So the process tends to damp itself off. Jupiter won't explode. It won't turn into a star, either. Stars work by maintaining fusion in their cores. Now, I just said fusion isn't self-sustaining, so how do stars keep it going? They do it by containing the hydrogen in a small volume. This is accomplished by piling a lot of mass on top of the hydrogen: the mass of the star.

The star has enough gravity that all that mass squeezes and heats the core enough for fusion to not only take place, but to continue at a relatively stable pace. But it turns out there is a lower limit to that mass; if you don't have enough, then you don't get the high temperatures and pressures necessary to ignite fusion. That mass is about 0.077 times the mass of the Sun, or 80 times Jupiter's mass. In other words, Jupiter is 1/80th the mass it needs to turn into a star. Some people call Jupiter a failed star, but in reality it ain't even close.

Conclusion: Jupiter won't explode, or turn into a star, because it lacks the containment to keep fusion going.

If I have time I will add to this article over the next few days, but I think I've made it pretty clear that this idea that Galileo will somehow cause a nuclear explosion on Jupiter is wrong. Remember, if you hear something on the web about how some astronomical event may cause doomsday here on Earth, read it with a very skeptical eye. And check Bad Astronomy before you start putting your affairs in order!