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An Introduction to Celestial Mechanics (Dover Books on Astronomy) 2nd Revised ed. Edition

3.9 out of 5 stars 14 customer reviews
ISBN-13: 080-0759646876
ISBN-10: 0486646874
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Product Details

  • Series: Dover Books on Astronomy
  • Paperback: 464 pages
  • Publisher: Dover Publications; 2nd Revised ed. edition (June 1, 1984)
  • Language: English
  • ISBN-10: 0486646874
  • ISBN-13: 978-0486646879
  • Product Dimensions: 5.4 x 0.9 x 8.4 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #350,573 in Books (See Top 100 in Books)

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If you happen to be unfortunate enough to be using Goldstein's, Classical Mechanics, you will find that Kepler's Laws are not fully explored. I found the Moulton book to fill in alot of gaps. I do mean....alot of gaps! The book gives great detail into series expansions. Not only does it address the series, but it addresses the exact origin and derivation of the series expansions. The only thing it lacks is the recursion formula! Moulton treats all of the equations like this. He shows you complete derivations of everything. And, he is good in showing you applications of what you've learned.

In itself, the book is a textbook, but it serves as a great companion to any modern text. This book is actually quite old, so it gives you alot of insight into "antequated knowledge." You know, the "stuff" teachers already assume you know.

So, I recommend this book to anyone. It is very readable. It explains concepts in a very simplistic manner. Unlike modern books that give you point "A" and expect you to fill in all the gaps to point "Z," Moulton uses the "old style of teaching" where he takes you from point "A" to point "Z" to fully prepare you, and then, he slams you with the impossible problems at the end. But, you find the problems are not nearly as difficult due to his preparations.

Great Book!!
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This is an excellent textbook covering not only celestial mechanics, but a wide range of astrophysics topics. It was written in 1902 and updated in 1914. At that time nuclear processes were not known, and the composition of the sun was thought to be mainly iron. Given these limitations, however, the math is clear, the definitions are still used, and the historical background is interesting and informative. For a more up-to-date discussion of the subject, I recommend "Fundamentals of Astrodynamics", Bate, Mueller, White (1971), but get this one for the background.
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Moulton assumes you know many things, or have access to them, for instance, the geometry of ellipses is used extensively, but is never explained in the book. You probably will want an analytic geometry book for reference. Moulton uses intermediate-level calculus from the very beginning, and he assumes you have a good working knowledge of it. Other than these minor gripes, Moulton is very good at explaining from the very basics, for instance, he includes an interesting geometric proof of Kepler's law of areas, which he attributes to Newton. He gives some nice geometric explanations of perturbations. Little or no math used at all in these! His derivations start much farther back than many authors, for instance, in introducing equations of motion, he first starts with some general properties of particles moving on an x-y plane, gets into particles moving around a central origin, and moves on into the well-known Newtonian equations of motion, and a few hypothetical ones. He gives many references to further study of these, all rather old, of course, but many of them intersting because they are the original works: Newton's "Principia", Gauss' "Theoria Motus", for instance. He does, here and there, plop an equation in your lap with "a well known equation for (something) is...", usually unrelated to whatever his primary explanation is, but slightly annoying. If you are used to modern vector notation, Moulton is a little confusing at first. Rather than vectors, he explains everything using old-fashioned systems of equations (in x,y,z). This makes some derivations more complicated, and you must be careful to distinguish components of, for instance, velocity and acceleration in x,y,z from the overall velocity and acceleration, because the notations look similar. At the end of most chapters, Moulton gives a summary of the historical details of the chapter's contents, who discovered what and when, complete with references! Just skimming the book for these summaries is rather interesting!
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By Danny on September 6, 2008
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The Title is a little misleading. As an introduction, the coverage and detail this book deals with is by no means introductory, and is written for the college level student in mathematics. I needed to revise my knowledge of calculus and advanced mathematics, before I started to read this one.

However, I was pleasantly surprised by its clarity, ease of use, and explanation and example. It was worth the expense, and has made my understanding of the area much more broad and detailed. I am pleased with my purchase. I would not recommend it to someone who is unfamiliar with mathematics in terms of the complexity - it deals with calculus, advanced trigonometry and many properties of various spherical triangles and the like are assumed background knowledge. It is more a middle-level rather than a introductory textbook in my view.
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This text by Moulton is perhaps the finest single treatment on Newtonian Celestial Mechanics available. The content is very methodically shared in detail and progresses in a logical, building block manner accentuated with brief discussions on the historical development of the theories.

Moulton covers the basics of linear motion as a short refresher in the begin of Chp 2 but does assume the reader is already familiar with linear algebra determinants, and Lagrangian mechanics when covering perturbation theory.

Not in the text are conversations on the Roche Limit, Lagrangian Points, and Relativistic Celestial Mechanics. The text does discus surface equipotentials in chapter VII The Problem of Three Bodies.

Some of my favorite sections of the text being:

Chp I Fundamental Principles and Definitions
I.16 pertaining to Kepler and discussion on Areal Velocity

Chp II Rectilinear Motion
II.33 Attractive Force Varying Inversely as the Square of the Distance

Chp III Central Force
III.55 Newton's Law of Gravitation
III.62 Force Varying as the Square of the Distance

Chp IV The Potential and Attractions of Bodies
IV.78 The Potential and Attraction of a Solid Homogeneous Oblate Spheroid upon a Distant Unit Particle
IV.81 The Attraction of Spheroids

Chp V The Problem of Two Bodies
V.97 Graphical Solution of Kepler's Equation
V.104 The Heliocentric Position in the Ecliptic System

Chp VIII The Problem of Three Bodies
VIII.163 Application to the Gegenschein

Chp IX Perturbations-Geometrical Considerations
IX.175 Disturbing Effects of the Orthogonal Components
IX.188 Perturbations of the Inclination
IX.189 Precession of the Equinoxes. Nutation
IX.197 The Motion of the Line of Apsides
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An Introduction to Celestial Mechanics (Dover Books on Astronomy)
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