I was just wondering if anyone had computed this. I read that the pressure in the Sun's core is 3.84 trillion psi. Obviously the mass of an Earth-sized object in the core would be millions of times that of Earth. So how much volume would the mass of Earth occupy? Would it be more than a billiard ball?
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$\begingroup$ What do you mean by "Something the size of a billiard ball?" and "pressure in the Sun's core is 3.84 trillion psi" ? $\endgroup$– Brendan DarrerCommented Dec 1, 2021 at 12:11
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$\begingroup$ The PSI thing is just there as an interesting factoid. I edited the billiard ball reference to be clearer. $\endgroup$– Tom RussellCommented Dec 1, 2021 at 12:19
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According to The Sun's vital statistics the density at the center of the sun is $160$ g/cm$^3$. On the other hand, the average density of the earth is $5.5$ g/cm$^3$, which is $1/29$ of the sun's center density.
So a mass equal to the mass of the earth at the center of the sun has $1/29$ the volume of the earth. That is sphere with $1/\sqrt[3]{29}\approx 1/3$ of the earth's radius.
answered Dec 1, 2021 at 12:20
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3$\begingroup$ @TomRussell The Sun is gaseous (plasma-eous) so its density profile is different from Earth’s. Roughly 90% of the Sun’s mass is contained within 50% of its radius (or 1/8 of its volume). Outside of $0.9 R_\text{sun}$ (that is, the outer 30% of the Sun’s volume) the solar medium is less dense than water. The source linked here says that the photosphere is a pretty good vacuum; the data in my source stop at about the density of air. $\endgroup$– rob ♦Commented Dec 1, 2021 at 13:08
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$\begingroup$ <edited> I was expecting a different result. It's amazing how much pressure results in only a moderate reduction of volume. Also, I see that the avg solar density is only 1.41, considerably less than that of Earth despite being near the bottom of a deep gravity well. Weird. $\endgroup$ Commented Dec 1, 2021 at 18:06
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1$\begingroup$ @TomRussell Gravity has nothing to do with it - A trillion tons of ice and a trillion tons of iron continue in orbit identically so long as their interactions are only gravitational. If they collide gently, they'll coalesce (friction dissipating the excess kinetic energy.) Only then does the fact that the two substances have different volumes become an issue, and energy is then minimised by the denser substance sinking to the core (again, friction dissipates excess energy.) Sun's high gravity actually helps hold low density gas. At the sun's temperature, Earth would quickly lose her atmosphere $\endgroup$ Commented Dec 1, 2021 at 21:49
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$\begingroup$ Hmm. Does supercriticality explain the relatively low (compared to Earth, etc) avg density of the sun? $\endgroup$ Commented Dec 2, 2021 at 0:10
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2$\begingroup$ As I learned on here the other day, the power density inside the sun is about $100 \,\text{W} / \text{m}^3$, which is tiny: the sun is just very large. $\endgroup$ Commented Dec 2, 2021 at 4:33