Question

Obtain an expression for acceleration due to gravity at a height $h$ above the earth's surface.

Answer 1

let we consider,

radius of earth $R$ and mass is $M$

and we know that acceleration due to gravity at surface

$g=\frac{GM}{R^2}$ ---- $\left(i\right)$

$G$ is universal gravitational constant.

consider, a mass $m$ is at above the earth at height $h$ and $g^{\prime }$ is acceleration due to gravity at height $h$.

Therefore, $g\prime =\frac{GM}{(R+h{)}^2}$ ----- $\left(ii\right)$

divide, $\left(ii\right)$ by $\left(i\right)$

$\frac{g^{\prime }}{g}=\frac{R^2}{(R+h{)}^2}$

$g^{\prime }=\frac{g{R}^2}{(R+h{)}^2}$

For $h<<<R$,

$g^{\prime }=g(1-\frac{2h}{R})$