Question

A space craft is launched in a circular orbit very close to the earth. What additional velocity should be given to the space craft so that it might escape the earth's gravitational pull:

• A. $20.2Km{s}^{-1}$
• B. $3.25Km{s}^{-1}$
• C. $8Km{s}^{-1}$
• D. $11.2Km{s}^{-1}$

Answer 1

The correct option is B $3.25Km{s}^{-1}$

Since the spacecraft is moving very close to the surface of earth, we assume its orbital radius to be R(the radius of the earth); implying its current orbital velocity is: $V_o=\sqrt{gR}$.
But by definition of escape velocity, we know that to escape the surface of earth, the speed required is $V_e=\sqrt{2gR}$.
Hence, the additional speed to be given to the spacecraft is $V_e-V_o$.
Using $g=9.81$ and $R=6400km$, we get the required additional speed as $3.25km{s}^{-1}$.