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 $R_2$ $(R_2 > R_1)$ is

• A. $GmM\left(\frac{1}{R^{2}_{1}}-\frac{1}{R^{2}_{2}}\right)$
• 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)

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

Answer 2

As$-\frac{GMm}{2R_{1}}+KE=\frac{-GMm}{2R_{2}}$
$\quad\quad\quad\therefore\quad KE=\frac{1}{2}GMm\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right).$