Will melting ice change the shape of the earth?
If the ice caps melt and the weight of all that water gets redistributed about the planet given that the planet’s just a ball of molten stuff underneath a relatively thin crust will the shape of the Earth change when all the ice goes?
It depends on how long a time scale you are looking at. Over a few tens of years then probably not, the mantle below the crust behaves pretty much as a solid over periods of tens of years. But if you look over thousands or millions of years, then yes the areas where the ice has melted from will lift slightly and the areas the water has moved to will sink. During the last ice age Scotland was pushed down a few metres by the 2km of ice sitting on top of it, and since the ice melted, 10 000 years ago, the crust has been floating back up again in a process called isostatic rebound. This affect is very small though in comparison with the size of the planet though.