Dirk writes: << If you consider the spherical shape of the earth and the gravity not pointing in the same direction everywhere, I think it will be different (but I did no calculations). In the extreme case, when all the surface of a water planet is covered by ice, the ice will not sink at all because the gravity cancels out everywhere. When this ice block melts, the water level will rise...

...

Surely there is more involved in this spherical ice shell than mere floating! (Imagine a spherical shell of radius ~1 meter, with thickness = 1/10 meter, made of iron, and now cut it into, say, 4 spherically-curved 120-degree triangular slabs, leaving them in position. Now imagine trying to push all 4 pieces towards the center at the same time. They will get in each others' way.) If instead we chop up the spherical shell of ice into pieces -- and get rid of some ice so that [the cones on the pieces from the earth's center] are mutually disjoint -- then starting from this situation instead of from the complete spherical shell of ice -- then when *this* ice all melts, the water level should not change perceptibly. I don't see any gravity cancellation here, or in the original situation. --Dan