So, in one science fiction story, that tries to be as realistic as possible apart from a few space magics, humanity has a contingency plan to blow up Jupiter. As in, totally destroy it in one massive nuclear explosion.
I'd like to know the effects of such an event. Would it totally wreck the Solar System or would the whole thing be a non-issue?
Best Answer
Note: Lumo's answer went up as I was writing this. His addresses what would happen if you turned Jupiter into a gigantic thermonuclear bomb. This is actually overkill. You only need to provide the gravitational binding energy of Jupiter (it's crazy to say "only" in this context, but nevertheless it is a six order of magnitude difference). This is the scenario that my answer addresses.
Blowing up the Earth is hard, and blowing up Jupiter would be roughly 10000 times as hard. If you don't get everything up to escape velocity eventually some or all of the planet will recoalesce. The explosion needs to provide at least the gravitational binding energy (simplifying that the density is constant throughout the planet):
$$ E = - \frac{3 G M^2}{5r}, $$
which for Jupiter is of the order of $5\times10^{26}$ tons of TNT.
Supposing you manage this the remains of Jupiter will expand in all directions in an incandescent plasma fireball. This wind will scour the surface the Jupiter's moons but otherwise spread rather harmlessly through the solar system. (I'm basing this on the fact that Jupiter's sphere of influence is much smaller than the typical distances between the planets, so the kinetic energy of the debris will be greatly reduced by the time it reaches any other solar system bodies. There is also the inverse square decrease in flux of course. Note: the other answers suggest that there would be enough radiation to heat the Earth appreciably. To really answer this properly you need some idea about how the explosion is going to work. I'm assuming a fairly "efficient" device which puts most of the energy into simply lifting the material out of Jupiter's gravity well.) The surviving moons of Jupiter would fly off into the solar system and orbit the sun in roughly the orbit of Jupiter.
None of the planets would be greatly affected in their orbit, however Jupiter has a long term affect on the orbits of planets and asteroids by exerting periodic gravitational "tugs." These interactions would stop, but it's hard to say what the long term impact of that would be without running simulations. But nothing is going to go flying off in a dramatic way - it would take a very long time for this effect to build up over many orbits.