Air pressure at Earth's center
I wonder if anyone has any ideas as to how one might figure this out. If there were a tunnel from one side of the earth, through the center of the earth, and on out the other side, what would the air pressure be in the center? I have some ideas, but one catch is that the air pressure and air density would seem to be mutually interdependent..
\[V_{\textrm{int}}\left(r\right)=G\frac{M_{\oplus}}{2R_{\oplus}}\left[\left(\frac{r}{R_{\oplus}}\right)^{2}-3\right]\]
\[V_{\textrm{ext}}\left(r\right)=-G\frac{M_{\oplus}}{r}\]
Edit: It's the line going down with distance linearly.
Edit 2: Sorry, that's g. The line going down linearly with distance is the gradient, that is, g.