The Three-Body Problem [Hardcover]

Mauri Valtonen (Author), Hannu Karttunen (Author)

Book Description

Publication Date: March 6, 2006 | ISBN-10: 0521852242 | ISBN-13: 978-0521852241

How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. This book should be essential reading for students in a rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.

Editorial Reviews

Review

"In The Three-Body Problem, readers will find the necessary theoretical ingredients and will also enjoy the variety of technical explanations for phenomena in the solar system and beyond. The book would be useful for a graduate course in modern astrophysics and makes interesting reading for an amateur who has some background in classical physics."
Martin Gutzwiller, Physics Today

"This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level."
Patricia Yanguas, Mathematical Reviews

Book Description

How do three celestial bodies move under their mutual gravitational attraction? This is a problem that has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusions that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time, such methods are presented in a systematic way. The book surveys statistical methods as well as more traditional methods and is suitable for students of celestial mechanics at advanced undergraduate level.

See all Editorial Reviews

Product Details

• Hardcover: 356 pages
• Publisher: Cambridge University Press (March 6, 2006)
• Language: English
• ISBN-10: 0521852242
• ISBN-13: 978-0521852241
• Product Dimensions: 9.8 x 7.1 x 0.8 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 2.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #896,371 in Books (See Top 100 in Books)
  • #95 in Books > Professional & Technical > Professional Science > Physics > Gravity

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Customer Reviews

Most Helpful Customer Reviews

5 of 5 people found the following review helpful:

2.0 out of 5 stars For mathematical physicists, December 26, 2006

By 

David S. Mazel "www.bytesofscience.com" (Washington, DC) - See all my reviews
(REAL NAME)   

This review is from: The Three-Body Problem (Hardcover)

This book begins by recounting what the student would learn in a physics class on Newtonian mechanics and planetary motion and then goes into specifics of the three-body problem. While unsolvable in closed form, the solution, in general, involves chaotic dynamics. Nonetheless, there is much to be had in studying various forms of the problem under differing conditions. This book goes a long way to exploring these forms of how different scenarios can be approached.

The authors begin with a presentation of Newtonian mechanics and uses these to solve the two body problem. The authors use physics to motivate the mathematics and derive the equations of motion---here, and throughout the book. Thus, the discussions are complete and present the ideas from the view of mathematical physics.

After discussion of the two-body problem we are introduced to Hamiltonian mechanics and some restricted three-body problems such as satellite orbits, and scatterings of bodies from a binary orbit. Other topics include escapes, three body scattering, and capture. The final topics deal with perturbations and various astrophysical problems such as black holes and the evolution of comet orbits.

Throughout the book the authors present diagrams to illustrate their points but these diagrams are limited in their utility. The authors could have presented more illustrative diagrams and figures to better qualify the text.

When I started reading I thought the book would discuss chaos and its relationship to the three body problem. After all, that's the first thought that comes to mind today. There is mention of this phenomena but very little, and no attention given to simulating orbits of three body motion. For me, this was a disappointment.

Finally, the spirit of the book is mathematical physics and consequently, the authors often leave much work to the reader to sort through the mathematics. I often found, for example, that I had to review earlier parts of the text and seek equations---always present somewhere in the text but not explicitly noted nor cited---to follow the derivations and fill-in many of the steps.

In short, this is a good text on the mathematical physics of the problem for the experience practitioner. Everyone else, I'm afraid, will find it a challenge to read and follow the mathematics.

2 of 3 people found the following review helpful:

1.0 out of 5 stars Outdated, September 7, 2009

By 

Cybertronian (Finland) - See all my reviews

This review is from: The Three-Body Problem (Hardcover)

I do not agree with the previous reviewer(s) that the book is written for mathematical physicists. In my view it completely lacks any modern developments (geometric mechanics). The book starts off with the two-body problem from a simplistic, Newtonian point of view. After that, the Lagrangian formulation and Hamiltonian formulation are developed, but only in an undergraduate way. It's understandable if you have already seen it before, but don't be fooled: the text is not intended for people who do not know what it's about. Then, finally, the three-body problem is described. Mostly done from Valtonen's own research and that of his buddies in Finland. Some research that is outlined is done so poorly for two main reasons: the original papers aren't any more clear than what they present in the book, and it's highly guess-work. A lot of details come from "fitting nice functions" through numerical data (generated from simulations), and then doing some "interesting" physics.

In my opinion, the book lacks any direction. It's not intended for undergraduates, because the text does not contain enough information for them to grasp it, although their point of view has been kept in mind in writing it, but it's not for graduates either, because Poincaré's work is about as modern as it gets, from a mathematical point of view. Chaos is described very poorly, and most comes from doing numerical computations, although great mathematical work could have been shown. I think this book should be avoided at any cost. It's probably one of very few books on the topic, but it's not worth buying.

0 of 1 people found the following review helpful:

5.0 out of 5 stars Interesting and useful text on the multibody dynamics problem, April 2, 2009

By 

J. A. Bradley (Omaha NE USA) - See all my reviews
(REAL NAME)   

This review is from: The Three-Body Problem (Hardcover)

I was very impressed with the content and organization of this book. Yes, its material is treated at a very high level of sophistication, but the topic requires that. I think that this book would be useful and interesting to not only astrophysicists, but also graduate students and researchers in mathemathical physics (esp. chaotic dynamics), physics, and mathematics.