That's an idea Seth, some kind of accelator....hell, it sounds very Jules Verne/HG Wells-ish but, kinda like a giant gun, launching 'bullets' of nuclear waste space-craft into space.
Didn't the US play around with the idea of using nuclear explosions to propell things into orbit back in the 1970s? Project Thunder-something I think, or Project Anvil...I can't remember off hand. Either that or some kind of accelator device...punch it out of Earth, since it'll be unmanned, it doesn't matter about G-forces.
Of course, it'll have to be fairly well secured, just incase the 'gun' misfires and it lands up falling on someone