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Thats funny. Nuking Jupiter. You severly overestimate the firepower of a nuke. A Hydrogen bomb like Tsar would be for Jupiter like a fly landing on your shoes. This disturbance in the gas atmosphere of Jupiter was likely this: http://en.m.wikipedia.org/wiki/2009_Jupiter_impact_event

Here a quote:

The force of the explosion on Jupiter was thousands of times more powerful than the suspected comet or asteroid that exploded over the Tunguska River Valley in Siberia in June 1908.[2] (This would be over a million times more powerful than the bomb dropped on Hiroshima.)[10]




Also the costs of the mission would be BILLIONS. If one could undertake it a Bomb this big lets just say you would need a whole lot of bombs. I doubt humanity can even lift that much weight into an orbit around Jupiter

And what would be the point. Space is bathed in radiation anyway. Jupiter has a radiation belt that would put a H2 Bomb to shame. Just standing on IO would kill a human in hours despite suite.

Destroying anything in our solarsystem or damaging it requires energy/technology we can't even dream about on this level of development we have. At best we can put a few new craters on the moon and ad a little radiation.