# Gravitational Time Dilation

## Main Question or Discussion Point

Could somebody explain me the following:
According to GR time dilation due to gravitational field is expressed as:
T$_{g}$=T$_{f}$*$\sqrt{1-\frac{2GM}{rc^{2}}}$
where Tg is time with gravitation,
Tf is time somewhere without gravitation
G - gravitational constant
M - mass
r - radial coordinate of observer
and c - light speed.

Lets assume two explorers are working on two different planets with the same gravitation.
My understanding is that gravitation could be expressed as g=G$\frac{M}{r^{2}}$.
Mass M for spherical planet is equals to: M=$\frac{4}{3}$$\pi$r$^{3}$$\rho$, where $\rho$ is density.
If two gravitations are the same then:
g$_{1}$=g$_{2}$ and $\rho$$_{1}$r$_{1}$=$\rho$$_{2}$r$_{2}$ or $\rho$r=const
Getting back to the time dilation formula and replacing M with V*$\rho$:
T$_{g}$=T$_{f}$$\sqrt{1-\frac{2G}{c^{2}}\frac{4}{3}\pi{r^{2}\rho}}$
After replacing all constants with k (remember that $\rho$r is also a constant:
T$_{g}$=T$_{f}$$\sqrt{1-k*r}$

What a surprise: same gravitation, but different time dilation! (assuming planets radii are different)
Did I missed something?
Thanks.