gravity of a torus

Ever since high school, when I first learned to derive the gravity of a sphere, I’ve wondered what gravity on a torus (donut) would be like. I learned quite quickly, then (and again recently) that the integration required for a donut goes beyond my ability. (Even showing the gravity inside a spherical shell requires integration tricks that I no longer remember, even after I recently read about how to do it.) So a few months back, I started a small computer program to do a brute-force summation of small pieces of the donut. I’m not sure I believe the numbers I got, so won’t publish any of that. But I was able to find an article at io9, “What would the Earth be like if it was the shape of a donut”, which brought out a lot I didn’t think about. And MathPages has a full derivation of toroidal gravity, and makes me see why I couldn’t do the calculus myself. 🙂