Question

An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by $E$. The potential energy of the satellite is:

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

Answer 1

The correct option is B $2E$

Let an artificial satellite of mass $m$ revolves around the earth in circular orbit of radius $r$.

The centrifugal force acting on the satellite is balanced by the gravitation due to earth.

$\therefore F_c=F_G$ $⟹\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

$m{v}^2=\frac{GMm}{r}$ ............(1)

$\therefore$ Kinetic energy of the satellite $K.E=\frac{1}{2}m{v}^2=\frac{GMm}{2r}$

Potential energy of the satellite $P.E=-\frac{GMm}{r}$ ...............(2)

Total energy of the satellite $E=K.E+P.E=\frac{GMm}{2r}-\frac{GMm}{r}$

$⟹$ $E=\frac{-GMm}{2r}$ ..........(3)

From (2) and (3), we get $P.E=2E$