Question

Energy of a satellite in circular orbit is $-E_0$. The energy required to move the satellite to a circular orbit of $3$ times the radius of the initial orbit is

• A. $\frac{2}{3}{E}_0$
• B. $2E_0$
• C. $\frac{E_0}{3}$
• D. $\frac{3}{2}{E}_0$

Answer 1

The correct option is A $\frac{2}{3}{E}_0$

For a satellite of mass $m$ revolving around a planet of mass $M$ in a circular orbit of radius $r$. So the total mechanical energy of a satellite is given by

$E=\frac{-GMm}{2r}$

Total mechanical energy at radius $r$ will be

$E_1=\frac{-GMm}{2r}=E_0$

Total mechanical energy at radius $3r$ is

$E_2=\frac{-GMm}{2\left(3r\right)}=\frac{E_0}{3}$

Energy required is given by

$E_2-E_1=|\frac{E_0}{3}-E_0|=\frac{2E_0}{3}$

Therefore, option $\left(a\right)$ is correct.

Key Concept : The work done energy required to shift a satellite from one configuration to the other is equal to the difference between the total mechanical energy of the two configurations.