or to explain a possible mechanism for the accretion of mass and formation of the Solar System.