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Jupiter has about twice the density of Saturn (1.33 versus 0.69 g/cm^3) because it apparently has a higher mass percentage of rocky core and of metallic hydrogen in its interior. Available density references of this hydrogen state differ widely from 0.3 - 2.8 g/cm^3. Is there a theoretical density of metallic hydrogen, and would its density remain relatively constant given the varyng high pressures and temperatures found in these planetary interiors?

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There will be a density gradient of the hydrogen for the planet, but you can probably quote an average density for the planet if you need to estimate something.

There was work done by Ashcroft in 1968 (N. Ashcroft, PRL 21, 1748, 1968) which addresses the topic of metallic hydrogen and density thereof, working to the conclusion that metallic hydrogen may be a high temperature superconductor. This was actually cited as a possible justification for the large magnitude of the magnetic field of the planet Jupiter. I don't think that answers your question, but I think it's pretty neat. :)

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Jen: The metallic H density quotes I mentioned above were I believe, numbers from lab creation of the substance or from theoretical ideas. I'm confused by their range. –  Michael Luciuk May 13 '11 at 20:57
    
What do you mean, confused by their range? Are you asking why there is a range of material densities? Or why the values are so different? –  Jen May 13 '11 at 22:43
    
Jen: Why the values are so different. Seems to me that since metallic H is in a liuid phase (?) its density shouldn't vary from 0.3 - 2.8 g/cm^3 depending on the source. –  Michael Luciuk May 13 '11 at 23:41
    
I see two possibilities: either that very impulse shock measurement has such broad range of accuracy, or the values are about some supercritical state. I know from experiments on supercritical mercury, that the range of densities with metallic conduction was very broad. –  Georg May 16 '11 at 9:24
    
Why wouldn't the density vary? The density of many liquids varies depending on the specific experimental circumstances. Take water, for example - its case is not as extreme as the metallic hydrogen case identified above, but the density of water varies quite a bit between different temperatures. Do you have references for the metallic hydrogen studies? –  Jen May 16 '11 at 13:32
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