Question

A spaceship is launched into a circular orbit of radius R close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earths gravitational pull is : (g = acceleration due to gravity)

• A. 1.4147 Rg
• B. 1.414 $\sqrt{Rg}$
• C. 0.414 Rg
• D. 0.414 $\sqrt{Rg}$

Answer 1

Answer: (D)

Let a spaceship is launched in a circular orbit of orbital velocity $v_o.$ That spaceship should have escape velocity $v_{es}$ to overcome the earths gravitational pull. Now suppose v is the additional velocity to be imparted to the spaceship. Then according to above statement $v_0+v=v_{es}$ $\left[\begin{array}{rl}& \because v_0=\sqrt{Rg}\\ & v_{es}=\sqrt{2}Rg\end{array}\right]$ or $v=v_{es}-v_o$ $v=\sqrt{2}{v}_o-v_o=v_o(\sqrt{2}-1)=v_o(1.414-1)$ $=0.414\sqrt{Rg}$