Fundamentals of Celestial Mechanics

Danby discusses most subjects in a fast moving, somewhat terse way, a little too fast for my taste. I find that many of the student problems are exactly what I was looking for, and I would have preferred to see them discussed in detail in the text. His coverage of the equation of Kepler is good and relatively thorough. Some parts of the text are slightly dated, and this is partly because knowledge moves along quickly in the information age. For instance, he gives three methods for the numerical integration of the equations of motion, complete with BASIC code. The use of BASIC is itself a bit old-timey, and somewhat less easy to follow than the pseudo-code which many authors use. The most modern numerical integration methods he presents are the Runge-Kutta methods Fehlberg developed for NASA in the 1960s, which are indeed nice, and a good introduction to the subject, however newer methods are available. He gives a very terse treatment of relativity which only explains the motion of Mercury's perihelion, nothing more, although few authors cover that subject in any detail. His list of references is good, covers most of the classics, and has a few that are new to me. I noticed that he considers Plummer's "Introductory Treatise on Dynamical Astronomy" one of the best references available, which is a book I consider almost absurdly terse and cryptic… it goes from zero to Hansen's methods in the first 30 pages, with little explanation, and this is how Danby often leaves me feeling - more explanation please! Granted, I am no mathemetician, but I am ok with basic calculus, and I don't mind a long-winded derivation if it makes things clearer.