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. $-1/2M{v}^2$
• B. $1/2M{v}^2$
• C. $3/2M{v}^2$
• D. $M{v}^2$

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
$=\frac{1}{2}M{v}^2-M{v}^2=-\frac{1}{2}M{v}^2$