# What volume would the mass of Earth occupy in the core of the sun?

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?

• What do you mean by "Something the size of a billiard ball?" and "pressure in the Sun's core is 3.84 trillion psi" ? Dec 1, 2021 at 12:11
• The PSI thing is just there as an interesting factoid. I edited the billiard ball reference to be clearer. Dec 1, 2021 at 12:19

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.
• @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.
• 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. Dec 2, 2021 at 4:33