I stumbled upon a two part video explaining how to theoretically turn a sphere inside out. After I watched it (sober), I started to think "what if the earth could turn inside out?" and "what if the earth was a different shape, like a cube, pyramid, or donut shaped?" Like what sort of effects would it have on Gravity, the tides, etc etc? [ame]http://www.youtube.com/watch?v=BVVfs4zKrgk[/ame]
Turning a perfect, hollow sphere inside out would simply result in an identical sphere. And the Earth is not actually a perfect sphere - it bulges out around the middle - which is why gravity is strongest at the poles and weakest along the equator. Hypothetically speaking, if the Earth were somehow reconfigured into a different shape, with the same amount of mass evenly distributed throughout, the gravitational force on the surface would vary based on how close you were to the geometric center. So, if the configuration was a cube or an equal-sided pyramid, gravity would be weakest at the vertices and strongest at the center of the planar sides. It's a bit more complex to try to imagine a doughnut shape, maybe someone else can help with that.