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So, in one science fiction story, that tries to be realistic as possible apart from few space magics, humanity has 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 event. Would it totally wreck the solar system or would the whole plan be non-issue?

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why?? do you know something we don't?? *give sideway glances under the tinfoil hat* –  Olivier Dulac Mar 27 '13 at 12:22
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This should be submitted directly to what-if.xkcd.com –  Rory Alsop Mar 27 '13 at 14:20

3 Answers 3

up vote 17 down vote accepted

The mass of Jupiter is about $10^{27}$ kg which, via $E=mc^2$, translates to $10^{44}$ joules. If one turned the planet into thermonuclear fuel in some way and detonated it immediately, about 1% or $10^{42}$ 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 $10^{42}$ joules per half a second. It's $2\times 10^{42}$ watts.

The Sun only releases $4\times 10^{26}$ watts of power, so the blast would be $2\times 10^{16}$ 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 $5^2=25$. So the half-second blast seems about $10^{15}$ times stronger than the sunshine. The equilibrium temperature is, because of the $\sigma T^4$ law, about $10^4$ 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 $10^{15}$ 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 $10^{15}\times 342\times 4\pi \times 6,378,000^2\sim 2\times 10^{32}$ watts for half a second, about $10^{32}$ 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 $10^{29}$ kilogram-degrees to be heated. Divide it by the Earth mass below $10^{25}$ 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.

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I didn't interpret the question to mean that all of Jupiter is involved in a thermonuclear reaction, only that enough is to unbind the planet. So I've gone with a "minimal" scenario in my answer where all of the energy goes into unbinding Jupiter, with little left over for dangerous radiation. This a comparatively "safe" method, thought I must confess ignorance about which scenario is more plausible. :) –  Michael Brown Mar 27 '13 at 10:31
    
LOL, you may be right. At the end, we will choose a method to blow up Jupiter most creatively. ;) –  Luboš Motl Mar 27 '13 at 10:42
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I'll accept this, though Brown's answer is good too :) Different versions is a good thing, since there is not a clear whenever or not the entire Jupiter is used or just parts of it. –  Mandemon Mar 27 '13 at 11:58
    
re your last paragraph, 2010? –  Tobias Kienzler Mar 27 '13 at 12:14
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What if Earth and Jupiter were in opposite points in their orbits? Would the two extra AU have an appreciable difference? –  Mr.Mindor Mar 27 '13 at 14:34

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.

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There is a 'Universe Sandbox' simulator on steam at the moment, where you can blow up planets and see how it affects things. Will be interesting to try this and see the effects on the rest of the solar system –  RhysW Mar 27 '13 at 11:50
    
@RhysW: Universe Sandbox - great for playing around, not known for its accuracy. These tiny orbital perturbations would probably be below its numerical error level unless you run at its highest accuracy settings (4th order Runge-Kutta with a very short time step). Anyway, worth a try. –  Michael Brown Mar 27 '13 at 12:36
    
Oh yes definately not overly accurate, but if the effects are big enough it would be noticeable –  RhysW Mar 27 '13 at 14:00
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I think the real problem with this is the mass distribution. You assumed that we use just enough energy to disassociate Jupiter's mass. Then it certainly won't have the energy to escape the sun! And Jupiter's mass is 2.5 times all the other planets combined. Best case scenario Saturn would absorb a large fraction of it, but even if it did Earth would become completely covered in Hydrogen from Jupiter and life would be smothered. Eventually most would boil off, but new planets would form from Jupiter's massive cloud and affect the orbital resonances. –  Alan Rominger Mar 27 '13 at 14:48
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Also, if Jupiter's moons stick around, I doubt their initial orbits will be stable: the four big moons would end up in nearly intersecting eccentric orbits, and would likely start a game of gravitational billiards with each other, and possibly with other bodies in the solar system, until at least some of them got ejected or crashed into something. However, I also suspect that a blast capable of totally dispersing Jupiter might well transfer enough energy to the moons to put them on direct escape trajectories as well; after all, they'd be hit with quite a bit of fast-moving ejecta. –  Ilmari Karonen Mar 27 '13 at 14:55

Let's pluck several parameters from Wiki for blowing up the Jupiter. If we compare Earth with Jupiter in terms of mass and volume, it brings us a lot of wonderful numbers.

Volume: $1.4313×10^{15}\text{km}^3$ which can hold $1321$ Earths

Mass: $1.8986×10^{27} \text{kg}$ which is $318\ M_{Earth}$

It's indeed Sci-Fi. Because, simply using the mass-energy equivalence, we can see that it releases about $10^{45}J$, which is a lot of energy, indeed. First, the light along with the gamma rays from the nuclear explosion can easily cross 4 AU distance in about 36 mins to reach Earth. If we're planning to detonate the Jupiter's core, then we're gonna spread out its highly dense $H_2$ and $CH_3$ atmosphere, which can provide a medium for the shock-waves. Then, the highly radioactive radiations are gonna make their way to Earth within several weeks maybe. There will be a lot of consequences for this explosion like,

1) At the time light & gamma rays speed into Earth's atmosphere, we lose all our infrastructure on communications. Satellites in every orbit will be melted.

2) Next, we'll be watching jupiter on fire while we'd be slowly eroded (1 or 2 seconds, maybe) by the highly intense $\gamma$-rays, particles like neutrons and other EM radiation.

3) And, the most important thing. As I've said, the shockwaves would make their path through the spread-out atmosphere, taking the asteroid belt and some broken moons along with it.

Definitely, we won't be here to enjoy the fireworks ;-)

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