Re: [math-fun] Verticals

These ideas can of course be extended to lumpier worlds. Could a local vertical ever point directly away from the center?

Suppose the planet is a solid torus of uniform density. Then if you stand on the inner Equator, gravity will pull you directly away from the centre of the planet. (If you insist that the planet is homotopy-equivalent to a closed ball, just include an infinitely thin membrane spanning the hole.)