# What would gravity be like on a hemispherical planet?

On a hemispherical world half the size of Earth (ignoring that the planet should break apart and become a smaller sphere) what would the gravity be like? How would it change as you traveled from pole to pole along the curved side, as well as down the flat side? What other interesting or distinguishing facts would this planet have?

I suspect that if you 'fell' off the edge on the flat side it would at first be like falling off a cliff and then transition more and more into a slope and finally be level in the center. If so, how far would you fall before the slope feels like a 45 degree angle? A 30? A 60?

I also suspect that gravity at the poles would be greater than gravity at the curved side on the equator opposite the flat side. I'm not sure what percentage of Earth's gravity would be experienced at any given point.

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If what you want is a formal description, you might wish to state the problem in terms of electrostatics and go to Jackson. Solve the Laplace equation with density $\varrho(\rho,z)=\Theta(z)\varrho_{Earth}(\rho,z)$, set $\varrho_{Earth}(\rho,z)$ as realistic as you want...and have fun with the Bessel functions! – Jorge Campos Jun 8 '12 at 0:19