[skywhopper]

One answer is that it probably isn’t possible to do what you say, but if it were the failure states are wildly unacceptable. Any “cannon” (or rail gun) capable of accelerating an object to escape velocity from the surface would likely burn the object up during its flight through the atmosphere, spreading its radioactive contents into the air to float around as low level global fallout for decades.

But if instead you just launched it into space on a rocket... well what happens when a launch fails and the rocket blows up on the launch pad? If you’re lucky, you mark a few square miles as no-go zones and then move on to the next launch pad? Doesn’t strike me as a sustainable solution.

One of my favorite ideas is to encase the waste into giant glass blocks, and build pyramids in the desert... but I doubt that’s very practical either.