Space missions which reach destinations such as the moon, asteroids, or the satellites of Jupiter are complex and challenging to design, requiring new and unusual kinds of orbits to meet their goals, orbits that cannot be found by classical approaches to the problem. In addition, libration point orbits are seeing greater use.

This book guides the reader through the trajectory design of both libration point missions and a new class of low energy trajectories which have recently been discovered and make possible missions which classical trajectories (conic sections) could not. Low energy trajectories are achieved by making use of gravity as much as possible, using the natural dynamics arising from the presence of a third body (or more bodies). The term "low-energy" is used to refer to the low fuel and therefore low energy required to control the trajectory from a given starting condition to a targeted final condition.

Low energy trajectory technology allows space agencies and aerospace companies to envision missions in the near future involving long duration observations and/or constellations of spacecraft using little fuel. A proper understanding of low energy trajectory technology begins with a study of the restricted three-body problem, a classic problem of astrodynamics, which we approach from a rigorous and geometric point of view.

We develop systematic and computationally efficient methods for the design of both libration point orbits and low energy trajectories based on fundamental ideas of invariant manifold theory.

Furthermore, we develop the computational techniques needed to design trajectories for a spacecraft in the field of $n$ bodies by patching together solutions of the 3 body problem. These computational methods are key for the development of some NASA and ESA mission trajectories, such as low energy libration point orbit missions (e.g., the Genesis Discovery Mission and Terrestrial Planet Finder, to mention only two), low energy lunar missions and low energy tours of outer planet moon systems, such as the a mission to tour and explore in detail the icy moons of Jupiter.

This book can serve as a valuable resource for graduate students and advanced undergraduates in aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. The book contains a wealth of background material, but also brings the reader up to a portion of the research frontier. Furthermore, the book will also have appeal to students of applied mathematics, especially those with an interest in dynamical systems and real world applications.