Metallic hydrogen

[granpa]

After reflecting on it all day this is what I decided:

 

All planets from 1 Jupiter Mass to 60 Jupiter masses are known to have approximately the same radius.

The density of jupiter is 1.33 g/cm^3

A 60 jupiter mass brown dwarf is therefore about 60 times as dense and made mostly of metallic hydrogen/helium.

80 g/cm^3 = minimum density of the most dense form of Metallic hydrogen/helium

I assume there is another less dense form about 8 g/cm^3

 

What is the true radius of jupiter?

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

Below the Frenkel line the fluids are "rigid" and "solid-like", whereas above it fluids are "soft" and "gas-like".

76850km = polar radius of jupiter

(76850km-300km) = 76550km = Frenkel line for jupiter = true radius

 

Volume of sphere = (4/3) * pi * r^3

Mass of Jupiter = 317.8 earth masses

 

0.0794 g/cm^2 = estimated density of 739 grams of liquid hydrogen (0.071 g/cm^3) + 240 grams of liquid helium (0.125 g/cm^3)

mass of Jupiters liquid hydrogen ocean = ((4/3) * pi * (76550km)^3 -(4/3) * pi * (0.5*76550km)^3) * 0.0794 g/cm^3 in earth masses = 21.8 earth masses

 

Assuming that the rest of Jupiter's mass is in the metallic hydrogen/helium core we get:

(4/3) * pi * (0.5*76550km)^3 * 8 g/cm^3 in earth masses = 315 earth masses of metallic hydrogen/helium in jupiter

0.5*76550 km = radius of metallic hydrogen/helium core in jupiter

 

(1-0.5) * 76550km * (0.0794g/cm^3) * 2.528(9.8m/s^2) * (1-1/0.5)/(1-0.5) in bar = 1.5 million bar = pressure at which hydrogen becomes metallic inside Jupiter

(1-0.5)*76,550km = depth of liquid hydrogen /helium ocean

2.528 * (9.8 m/s^2) = surface gravity of Jupiter

(1-1/0.5)/(1-0.5) accounts for increase of gravity with depth = (integral of 1/x^2 from 1 to 0.5)/(integral of 1 from 1 to 0.5)

 

 

Saturn reaches 1.35 million bar at 0.25 from center

(1-0.25) * (54300km-357km) * (0.0794g/cm^3) * (10.44m/s^2) * (1-1/0.25)/(1-0.25) in bar = 1.35 million bar

 

 

Earth reaches 1.16 million bar at 2900 km depth which is enough to make metallic (but not degenerate) oxygen

(2900km) * (4g/cm^3) * (10m/s^2) in bar

Perhaps the inner core is metallic oxygen rather than iron

 

https://en.wikipedia.org/wiki/Solid_oxygen#Metallic_oxygen

 

Pressure in center of jupiter:

0.5 * 0.5 * 76550km * (8g/cm^3) * 4*2.528(9.8m/s^2) in bar = 150 million bar

 

 

 

 

 

If the sun began as a rapidly growing and rapidly rotating 60 jupiter mass brown dwarf then it was at that time almost entirely metallic hydrogen/helium surrounded by a thin (1300km) ocean of 1 earth mass of liquid hydrogen/helium.

 

The pressure at the bottom of this ocean would have been

1300km * (0.0794g/cm^3) * 60*2.528(9.8m/s^2) in bar = 1.5 million bar

(saturn has about 8 earth masses of liquid hydrogen/helium)

 

Based on the abundace of the elements, 1.5% (0.9 jupiter masses) of the protosun should have been carbon and oxygen so it is possible that between the liquid hydrogen/helium ocean and the metallic hydrogen/helium there may have been a 0.9 jupiter mass of metallic carbon and metallic oxygen (if 10 g/cm^3 then 2700 km thick)

(It might have been less than a 0.9 jupiter mass if part of it became fully degenerate and sank to the core of the protosun)

 

 

The layers would have looked like this:

 

Nondegenerate liquid hydrogen and helium (0.0794 g/cm^3)

Nondegenerate metallic carbon and oxygen

 

Partially degenerate metallic hydrogen and helium (8 g/cm^3)

Partially degenerate metallic carbon and oxygen

 

Fully degenerate hydrogen (>80 g/cm^3)

Fully degenerate carbon and oxygen

 

 

When the suns core finally collapsed it would have begun to spin faster due to conservation of angular momentum. If it spun fast enough then its outermost layers of liquid hydrogen and metallic oxygen and metallic carbon would have been thrown out into space where it would have coalesced into a moon which would have immediately begun receding from the rapidly rotating protosun due to tidal interactions.

 

If it continued to spin faster and faster then eventually part of its metallic hydrogen (now the outermost layer) would have been thrown out into space and would have formed a second moon which would also have immediately begun receding due to tidal interactions. The metallic hydrogen might have been solid originally which is why it didnt end up in saturn. After the core collapse and the beginning of fusion vast floods of metallic hydrogen lava probably covered the surface

 

Maybe, just maybe, saturn=1st moon and jupiter=2nd moon

I'm just throwing it out there as a possibility

 

Jupiter would have been 1/60th of the mass of the protosun. The Moon is 1/80th of the mass of Earth.

 

This would also explain why hot Jupiters are so common

 

outer 4000 km = 1 jupiter mass

60*10^9 km^2 * 4000 km * 8 g/cm^3 in earth masses = 321.5 earth masses

 

4000 km might be the depth at which metallic hydrogen transitions to a denser phase.

60*2.528(9.8m/s^2) * (saturn mass + jupiter mass) / (jupiter surface area) in bar =

60*2.528(9.8m/s^2) * (5.7*10^26kg + 1.9*10^27kg) / (61 * 10^9 km^2) in bar = 600 million bar

 

Even though the sun accounts for most of the mass of the solar system, Jupiter's orbital momentum accounts for the majority of the Solar System's angular momentum

 

Had Saturn and Jupiter continued to grow into Stars then one of them would have been ejected from the system (a 3-body system is unstable) and we would now be in a binary star system.

The planet that was not ejected would have grown until it also had 2 large moons at least 1 of which would have been ejected too.

In this way each star system spawns 2 more until the molecular cloud is destroyed by a supernova

 

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

 

If hydrogen only comes in two flavors, liquid hydrogen and metallic hydrogen, then it's very hard to see how a planet could keep the same radius as its mass increases from 1 Jupiter Mass to 60 Jupiter masses. I'm thinking it is necessary to suppose that metallic hydrogen comes in two forms, one much denser than the other. However the nice thing about that is that if that's true then an earlier process similar to the one described above could be responsible for the creation of Uranus and Neptune as well.

 

the pressure in the center of jupiter would reach 150 million bar if its metallic hydrogen has a density of 8 g/cm^3

0.5*0.5*76000km * (8g/cm^3) * 2.528(9.8m/s^2) in bar

its core would be 0.5*76000km in radius

by the time it reached 8 jupiter masses the core would be twice as big and the pressure in the center would be 4 times higher, 600 million bar

And its liquid hydrogen ocean would be 0.1*76550km deep

(1-0.5) * 76550km * (0.0794g/cm^3) * 2.528(9.8m/s^2) * (1-1/0.5)/(1-0.5) in bar = 1.34 million bar

Edited September 11, 2016 by granpa

[swansont]

After reflecting on it all day this is what I decided:

 

All planets from 1 Jupiter Mass to 60 Jupiter masses are known to have approximately the same radius.

!

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