Kepler's laws
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Kepler
A proof of Kepler's laws.

Introduction.
The following is a proof of Kepler's laws of planetary motion from Newton's laws of motion and universal gravitation. It assumes that the reader is familiar with vector calculus, at least in its basic form. (However, if you are not familiar with vectors and calculus, you will still be able to follow along anyway.)
Overview.
Here is a quick sketch of our proof.

First, we will introduce the concept of torque, and then demonstrate how the force of gravity on planets conserves angular momentum. We will then demonstrate how conservation of angular momentum implies Kepler's second law. Following that we will introduce polar basis vectors, which will then be employed to demonstrate Kepler's first law. After Kepler's first law has been proved, we will finish with the proof of Kepler's third and final law.

Contents.
Kepler's laws: Torque
     
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Kepler's laws: Conservation of angular momentum
     
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Kepler's laws: Kepler's second law
     
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Kepler's laws: Polar basis vectors
     
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Kepler's laws: Kepler's first law
     
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Kepler's laws: Kepler's third law
     
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Kepler's laws: Commentary
     
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Copyright © 1992 Erik Max Francis. All rights reserved.
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Kepler
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