Would a submarine float in the atmosphere of Jupiter, or would it get crushed?
[Physics] Would a submarine float in the atmosphere of Jupiter
astrophysicsbuoyancyjupiter
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While you can't turn Jupiter into a star, it is not ruled out that you could turn Jupiter into a catastrophic thermonuclear bomb. The limitations to this was calculated at Lawrence Livermore in the 1970s, as a continuation of the work done to check to make sure Earth's oceans wouldn't ignite due to the deuterium content of water. Necessary Conditions for the Initiation and Propagation of Nuclear Detonation Waves in Plane Atmospheres by Weaver and Wood, couldn't rule out a self-sustaining ignition shock-wave in a planetary atmosphere at a deuterium concentration of more than 1 percent at ordinary liquid densities.
Although this makes the oceans safe, Jupiter is big, and it might have segregated a deuterium layer deep inside which has a high enough concentration to allow a self-sustaining nuclear ignition. Then if you drop a configuration of plutonium designed to detonate the deuterium by a nuclear explosion at the appropriate depth, you could get a detonation wave that ignites the entire deuterium layer within a very short time, the time it takes a shock wave to encircle Jupiter.
The energy output could convert a non-negligible fraction of the deuterium in Jupiter to 3He/tritium, and release enormous amount of energy. If 1 Earth mass of deuterium is ignited by the ignition shock wave, the energy release is 1038 J, over a very short time, perhaps an hour or two and this is already 10,000 times the energy output of the Sun in a full year. The resulting explosion would destroy that part of the world facing Jupiter, and probably bake the rest. I don't lose sleep over this, though.
If there is a natural trigger for such an explosion, perhaps the collision of a rocky planet with a gas giant, one might experimentally observe such planetary mini-supernovas somewhere. This was suggested in section VIII of Weaver and Wood's paper.
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.
Best Answer
As the comments above indicate, factors like density, pressure and temperature are important for a Jupiter submariner. Of course nobody yet has the exact details of Jupiter's interior structure, but there's a diagram in this LASP page[WebCite archived version] that indicates the following: At the intersection of Jupiter's liquid hydrogen/metallic hydrogen layer, the density is about $1\text{ g}/\text{cm}^3$, which would permit the submarine to float. However, the temperature there is $\sim5000\text{ K}$, and the pressure is $\sim2 \times 10^6\text{ bar}$, so it can't be done with normal equipment.