Assuming Earth, an uniform sphere of mass M and radius R. At a point P inside Earth at a distance r measured from centre of Earth (r < R)

Pressure (p) caused by gravitational compression is $\frac{3}{8}[1+\frac{r^2}{R^2}]\frac{G{M}^2}{\pi R^3}$

Gravitational field Intensity at the centre is zero.

Gravitational field Intensity at the centre is  $\frac{3}{2}\frac{GM}{R^2}$

Pressure (p) caused by gravitational compression is $\frac{3}{8}[1-\frac{r^2}{R^2}]\frac{G{M}^2}{\pi R^4}$