Deriving Kepler’s Laws
The purpose of what remains is to derive Kepler’s Laws from physics, that is to say, Newton’s Laws. My only contribution to this, if any, is extracting the results from (Spaceflight Dynamics, William E. Wiesel, third edition). This is an “extraction” rather than an “exposition” as Wiesel is doing quite a few other worthwhile things at the same time he is deriving Kepler’s Laws. My aim is to put the focus on the derivation of Kepler’s Laws themselves.
On a personal note, let me say I have approached this from a mathematician’s point of view, but I only made progress when I came to the understanding that this is physics. However much mathematicians would like to claim him, Newton was a physicist.
I’ve found a couple of different approaches in the literature--(Wiesel) and (The Sheer Joy of Celestial Mechanics, Nathaniel Grossman)--and have chosen to follow (Wiesel) because it simply has a better “feel to it.”