Question

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 $R_{2}\left(R_{2} > R_{1}\right)$ 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. $\frac{1}{2}GmM\left(\frac{1}{R_{1}} - \frac{1}{R_{2}}\right)$

Answer 1

Answer: (D)

$KE=\left(- \frac{GMm}{2 R_{2}}\right)-\left(- \frac{GMm}{2 R_{1}}\right)$
$KE=\frac{GMm}{2}\left[\frac{1}{R_{1}} - \frac{1}{R_{2}}\right]$