Question

At what height above the earth's surface the value of g will be half of that on the earth's surface ?

Answer 1

We know that the value of g at earth's surface is

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

While the value of g at a height h above the earth's surface is given by

$g^{/}$ = $\frac{GM}{{R+h}^2}$ ..........(2)

Dividing equation (2) by equation (1), we get

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

Here, $g^{/}$ = $\frac{g}{2}$

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

or $\frac{R+h}{R}$ = $\sqrt{2}$

or R+h = $\sqrt{2}$R

h = ( $\sqrt{2}$-1)R

or h = (1.41 - 1)*6400 = 0.41*6400

= 2624 km