Q. The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $R_{1}$ to another of radius $R_{2}(R_{2} > R_{1})$ is
A) $GmM\left( \frac{1}{R_{1}^{2}} - \frac{1}{R_{2}^{2}} \right)$
B) $GmM\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
C) $2GmM\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
D) $\frac{1}{2}GmM\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
Explanation
(d) $- \frac{GMm}{2R_{1}} + KE = - \frac{GMm}{2R_{2}}$
$KE = \frac{GMm}{2}\left\lbrack \frac{1}{R_{1}} - \frac{1}{R_{2}} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.