An Introduction to Celestial Mechanics, Richard Fitzpatrick, Cambridge U. Press, New York, 2012. $65.00 (288 pp.). ISBN 978-1-107-02381-9
Celestial mechanics is a venerable discipline more than two centuries old. It demonstrated stunning early victories, including the discovery of Neptune in 1846, and is now expanding into new areas such as exoplanetary research and solar-system evolution and navigation. Prior to the present generation of researchers, most techniques in the field were presented in essentially the same language that Leonhard Euler, Joseph Louis Lagrange, and Pierre Simon Laplace used at the turn of the 19th century: one that is incredibly and unnecessarily opaque.
Some textbook authors have attempted to make the field more approachable and understandable. Progress has been slow, but notable attempts include Dirk Brouwer and Gerald Clemence’s Methods of Celestial Mechanics (Academic Press, 1961) and Carl Murray and Stanley Dermott’s Solar System Dynamics (Cambridge University Press, 1999). But despite those efforts, a gap has long existed between material available for teaching the simple laws of Keplerian orbits and material for teaching the range of topics covered in existing advanced texts, including the three-body problem, secular perturbation theory, libration, and spin–orbit coupling.
An Introduction to Celestial Mechanics by University of Texas at Austin physics professor Richard Fitzpatrick aims to bridge that gap. His goal is to provide a textbook for the undergraduate or first-year graduate student who has seen derivations of Kepler’s laws but needs to understand more complicated systems and deeper derivations based on Lagrangian and more sophisticated techniques. Fitzpatrick’s text is excellent and makes a significant, though incomplete, improvement in presenting celestial mechanics to undergraduates.
Fitzpatrick’s exposition is relatively flawless in its execution, but it could go further in offering more intuition for some of the results derived. The three-body problem is a good example. When I teach it to upper-level physics undergraduates, I motivate the derivation of the rotating pseudopotential results regarding Lagrange points by giving a “sneak peek” expressed in terms of a force formalism. That’s useful, and it’s easy to do. Then I show that results using pseudopotentials are more comprehensive and more generally applicable.
An Introduction to Celestial Mechanics is a valuable addition to the pedagogy of the field and has perhaps the clearest exposition of any celestial mechanics text for upper-level undergraduate students. For some students, Fitzpatrick will be approaching perfection. But for many others his text will need to be supplemented in parts with preparatory material. Instructors will need to be alert to how much extra motivation their classes will require.
