The Kepler Problem (Part 2)

I’ve been working on a math project involving the periodic table of elements and the Kepler problem—that is, the problem of a particle moving in an inverse square force law. I started it in 2021, but I just finished. I want to explain it. But I need some things to be fresh in your mind, so I’m going to republish some old blog articles, starting with this one. (For Part 1 go here, but you won’t need that for what’s to come.)

Let’s start with the ‘eccentricity vector’. This is a conserved qu...