Question

A space ship is launched into a circular orbit close to the Earth's surface. What additional velocity has now to be imparted to the space ship in the orbit to overcome the gravitational pull ?
(Radius of Earth = 6400 km:g= 9.8 $m{s}^{-2}$

Answer 1

When a satellite is orbiting earth, its velocity is its orbital velocity, given by

Orbital velocity, $V_e=\sqrt{\frac{2GM}{r}}$

Additional velocity required is

$v=V_e-V_o=\sqrt{2gR}-\sqrt{gR}=\sqrt{gR}(\sqrt{2}-1)$

Given, that $R=6400km=6.4\times {10}^{6}m$

$g=9.8m{s}^{-2}$

$v=\sqrt{gR}(\sqrt{2}-1)=\sqrt{9.8\times 6.4\times {10}^6}(\sqrt{2}-1)=3.28\times {10}^{3}m/s$

Hence, additional velocity required is $3.28\times {10}^{3}m/s$