This book is directed toward readers who are interested
in learning about the Newtonian $N$-body problem, as well as toward
students and experts in this area who are interested in new expositions of past
results, previously unpublished research conclusions, and new research
problems. As many readers will have no previous knowledge about this
fascinating area, each chapter starts with introductory material that is
motivated by unanswered research questions, includes some history with an
occasional anecdote, provides discussions intended to develop intuition,
introduces new technical approaches that answer open questions, and raises
unsolved research problems. The first chapter, for instance, starts with simple
explanations of the apparent âloopingâ orbit of Mars and the
unexpected âSunrise, Sunsetâ behavior as viewed from Mercury, to
lead up to the unexplained and weird dynamics exhibited by Saturn's F-ring. The
second chapter, which introduces a way to decompose the velocity of the system,
is motivated by a seemingly easy but unanswered conjecture involving the
dynamics of the system when the system's diameter is a constant. The third
chapter, which describes questions about the structure of the rings of Saturn,
introduces new and surprisingly simple ways to find configurations of the
particles that are âcentralâ to any discussion of the
$N$-body problem, or even about those expanding cracks in a car's
windshield. The fourth chapter analyzes collisions, while the last chapter
discusses the likelihood of collisions and other events.
Readership
Graduate students and research mathematicians interested in celestial
mechanics.