Why is the value of the constant g different on Earth and on the Moon? Explain in detail.

Acceleration due to gravity is defined as the gravitational force acting on the massive body when a freely falling object experiences acceleration and is represented by measured using an SI unit$m/s^2$ The value of acceleration due to gravity depends on the mass and radius of a massive body.

The acceleration due to gravity formula is given by,

$g=\frac{GM}{R^2}....................................\left(1\right)$

Where G is the universal gravitational constant $G=6.674\times {10}^{-11}{m}^3/kg.s^2$.

M = mass of the massive body.

R= radius of the massive body.

For Moon,

$$\begin{gathered} M=7.35\times {10}^{22}kg \\ R=1.74\times {10}^{6}m \end{gathered}$$

Substituting the above value in the equation(1), we get,

$$\begin{gathered} g=\frac{\left(6.67\times {10}^{-11}{m}^3/kg.s^2\right)\left(7.35\times {10}^{22}kg\right)}{\left(1.74\times {10}^{6}m\right)} \\ g=1.625m/s^2 \end{gathered}$$

For Earth,

$$\begin{gathered} M=6\times {10}^{24}kg \\ R=6.4\times {10}^{6}m \end{gathered}$$

Substituting the values in the equation (1), we get

$$\begin{gathered} g=\frac{\left(6.67\times {10}^{11}m/kg.s^2\right)\left(6\times {10}^{24}kg\right)}{\left(6.4\times {10}^{6}m\right)} \\ g=9.8m/s^2 \end{gathered}$$

Thus, the acceleration due to gravity varies with different bodies to bodies because it depends on the mass and radius of the body. For example, g on the Moon is $1.625m/s^2$ , and g on the Earth is$9.8m/s^2$