A satellite with kinetic energy E is revolving round the earth in a circular orbit. The minimum additional kinetic energy required for it to escape to outer space is

E

$\frac{GMm}{r^2}=\frac{mv_0^2}{r}$

$v_0=\sqrt{\frac{GM}{r}} ; v_{e}=\sqrt{\frac{2 GM}{r}}$

orbital KE = $\frac{1}{2} mv_0^2$

$=\frac{1}{2} m \frac{GM}{r}$

KE of escape = $\frac{1}{2} mv_0^2$

$=\frac{1}{2} m\left(\frac{2 GM}{r}\right)=\frac{GMm}{r}=2 E$

Additional KE required = 2E – E = E