An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition

Rating:
Summary: From a Student of Astrodynamics
Review: The following comments refer to 1987 edition. These comments were communicated to Professor Battin, who, very kindly, acknowledged them. The 1999 edition may be free of these shortcomings.

The book by Richard H. Battin, Adjunct Professor of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA, covers essential mathematical background needed to work with astrodynamical problems. Topics covered include hypergeometric functions, elliptic integrals, continued fractions, coördinate transformations as well as essentials of two-body-central-force motion.

The author's way of discussing these topics with historical introduction and personal narrative makes the book interesting to read. There are minimal typographical errors, probably, because the book was, personally, typeset by the author. However, there are a few omissions and oversights. For example, on page 172 captions are given for Fig. 4.15 and Fig. 4.16, whereas the actual figures are missing. In addition:

a) On pages 10-11 it is stated: "If you want to drive a vector to zero, it is sufficient to align the time rate of change of the vector with the vector itself." This is not true, in general, but only if time rate of change is negative.

b) On page 13 the author tries to show that constant in the equation: [(DEL) x v(SUB)c]/(RHO) = constant, vanishes by the following argument. "The demonstration concludes with an argument that the fluid is converging on the target point r(SUB)T so that the density in the vicinity r(SUB)T of is becoming infinite. Hence, the constant is zero." This is true, only if the numerator is finite. B = infinity, implies A/B = 0, only if A is not equal to infinity. Otherwise, one has to apply l'Hospital rule.

c) On page 109 equation of motion in a frame of reference moving with acceleration -a(SUB)1 is written as: m(SUB)2[a(SUB)2 - a(SUB)1] = ... Since the frame is noninertial (accelerated) Newton's second law, F = ma, is not applicable in his frame.

d) On page 223 it is stated: "When we compare Eqns. (5.57) and (5.58), it is clear that we must have sinE = SQRT[6(E - sinE)/sinE]." This is not the only choice for sinE, which reduces (5.58) to (5.57) in the limit E tends to 0. The word "must" is inappropriately used here.

e) On page 227 a factor of 4 is mentioned on the right-hand side of eq. (6.95). Calculation shows that there should be a factor of 2 instead of a factor of 4.

I would recommend this book very strongly to anyone seriosly interested in learning astrodynamics.