Question

An artificial satellite moving in a circular orbit around the earth has a total $(K.E.+P.E.)$ is $E_0$. Its potential energy is

• A. $-E_0$
• B. $1.5E_0$
• C. $2E_0$
• D. $E_0$

Answer 1

Answer: (C)

$2E_0$

Total energy of satellite in circular orbit is

$E_0=\frac{1}{2}m{v}^2-\frac{GMm}{R}$

But, from Newton's second law,

$\frac{m{v}^2}{R}=\frac{GMm}{R^2}$

$v=\sqrt{\frac{GM}{R}}$

Thus,

$E_0=\frac{1}{2}m\left(\frac{GM}{R}\right)-\frac{GMm}{R}=-\frac{GMm}{2R}$

Thus,

$PE=-\frac{GMm}{R}=2E_0$