A satellite of mass m is orbiting the earth at a height H from its surface. If M be the mass of earth and R, its radius, then the energy required to pull the satellite from earth's gravitational field will be

Distance of the satellite from the centre of earth
$\mathrm{r}=(\mathrm{R}+\mathrm{h})$
$\therefore \frac{{\mathrm{mv}}^2}{(\mathrm{R}+\mathrm{h})}=\frac{\mathrm{GmM}}{(\mathrm{R}+\mathrm{h}{)}^2}\text{ or }\frac{1}{2}{\mathrm{mv}}^2=\frac{\mathrm{GMm}}{2(\mathrm{R}+\mathrm{h})}$
or $\mathrm{K}.\mathrm{E}.=\frac{\mathrm{GMm}}{2(\mathrm{R}+\mathrm{h})}$
$\text{ P.E. }=-\frac{\mathrm{GmM}}{\mathrm{r}}=-\frac{\mathrm{GmM}}{(\mathrm{R}+\mathrm{h})}$
Total energy = K.E. + P.E.
$=\frac{\mathrm{GmM}}{2(\mathrm{R}+\mathrm{h})}-\frac{\mathrm{GmM}}{(\mathrm{R}+\mathrm{h})}=-\frac{\mathrm{GmM}}{2(\mathrm{R}+\mathrm{h})}$
So, energy needed = $[\mathrm{GmM}/2(\mathrm{R}+\mathrm{h}\left)\right]$