Originally Posted by antoniseb

It depends on the material, but it is easy enough to calculate what it would take for something where you know the specific energy required to vaporize something.

Let's say that you have a cubic centimeter of ice at 0 C sitting 1000 km from a big bomb explosion. That ice will vaporize at 100 C, and that will take a little over 400 Joules to accomplish (standard Earth Science). So the question is How big does the explosion have to be for a square centimeter to absorb 400 Joules when it is a million meters from the source?

Four Pi R-squared is the surface area of that sphere, so 4 trillion square meters, and one square centimeter is a ten thousandth of that, so the energy of the blast would have to be 40 quadrillion times the energy required to melt the cube, which is 16 quintillion Joules.

You probably are thinking about this in terms of megatons. Google found me a nice Joule to megaton converter... 4 quadrillion Joules per megaton... That means that a 4 gigaton bomb would be about what it would take to vaporize that block of ice.