Jupiter Core is Solid Hydrogen

I was watching a show on the science channel about gas giants; there is something I do not understand. I am not a scientist, so this may be obvious to some. I learned that there a three states of an given physical object; solid, liquid, and gas depending on how cold or hot the object is. An easy example is ice, water and steam from coldest to hottest. So the theory is that Jupiter has a super-heated solid and very dense core that is made up of hydrogen. How does a gas like hydrogen become a solid while being super-heated? Is it that the pressure is so much that the gas is compressed into a solid? If so how much pressure does it take to compress hydrogen into a solid? How does the heat play into the equation?

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First, before we go any further, we need to understand pressure. Imagine piling sand on top of you on the beach--just a little layer, you don't feel much weight, but as you get buried deeper and deeper, you feel more and more force pushing down on you. This makes sense, since your body has to hold up the weight of all of the sand on top of you.

It's exactly the same in Jupiter's atmosphere--the lowest layer of gas has to hold up all of the weight of the gas on top of it, which means that the core has an incredibly large pressure. Pressurized gasses tend to turn liquid or solid--think of the cans of air that you buy for dusting--if you slosh them around, there is liquid inside, because the air is pressurized to a fluid.

But you are also right to point out that compressing fluids tends to heat them up, and that hotter things tend to evaporate/melt. So, the question is about which trend wins in this case. And for that, the most useful tool we have is a phase diagram. Below, we have one for carbon dioxide${}^{1}$ (source: wikipedia):

Notice that, at very high pressures, the solid state is dominant, even when the temperature is high. The core of Jupiter will be a very high pressure, indeed.

${}^{1}$ Be wary of phase diagrams for water. In many ways, water is an atypical molecule. Non-polar $H_{2}$ is much more similar to $CO_{2}$ than it is to water.

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Water is weird. It doesn't behave at all in line with hydrogen sulfide, hydrogen selenide, or hydrogen telluride due to its polar nature. –  Ignacio Vazquez-Abrams Oct 30 '12 at 3:07
I'd be interested in a reference for the (through the drawing) implicitly claimed fact that the melting curve extends to beyond the critical temperature? –  Arnold Neumaier Oct 30 '12 at 10:09
@ArnoldNeumaier: I don't know enough about $H_{2}$ to know if there is some supercritical solid/gas phase. It would, of course, make total sense if there was one. –  Jerry Schirmer Oct 30 '12 at 13:02
@ArnoldNeumaier: apparently the shape of the curve is only known up to gigapascals: pnas.org/content/107/29/12799/F1.expansion.html I don't see a solid/liquid critical point on that curve (and it looks like there is a point of inflection 'above' the upper limit of the graph I linked to), also, there appears to be a fifth phase where the high pressure liquid is pressurized enough to break the $H -- H$ bond in the hydrogen, and you get a liquid of $H$ atoms. –  Jerry Schirmer Oct 30 '12 at 13:22