Although "Astrodynamics" is a discipline only about 50 years old - the name is attributed to the late Samuel Herrick - it has a distinguished history. For one thing, it is a branch of celestial mechanics, whose history can be traced all the way back to Ptolemy's "Almagest." Along the way are found many venerable masterpieces, including Copernicus's "De revolutionibus orbium coelestium," Kepler's "Harmonices Mundi," Newton's "Principia," and Laplace's "Mecanique Celeste."
Only time will tell exactly where Richard Battin's book fits into this pantheon, but there is no question it is an outstanding book. Actually, the book may be considered to be three books: a) a history of Apollo navigation; b) an exposition of classical celestial mechanics/astrodynamics; and c) a book on applied mathematics covering hypergeometric functions, continued fractions, and elliptic functions.
The material on Apollo navigation is fascinating, and perhaps nowhere else so easily accessible. Prior to reading Battin's "Astrodynamics [for short]" I was somewhat familiar with this topic (I started my career with Apollo), but I discovered much that was new and fascinating. For example, I knew that optical navigation was a backup to radio navigation on Apollo, but I did not fully appreciate why. It turns out that NASA was afraid the Soviet Union would try to disrupt radio navigation in an attempt to make Apollo fail. Optical navigation would then be the backup safety-net to complete the mission. Fortunately, these fears were not realized, and Apollo was a huge success.
The material on celestial mechanics is very thorough and well done. Battin includes all the obligatory material, but includes much addition material such as quaternions, Lagrange's perturbation equations, F and G series, universal variables, and much more. He spends considerable space - some would say too much space (see below) -- to solving Kepler's equation by various means. He leaves much material to the proverbial "student exercises" -- and these are often hard!
It is almost irresistible to compare this book with the similar book by Samuel Herrick, "Astrodynamics". Harrick's book is generally on a more elementary level. Also, Herrick avoids vector and matrix notation. This may make Herrick easier to read for beginners, but in general, it gives Herrick's book a much more "old fashioned" feel.
My own favorite part of Battin's book is the "applied math" part - hypergeometric, continued fractions, etc. But why did the author decide to include this material? I suspect, if asked, he might say he included this material because of the importance of elliptic functions to an understanding of certain classical solution, and that continued fractions are best for evaluating elliptic functions. I heartily agree with the first, but have reservations about the second. It is true that elliptic functions enter into many classical solutions, and a deep understanding of these requires a fair knowledge of elliptic function. It is also true that continued fractions may provide an efficient means of evaluating elliptic functions. However, almost no one uses "home brew" code to evaluate functions anymore - one gets a commercial math package. So, my belief is, in the final analysis, Battin added this material because: a) he loves this subject; b) he fears that knowledge of continued fractions is slowly being lost; and c) he wants to reverse this trend. I for one am glad he included continued fractions, for I love the topic and it IS REALLY DIFFICULT to find first class material on it.
Perhaps what would serve best is to take the applied math material and add additional chapters covering: a) the two-fixed-centers-of-force solution; b) selected n-body-problem material; c) almost periodic functions; and d) chaos theory; then turn this material into a separate book.
Hmmm ... now there's an idea ... would anyone care to collaborate on such a project?
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