# How large would the sun be if it were frozen?

• B
dennis_n
How much smaller would the sun be if all it's hydrogen and helium turned to liquid?
I can't figure out how to calculate this. But I thought it would be fun to visualize how much smaller in size a frozen sun would be compared to it's gas/plasma state.
Anyone?

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This should be pretty easy to compute. The Sun's mass composition can be readily found on the internet, as can the densities of liquid hydrogen and helium, which are the Sun's main components. Just take the masses of hydrogen and helium and compute the corresponding volume using the densities.

• unusually_wrong, PeroK and russ_watters
snorkack
This should be pretty easy to compute. The Sun's mass composition can be readily found on the internet, as can the densities of liquid hydrogen and helium, which are the Sun's main components. Just take the masses of hydrogen and helium and compute the corresponding volume using the densities.

No, it isn´t.
Hydrogen and helium will be self-compressed by gravity.

White dwarf mass-radius relationships won´t help, either, because white dwarfs are carbon or heavier.

dennis_n
This should be pretty easy to compute. The Sun's mass composition can be readily found on the internet, as can the densities of liquid hydrogen and helium, which are the Sun's main components. Just take the masses of hydrogen and helium and compute the corresponding volume using the densities.
I thought that too, but then the gases change density from surface to core, so I thought a simple computation might not solve this.

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No, it isn´t.
Hydrogen and helium will be self-compressed by gravity.

White dwarf mass-radius relationships won´t help, either, because white dwarfs are carbon or heavier.
But this was not the question as I read it. The question as I read it is just "if the hydrogen and helium were liquid of the typical densities, how much volume would it occupy". It is obviously not going to happen in reality.

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I thought that too, but then the gases change density from surface to core, so I thought a simple computation might not solve this.
You do not need the volume of the gases. You just need the mass.

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The average density of the Sun is 1410 kg/m3
Liquid hydrogen has a density of only 70 kg/m3
Thus the Sun is already denser than liquid hydrogen would be.
If you were to remove the energy source that keeps the Sun from collapsing, it would compress until its core reaches a state of electron degeneracy. At this point you have the equivalent of a White Dwarf, and an object with a radius comparable to the Earth's.

• dennis_n and Imager
dennis_n
The average density of the Sun is 1410 kg/m3
Liquid hydrogen has a density of only 70 kg/m3
Thus the Sun is already denser than liquid hydrogen would be.
If you were to remove the energy source that keeps the Sun from collapsing, it would compress until its core reaches a state of electron degeneracy. At this point you have the equivalent of a White Dwarf, and an object with a radius comparable to the Earth's.

I never thought to search for average density. It was faulty logic to assume that an extremely compressed plasma core wouldn't increase the average density to more than that of a liquid or solid state. Might be the public misconception that stars are mainly bodies of "Gas" and "Plasma" and we conceive both of these as very light, only experiencing gas as the air around us and thinking of plasma as an even more expanded form of it. Thanks! I learned something new today.

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Weird.
So a liquefied sun would be 2.7 times larger in diameter. (Using Janus's hydrogen density)

snorkack
I tried to figure out how big droplet of liquid He can exist.

By my estimate, somewhat smaller than Pluto, unless extra heating is provided. On account of the extra heating from relic radiation, a Pluto sized drop of He can be liquid without other heating.

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So, how is it that Jupiter has approximately the same density as the sun?

1300 kg/m^3 Jupiter
1410 kg/m^3 Sun​

Thanks! I learned something new today.

I learned, by going down your rabbit hole, that I know way too little about how things work, on not-even-a-cosmic scale.

• nikkkom
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