Question

A space-ship is put into a circular orbit close to Earth's surface. What additional velocity must be imparted to the ship so that it is able to escape the gravitational pull of Earth(approximately)? $(R=6400km,g=9.8\frac{m}{s^2})$

• A. $11.2\frac{km}{s}$
• B. $3.3\frac{km}{s}$
• C. $6.8\frac{km}{s}$
• D. $9.3\frac{km}{s}$

Answer 1

The correct option is B

$3.3\frac{km}{s}$

The orbital velocity in a circular orbit close to Earth is:

$v=\sqrt{gR}$.

The velocity required to escape is $v_e=\sqrt{2gR}$

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

Hence additional velocity required is: $v_e-v=0.414\times \sqrt{9.8\times 6400\times {10}^3}=3278.71\frac{m}{s}=3.278\frac{km}{s}$.