Question

A satellite moves around the earth in a circular orbit of radius $r$ with speed $v$. If the mass of the satellite is $M$, its total energy is

• A. $ -1/2\,Mv^{2}$
• B. $ 1/2\,Mv^{2}$
• C. $ 3/2\,Mv^{2}$
• D. $ Mv^{2}$

Answer 1

Answer: (A)

Kinetic energy of the satellite $=\frac{1}{2} M v^{2}$
Potential energy of the satellite
$(U)=-\frac{G M_{e} M}{R_{e}}$ But, $G M_{e}=g R_{e}^{2}$
$\therefore U=-\frac{g R_{e}^{2} M}{R_{e}}=-g R_{e} M$
Orbital velocity of a satellite
$v=\sqrt{g R_{e}} \therefore U=-M v^{2}$
$\therefore $ Total energy of the satellite
$=\frac{1}{2} M v^{2}-M v^{2}=-\frac{1}{2} M v^{2}$