As a general rule, I try to stay away from using too much modern math as I work through the Almagest. The goal of this project is to try to understand how astronomers worked in a historical context – not simply examining their work through a modern lens.
However, Ptolemy’s discussion around Mercury has been greatly frustrating me. There’s several reasons for this. A large one is certainly that the language Ptolemy used is clunky which is challenging for a model that is so complex.
Therefore, I want to dig deeper into what’s happening with the double perigee and make sure I fully understand it. In particular, I previously showed a diagram from Pedersen which looked at the path the center of the epicycle would trace out for various eccentricities. This graphically showed the distance from earth over time, but I wanted something more quantitative, so in this post, we’ll derive an equation to determine the distance between the center of Mercury’s epicycle and earth as a function of the angle from apogee.
This method comes straight from Pedersen but I’ll be doing it in the context of Toomer’s translation. Continue reading “Almagest Book IX: Exploring Mercury’s Double Perigee”