The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular speed ω. The acceleration due to gravity on planet’s surface will be:

$\frac{r^3 \omega^2}{R^2}$

Let M be the mass of the planet and m the mass of satellite. Then

$mr \omega^2=\frac{GMm}{r^2} ⇒ GM = r^3 \omega^2$

Now g = $\frac{GM}{R^2}=\frac{r^3 \omega^2}{R^2}$