astronomy

I read this book for pleasure as a first introduction to celestial mechanics (I am an astrohypsics major at my college), and found the selected topics coherently explained in comprehensible language. Perhaps more importantly, the mathematics (at least at the beginning) is covered more or less step-by-step - you won't get lost by any "it is therefore obvious..." and then a skip of five or six steps.
Unfortunately - - The books is rife with typos, and nothing so simple as a misspelling. At least every other page (and often several times on one page) an equation would have an exponent or operation error (such no division sign) and references in the explanations to earlier equations were regularly mistaken.
With a few more thorough proof-readings (and some more work on the second half of the book, which whizzes through a topic many times more complicated than the first half but in the same amount of time/pages), this book could easily move up to 5-stars.

This book is an introduction to celestial mechanics. It assumes some knowledge of calculus and vectors; given the subject matter, an unavoidable assumption. It contains a number of nicely chosen numerical and mathematical examples in each chapter so that the reader can see both application and extension of the results presented in the chapter. Each chapter ends with some problems, without answers, that continue to extend the basics from the main text. Each chapter contains references to books and papers that supplement and extend the subject matter of the chapter. It ends with a glossary, an appendix of physical constants, and an annotated list of books for further reading for the very interested reader. The book list is particularly valuable if the reader wishes to continue learning celestial mechanics; it covers elementary to advanced texts.

The first chapter provides a historical review of progress in celestial mechanics with a list of notable (dead) practitioners of celestial mechanics. A subjective list of living practitioners might have been helpful in this chapter. Chapters two through six establish the basis of orbital motion, starting with circular motion in chapter two. The mathematical basis for orbital motion is established in chapter three using the law of gravitation and Newton's laws of motion. Successive chapters generalize and expand on the results of chapters two and three. Chapter five introduces rockets and powered flight trajectories. Chapter six introduces parabolic and hyperbolic orbits.

Chapter seven discusses two topics of great practical importance, Kepler's law and Lambert's theorem. While both of these topics are several hundred years old they continue to be rich areas for current development in celestial mechanics. These two crucial topics are well covered. Chapter eight applies the previous material to the subject of orbital transfer; this chapter is the basis for flight between planets. Chapter nine digresses into spacecraft attitude dynamics, a complete discipline in its own right. It introduces the mathematics of the physical motion of a spacecraft about a local reference system. At 25 pages, it is a tight and tidy introduction to the subject. Chapter ten is titled "Planetary Exploration" although it also covers the creation of the solar system and trajectory modification by gravity assistance. More heavily illustrated than the other chapters, chapter ten's main topic is exploration of the solar system by spacecraft. Chapter eleven introduces perturbation theory; what happens to an orbit when more than two bodies make up the gravitational system. Chapter twelve applies perturbation theory to artificial satellites of Earth. (Chapters nine and twelve ought to make you appreciate how hard it is to get those great Hubble Space Telescope images.) Chapter thirteen must have been both the easiest and hardest chapter to write since Szebehely was one of the masters of this subject. It introduces the three-body problem and solar system stability with a nod to chaos theory.

All in all, this book is an excellent introduction to the topic of celestial mechanics. To the depth that the subject is explored, there are no loose ends. (The reviewer does regret that the Introduction from the first edition of this book was omitted from the second edition.)