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. $-\frac{1}{2}{\text{Mv}}^2$
• B. $\frac{1}{2}{\text{Mv}}^2$
• C. $-\frac{3}{2}{\text{Mv}}^2$
• D. ${\text{Mv}}^2$

Answer 1

The correct option is A $-\frac{1}{2}{\text{Mv}}^2$


$=\frac{1}{2}M{\text{v}}^2-\frac{G{M}_{e}M}{r}$

But orbital speed $\text{v}=\sqrt{\frac{G{M}_e}{r}}$
$⟹\frac{G{M}_e}{r}={\text{v}}^2$

So, total energy = $-\frac{1}{2}M{\text{v}}^2$