Density of the Sun

Being either on the surface or somewhere inside; where is the density of the gases of the Sun equal to the density of the ground we stand on here on earth?

• You can quickly estimate the mean density of the Sun (total mass by vol) and easily find the density of dirt with a quick internet search, no? – Kyle Kanos Aug 19 '15 at 1:34
• Doesn't the density of the Sun vary in depth? I wasn't interested in mean density. I also don't think the changes in density are linear. But I simply don't know. Kanos came across as quite dismissive... I felt like this was actually a very nuanced question. – Steve Farkus Aug 19 '15 at 2:20
• Yes, the density varies with depth, but the assumption of a constant density is a decent first-order approximation to show that, depending on your internet search, the two are the same ($\langle\rho_{\odot}\rangle\simeq\rho_{dirt}$). – Kyle Kanos Aug 19 '15 at 2:36
• If I was looking for 1st order approximations I would have looked elsewhere. This site is where the brainy folks are.... – Steve Farkus Aug 19 '15 at 2:39
• Here is a link to a summary description of the Sun's interior: csep10.phys.utk.edu/astr162/lect/sun/interior.html. Density is on average less than Earth's because of the lighter elements hydrogen and helium that predominate in the Sun's composition. – Ernie Aug 19 '15 at 3:28

The image below represents the Sun's density gradient, which shows how the density changes with the radius. The ground we stand on should have a density between 2 to 3 $$g/cm^{3}$$. That should put you just above the water point on the vertical axis. The corresponding radius is then about 0.45 of the solar radius.

Note that the vertical axis is in a logarithmic scale.

More links to this data and its source in this answer. As @KyleKanos point out, "the answer is a google search away", but it's not quite as simple as he suggests. The mean density doesn't answer your question (the mean density turns out to be about 1.4 times the density of water by the way).

An ill-defined idea in your question is the "surface" of the sun. Where is the "surface" of the sun given that none of the sun is solid? For sake of argument let's define the surface as being somewhere in the photosphere, and call this "one solar radius".