Kepler's laws


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



Kepler's laws: Conservation of angular momentum



Kepler's laws: Kepler's second law



Kepler's laws: Polar basis vectors



Kepler's laws: Kepler's first law



Kepler's laws: Kepler's third law



Kepler's laws: Commentary



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