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Q.
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 ?
Bihar CECEBihar CECE 2003Gravitation
Solution:
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 $\left(v_{e s}\right)$. We know that
$v_{e s}=\sqrt{2 g R} \text { and } v_{o}=\sqrt{g R}$
$\therefore $ Increase in velocity required
$=\frac{v_{e s}-v_{o}}{v_{o}}=\frac{\sqrt{2 g R}-\sqrt{g R}}{\sqrt{g R}}$
$=\sqrt{2}-1$
$=0.414$
Percent increase in velocity required
$=0.414 \times 100$
$=41.4 \%$