North Korea set off an incredibly wimpy nuke (500 tons?) and everybody in the world and their dog noticed, why would the US setting off a nuke be any different? A lot of nations have spy satellites flying around; if the US did set off a nuke half the industrialised nations on the planet would have to have been 'paid off' not to spill the beans.

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"Bessie Braddock to Churchill "Winston, your drunk!"
Churchill: "Bessie, you're ugly, and tomorrow morning I shall be sober""
the solar system