Ask Ethan: Why don’t we shoot Earth’s garbage into the Sun?
Ethan Siegel
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What about the idea of putting the nuclear wast into hardened containers, shaped into a point on the heavy end, and simply dropping them right on the diving edge of a subduction zone in a very deep part of the ocean? They would weigh so much that the containers would tunnel into the ocean floor a fair bit and then over the next many many centuries they would sucked deeper and deeper into the earth’s core until they became just a bit of molten magma.
A treaty with Russia (and any other country that eventually develops deep ocean mining capabilities — so far none) to patrol the area would be needed to ensure no country (or person) tried to recover the containers, but eventually the containers would be beyond recovery.

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