Question

A spaceship is launched into a circular orbit close to the Earth's surface. The additional velocity has to be imparted to the spaceship to overcome the gravitational pull?

Answer 1

The orbital velocity near the surface of earth is

$v_0=\sqrt{\frac{GM}{R}}$

Now, to overcome gravitational pull, conserving energy, escape velocity is

$v_e=\sqrt{\frac{2GM}{R}}$

Hence, additional velocity required is

$v=\sqrt{\frac{2GM}{R}}-\sqrt{\frac{GM}{R}}=(\sqrt{2}-1)\sqrt{\frac{GM}{R}}$