Question

A space ship is launched into a circular orbit close to the surface of the earth. The additional velocity now imparted to the spaceship in the orbit to overcome the gravitational pull is

• A. $11.2km{s}^{-1}$
• B. $8km{s}^{-1}$
• C. $3.2km{s}^{-1}$
• D. $1.414\times 8km{s}^{-1}$

Answer 1

Answer: (C)

$3.2km{s}^{-1}$

Given: $R=6400km$ $g=9.8m/s^2$

Orbital velocity of space ship revolving in an orbit of radius r, $v_o=\sqrt{\frac{g{R}^2}{r}}$

For $r=R$ $⟹v_o=\sqrt{gR}=\sqrt{9.8\times 6400\times 1000}\approx 7.919km/s$

Escape velocity, $v_e=\sqrt{2gR}=\sqrt{2\left(9.8\right)\times 6400\times 1000}=11.2km/s$

Thus additional velocity imparted $=11.2-7.919\approx 3.29km/s$