Question

A satellite is orbiting around the earth. By what percentage should we increase its velocity, so as to enable it escape away from the earth ?

• A. 41.4%
• B. 50%
• C. 82.8%
• D. 100%

Answer 1

Answer: (A)

The velocity with which satellite is orbiting around the earth is the orbital velocity $(v_0)$ and that required to escape out of gravitational pull of earth is the escape velocity $\left(v_{es}\right)$. We know that
$v_{es}=\sqrt{2gR}\text{ and }{v}_o=\sqrt{gR}$
$\therefore$ Increase in velocity required
$=\frac{v_{es}-v_o}{v_o}=\frac{\sqrt{2gR}-\sqrt{gR}}{\sqrt{gR}}$
$=\sqrt{2}-1$
$=0.414$
Percent increase in velocity required
$=0.414\times 100$
$=41.4\%$