Relation between gravitational acceleration and gravitational force

Relation between $g$ and $G$ →

Let us consider:
The mass of earth = $M_{e}$
The radius of earth = $R_{e}$
The mass of the object = $m$

If the object is placed on the surface of the earth then the gravitational force on the object is →

$F=G \frac{M_{e} m}{R_{e}^{2}} \qquad(1)$

The force on the object due to gravitational acceleration is →

$F=mg \qquad(2)$

From equation $(1)$ and equation $(2)$

$mg=G \frac{M_{e} m}{R_{e}^{2}}$

$g=G \frac{M_{e}}{R_{e}^{2}}$

$G M_{e}=g R_{e}^{2}$