Classical Textbooks of celestial mechanics

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The discussion centers on a request for classical mechanics resources, particularly those with a focus on celestial mechanics and mathematical rigor. The original poster expresses interest in understanding Kepler orbits and seeks textbooks that provide rigorous mathematical derivations, such as why orbits around the sun are elliptical. However, a response cautions that while Abraham and Marsden's "Foundations of Mechanics" offers a highly abstract and sophisticated mathematical treatment, it may not effectively teach practical physics or problem-solving skills. The conversation also highlights the necessity of understanding Hamiltonian formalism and perturbation theories for a serious study of celestial mechanics, suggesting that many existing textbooks in this area are challenging and somewhat outdated.
Santiago24
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Hi I'm reading classical mechanics by Taylor and there is a section about Kepler orbits that i find very interesting so i'd like to see more of classical mechanics with space applications. I appreciate rigouros mathematical books, thanks
 
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Are you sure you're after mathematical rigour? Abraham and Marsden's book Foundations of Mechanics contains a ridiculously abstract and mathematically-sophisticated exposition of celestial mechanics but it won't teach you much physics, or indeed how to solve many practical problems (!).
 
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Well, mathematical rigor and mathematical sophistication are not the same things.

In any case, I'm also interested in introductory textbooks for Celestial mechanics. I'm under the impression that any serious study of celestial mechanics requires a lot of knowledge of the Hamiltonian formalism and Hamiltonian perturbation theories (but that comes from reading books on analytical mechanics). The few books I know on celestial mechanics are quite hard and somewhat old.
 
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ergospherical said:
Are you sure you're after mathematical rigour? Abraham and Marsden's book Foundations of Mechanics contains a ridiculously abstract and mathematically-sophisticated exposition of celestial mechanics but it won't teach you much physics, or indeed how to solve many practical problems (!).
I want to see the mathematical derivation of things like why orbits around the sun are elliptical in Taylor book, thanks for the recommendations!
 

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