# How can gaseous Saturn be only 8 times less dense than Earth

Saturn's mass is roughly $6\cdot 10^{26}$ kg, and that of the Earth is around $6\cdot 10^{24}$ kg. Saturn's volume can hold a little more than 760 Earths according to Wikipedia, which makes it something like 7.6 times less dense, on average, than our rocky planet. I find 7.6 is a surprisingly small figure when comparing rock or liquid with gas. Are the gases that make Saturn just very heavy gases (e.g. per mole) or is it something to do with the fact that its large total mass induces a strong gravitational pull compressing the gases to a further extent than we are familiar with on Earth ?

There is a misconception here that gases cannot be dense. That is not the case. A gas that is crushed by gravity to very high densities may remain in a gaseous state if its temperature remains high enough. The basic idea is that the thermal energy remains large compared with any intermolecular or interatomic potential energy.

As an example, consider the Sun. This is most definitely gaseous (technically, a plasma) throughout, but has an average density of 1.41 g/cc (only 25% that of Earth) and has a central density of 162 g/cc. A more extreme example is a hot white dwarf, most definitely gaseous but with an average density of about a million g/cc.

However, that is not the full story in "gas giant" planets. Their interiors are in general not hot enough to maintain the assumption that inter-particle forces are negligible; they transform into fluids that are more similar to liquids. The bulk of the mass in both Saturn and Jupiter is thought to be in a liquid state with a small solid core (still to be established in the case of Jupiter).

• While it is probably too much detail to talk about the properties of supercritical fluids in this post it might be nice to include the term so that interested readers can follow-up on it. – dmckee --- ex-moderator kitten Jun 23 '17 at 16:49

Gases above the critical point are better described as supercritical fluids rather than gases. This is certainly the case inside Jupiter and Saturn as molecular hydrogen's critical point is a temperature of 32.938 kelvin and a pressure of 12.69 atmospheres. While supercritical fluid do not exhibit a phase transition from gas to liquid, this does not mean that those fluids behave like gases. With enough pressure, they behave much more like liquids than gases.

Liquids and gases exhibit marked up different behavior with regard to viscosity, the speed of sound, and thermal conductivity. Each of these tends to increase with increasing temperature in a gas but decrease with increasing temperature in a liquid. The Frankel line extends the line that distinguishes gas from liquid in a PT diagram into the supercritical region by based on the behavior of those bulk properties. The molecular hydrogen deep inside gas giants is more liquid-like than it is gas-like.

Liquids and solids are oftentimes called incompressible. This is not the case. Consider the Earth's solid iron/nickel core. It's central density is 13.09 grams/cm3, about 66% higher than the density of iron at standard temperature and pressure. Solid iron compresses. Supercritical hydrogen is much more compressible than is solid iron. Deep inside Saturn (and not so deep inside Jupiter), the density of the supercritical hydrogen/helium mixture that comprise the vast majority of the atmospheres of those two planets becomes greater than that of water.

Gas planets aren't pure gas; they have a solid or liquid core. Think of gas giants as regular planets that have a really thick, tall atmosphere; there is still rock or metal in the center. In Saturn's particular case, there seems to be debate whether it's molten rock or solid rock, but regardless, the core is not gas.

In fact, the large mass of the solid core is how the planet has enough gravity to attract all that gas in the first place.

• In the case of Jupiter I think that the current belief is that it is unknown whether or not it has any rock in its core. It is believed that there is a lot of fluid, metallic hydrogen in the core, though. So if Jupiter did at one time have a rocky core in order to gravitationally attract all that hydrogen in the first place, it's possible that the rock core was broken up or dispersed long ago by the convection of the dense, fluid metallic hydrogen. – user93237 Jun 23 '17 at 5:55