This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.

The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.

"This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc. As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy."--

The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.

The Workshop on Chaos in Gravitational N -Body Systems was held in La Plata, Argentina, from July 31 through August 3, 1995. The School of Astronomy and Geophysics of La Plata National University, best known as La Plata Observatory, was the host institution. The Observatory (cover photo) was founded in 1883, and it has nowadays about 120 faculty members and 70 non-faculty members devoted to teaching and research in different areas of astronomy and geophysics. It was very nice to see how many people, from young students to well recognized authorities in the field, came to participate in the meeting. This audience success was due to the increasing understanding of the neces sity to gather together people from Celestial Mechanics and Stellar Dynamics to explore the problems that exist at the frontier of these two disciplines and their common interest in chaotic phenomena and integrability (the famous Argentine beef was, certainly, also an attraction!). All the papers of the present volume were refereed. Most were accepted after some revision, while some needed no change at all (compli ments to their authors!) and, sadly, a few could not be included. About half a dozen authors did not submit their contributions for publication, mainly because they were already in print elsewhere. Therefore, the special issue of Celestial Mechanics and Dynamical Astronomy includes all the invited lectures of the workshop, while the proceedings volume includes those same lectures plus the bulk of, but Bot all, the contributions to the meeting.

When a leaf falls on a windy day, it drifts and tumbles, tossed every which way on the breeze. This is chaos in action. In Fly Me to the Moon, Edward Belbruno shows how to harness the same principle for low-fuel space travel--or, as he puts it, "surfing the gravitational field." Belbruno devised one of the most exciting concepts now being used in space flight, that of swinging through the cosmos on the subtle fluctuations of the planets' gravitational pulls. His idea was met with skepticism until 1991, when he used it to get a stray Japanese satellite back on course to the Moon. The successful rescue represented the first application of chaos to space travel and ushered in an emerging new field. Part memoir, part scientific adventure story, Fly Me to the Moon gives a gripping insider's account of that mission and of Belbruno's personal struggles with the science establishment. Along the way, Belbruno introduces readers to recent breathtaking advances in American space exploration. He discusses ways to capture and redirect asteroids; presents new research on the origin of the Moon; weighs in on discoveries like 2003 UB313 (now named Eris), a dwarf planet detected in the far outer reaches of our solar system--and much more. Grounded in Belbruno's own rigorous theoretical research but written for a general audience, Fly Me to the Moon is for anybody who has ever felt moved by the spirit of discovery.

For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.