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)

0.414 $\sqrt{Rg}$

Answer 2

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 ${{v}_{0}}+v={{v}_{es}}$ $\left[ \begin{aligned} & \because \,{{v}_{0}}=\sqrt{Rg} \\\ & {{v}_{es}}=\sqrt{2}Rg \\\ \end{aligned} \right]$ or $v={{v}_{es}}-{{v}_{o}}$ $v=\sqrt{2}{{v}_{o}}-{{v}_{o}}={{v}_{o}}(\sqrt{2}-1)={{v}_{o}}(1.414-1)$ $=0.414\sqrt{Rg}$