19.4 Earth Masses Of Ice Inside Saturn

[granpa]

19.4 earth masses of ice inside Saturn if density of metallic hydrogen = 2.2 g/cm^3

The surface of the gas giant is defined as the point where the pressure of the atmosphere is 1 bar,
Scale height = the vertical distance over which the density and pressure fall by a factor of 1/e.
saturn Scale height: 59.5 km
jupiter Scale height: 27 km
https://en.wikipedia.org/wiki/Frenkel_line
Below the Frenkel line the fluids are "rigid" and "solid-like", whereas above it fluids are "soft" and "gas-like".

(1-((1.326/2.2)^0.333)) * (76850km-270km) * (0.08g/cm^3) * 2.53 * (10m/s^2) * (1/((1.326/2.2)^0.333)) in bar
    = 284 638 bar (according to google) = pressure at which hydrogen becomes metallic inside Jupiter

1.326 = density of Jupiter
2.2 g/cm^3 = Metallic hydrogen density
(1.326/2.2)^0.333) = radius of metallic hydrogen core = rmhc = 0.845*radius of Jupiter
76,850km-270 km = polar radius of Jupiter - 10 scale heights = Frenkel line
(1-((1.326/2.2)^0.333)) * (76,850km - 270km) = depth of liquid hydrogen = 11 881 km
0.08 g/cm^2 = estimated density of 0.75 liquid hydrogen (0.071) + 0.25 liquid helium (0.125)
2.53 * (10 m/s^2) = surface gravity of Jupiter
1/((1.326/2.2)^0.333) accounts for increase of gravity with depth = (integral of 1/x^2 from surface to rmhc)/(integral of 1 from surface to rmhc) = 1/rmhc

Mass of Jupiter = 317.8 earth masses
mass of Jupiters liquid hydrogen atmosphere = (0.08/1.326)*(1-0.845^3)*317.8 earth masses = 7.6 earth masses



Saturn reaches 286,426 bar at 0.6 from center
(1-0.6) * (54300km-595km) * (0.08g/cm^3) * (10m/s^2) * (1/0.6) in bar
     286 426 bar

54,300 km - 595 km = Saturn polar radius - 10 scale heights
1 * (10 m/s^2) = surface gravity of Saturn

mass of Saturns liquid hydrogen atmosphere = (0.08/0.6)*(1-0.6^3)*95.16 earth masses = 9.95 earth masses
mass of Saturns metallic hydrogen core = (2.2/0.687)*(0.6^3)*95.16 = 65.8 earth masses
mass of Saturns inner ice core = 95.16 - 65.8 - 9.95 = 19.4 earth masses

This makes sense because Neptune is 17 earth masses and is mostly ice 
And Uranus is 14.5 earth masses and is mostly ice

[granpa]

https://en.wikipedia.org/wiki/Volatiles

 

In planetary science, volatiles are the group of chemical elements and chemical compounds with low boiling points that are associated with a planet's or moon's crust and/or atmosphere. Examples include nitrogen, water, carbon dioxide, ammonia, hydrogen, methane and sulfur dioxide. In astrogeology, these compounds, in their solid state, often comprise large proportions of the crusts of moons and dwarf planets.

In contrast with volatiles, elements and compounds with high boiling points are known as refractory substances.^[1]

Planetary scientists often classify volatiles with exceptionally low melting points, such as hydrogen and helium, as gases (as in gas giant), while those volatiles with melting points above about 100 K are referred to as ices. The terms "gas" and "ice" in this context can apply to compounds that may be solids, liquids or gases. Thus, Jupiter and Saturn are referred to as "gas giants", and Uranus and Neptune are referred to as "ice giants", even though the vast majority of the "gas" and "ice" in their interiors is a hot, highly dense fluid that gets denser as the center of the planet is approached

Edited February 9, 2016 by granpa

[granpa]

Saturn has a hot interior, reaching 11,700 °C at its core, and it radiates 2.5 times more energy into space than it receives from the Sun.

 

I think hydrogen is dissolving in the metallic hydrogen and getting subducted down so deep it becomes metallic hydrogen.

I think that explains the present-day luminosity of the planet

 

 

Edited February 9, 2016 by granpa