The mass of earth = $M_{e}$
The radius of earth = $R_{e}$
The mass of the object = $m$
| $g=G \frac{M_{e}}{R_{e}^{2}}$ |
| $G M_{e}=g R_{e}^{2}$ |
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 $(2)$
$mg=G \frac{M_{e} m}{R_{e}^{2}}$
The mass of earth = $M_{e}$
The radius of earth = $R_{e}$
The mass of the object = $m$
