How different would the effects of gravity be if the planet we're on is in the shape of a torus (doughnut-shaped)?
For an (approximately) spherical planet, it's slightly clear that objects would tend to be gravitationally attracted towards the center. However a torus would have a hole in its center, and I'm not sure if the attraction towards the center still applies.
In particular, could a person on such a planet walk in the vicinity of the hole without falling off?
Similar question, but now consider a planet in the shape of a Möbius strip. Not only do you have to contend with the hole, but with the "kink" as well. Can a person stand up on the kink?