Blowing Up Jupiter

Best explanation on the internet:The mass of Jupiter is about 1027 kg which, via E=mc2, translates to 1044 joules. If one turned the planet into thermonuclear fuel in some way and detonated it immediately, about 1% or 1042 joules would be released. Because the diameter of Jupiter is about 130,000 km, the blast would last at least half a second or so. So we have 1042 joules per half a second. It's 2×1042 watts.

The Sun only releases 4×1026 watts of power, so the blast would be 2×1016 times stronger than the Sun. However, looking at the effects on the Earth, we must realize that Jupiter is about 5 times further from the Earth than the Sun, reducing the energy flux by a factor of 52=25. So the half-second blast seems about 1015 times stronger than the sunshine. The equilibrium temperature is, because of the σT4 law, about 104 times higher than that from the sunshine, about a million degrees.

The Sun warms the Earth by a degree in hours or so. A source that is 1015 times stronger obviously needs a tiny fraction of a second to reach thousands of degrees and evaporate the matter on the surface. So no doubt about it, the thermonuclear blast of Jupiter would burn and evaporate all nearby sides of all the planets – all of them are comparably far from the ground zero.

On the other hand, would the incoming energy be able to evaporate the whole Earth? We would be getting 1015×342×4π×6,378,0002∼2×1032 watts for half a second, about 1032 joules per the blast and per the surface of the Earth. The specific heats of materials are comparable to 1,000 joules per Celsius degree and kilogram so we have 1029 kilogram-degrees to be heated. Divide it by the Earth mass below 1025 kg to see that you may still heat the material by tens of thousands of degrees by the incoming light. So I do think that this could evaporate the whole Earth but not the largest planets like Saturn.

Needless to say, the Sun itself would be pretty much untouched. Its surface already has 6,000 degrees or so. The strong radiation from Jupiter could bring it to a million of degrees, by the calculation above, but it's the same as the temperature of the interior layers. So the Sun would get destabilized a bit but it would quickly converge back to the Sun we know, I guess.

The calculations above are completely unrealistic because at most, one could think about turning Jupiter into a small star that would still burn very slowly and would be far weaker than the Sun.

Mercury would be safe

It would probably take a while to feel any major effects.
Jupiter exerts roughly 0.0062% of the force on earths' orbit that the sun does.
A much more interesting question: What if the sun took a similar vacation?

If jupiter was 100 times more massive, it would have been a star.

Jupiter would only have to be about 93 times it's current size to become a real star, and since it is composed almost entirely of hydrogen and helium, it would be able to maintain fusion.
However, if it were only about 13 times more massive, it would begin fusing deuterium and become a brown dwarf. We might, as a species, survive such an event.
Interestingly enough, if Jupiter were a brown dwarf, it would still have roughly the same diameter. The sun is huge because the energy produced by fusion forces matter away from the core, but deuterium fusion does not produce enough energy to resist gravity.

If you were to design a payload for a "match-lighting" robot to send to Jupiter, how would you design it? How would it enter the atmosphere?