Okay, I'll voice my desire...

My understanding of this comes from Carl Sagan's original Cosmos miniseries...

Kepler and Brahe were reluctant allies. Brahe had the observational data Kepler needed to try to understand the motions of the planets...

...but how the hell did Kepler do it?

I've gone through Differential Equations, I've done Linear Algebra quite a bit, I'm good at computer graphics... I had to derive the equivalent of Bresenham's Ellipse drawing algorithm for a test... And I have no idea how it's even remotely possible for Kepler to have taken astronomical observational data, and derived the motions of the planets from that data.

Has anyone ever done a "For Dummies!" write up of how this was possible?