SAO, You little ninja. I'm here typing away at this long post.
She asked what would happen
IF you dropped nuclear waste waste into the sun, not what a pain in the butt (and wallet) it would be
TO drop the world's nuclear waste into the sun. But you are 110% Correct, SAO it would be a huge pain financially to do so and a massive engineering challenge. Particularly since nuclear waste is HEAVY elements. (And there's a lot of it.)
But of course, your many hours of Kerbal Space Program would also tell you that you don't sun-dive
From earth orbit, you transfer out to a higher orbit around the sun, then burn retrograde there, or use a planetary gravity assist. It takes longer but you use less DV. I don't think it matters what orbit or gravity assist you use though, just getting the entire world's nuclear waste into LEO is gonna be much more effort than its worth just to bury it underneath the salt flats or something.
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