Celestial Mechanics: A Computational Guide for the Practitioner

Rating:
Summary: Maybe replace "computational" with "editorial"
Review: The application of numerical methods to problems in celestial mechanics does not really seem to be the main focus of this text, as might be taken from the title. Instead, the reader is guided through many related topics that could be aimed at different audiences: some would be of more interest to observational astronomers, while others are perhaps relevant to astronautical applications involving Earth-orbiting satellites. One entire chapter is dedicated to "Odds and Ends," for example.

There are many anecdotal but ultimately useless admonishments, such as "I also remind the reader that any child can keep the CPU of the largest machines continuously going - it takes a bit more thought to have it compute something interesting or useful." (p. 394). Unlike the author's better book, Computational Spherical Astronomy, the presentation here is somewhat overbearing (the "Taff-Hall technique" [p. 282], "Taff's proof" [p. 266], etc.). While entertaining at times, the editorializing is overdone and results in a substantial loss of technical readability, if not credibility. This is regrettable, since some of the work in this book is seemingly original in presentation or idea. The author himself implies that some of his strong viewpoints are alienating (i.e. "It may be so much of a minority opinion that it is unique." (p. 288)). The subtitle "A Computational Guide for the Practitioner" seems ironic then, as one often finds unique philosophies at the very opposite of "practical".

To his credit, Dr. Taff intriguingly suggests that history's high regard for Gauss' re-discovery of Ceres using least-squares is based on historical myth (although I wasn't sure how this helped the practitioner in his own computations), and that Gauss himself was prone to exaggeration (p. 220) when claiming that it was possible to determine an initial plantetary orbit from a few days observations. But, the author counters that Gauss' classical method of initial orbit determination is generally unacceptable based on the partial justification "I have computed more initial orbits on high-eccentricity objects using angles-only data than has anyone else" (p. 274)! Since this books publication (and because of it), Gauss' method has seen sound defense in the open literature (i.e. Marsden (1991), Astron. J. 102 (4) p.1539).

In summary, this text is probably valuable as an example of how *not* to present technically-oriented material. However, the publisher's asking price for this paperback is nothing short of shocking: the curious reader would be best served by making his purchase from the plentiful supply of used copies or reviewing it at his local library.

Rating:
Summary: Title is deceptive
Review: This is an unusual book. Rather than filling the text with solid pages of formulas, which is what one usually finds in books on this subject, the author has instead chosen to editorialize on the successes and failures of the mathematical methods used in the solution of some of the classical problems which celestial mechanics attempts to solve (astrometry, determination of orbits, perturbation theory). The discursive writing style is refreshing to someone already familiar with the subject matter, but it seriously detracts from the use of the book as a reference.

It also contains misleading arguments and some serious omissions. The criticism of the preliminary orbit determination method of C. F. Gauss is mostly unfounded, as many astronomers engaged in this work will attest. The author's proof of the radius of convergence in time of the f and g series for elliptical orbits is much longer and complex than the classical proof by F. R. Moulton. The massive volume of literature on the Hamiltonian approach to perturbation theory is essentially ignored. And there is hardly any reference to numerical methods, particularly integration methods, indispenable tools to anyone working in orbital mechanics.

In my opinion, the book belies its title and cannot realistically be called a "guide" at all. Spend your money instead on an old copy of the classic book by Brouwer and Clemence on solar system celestial mechanics, or on Herrick's "Astrodynamics" for space flight applications. If you can find them, that is.