Question

The orbital velocity of satellite very near to the surface of earth is $v$. What will be its orbital velocity at an altitude $7$ times the radius of the earth?

• A. $v=\frac{\sqrt{GM}}{r}$
• B. $gm/2$
• C. $gm/2\sqrt{2}$
• D. $gm/4$

Answer 1

The correct option is A $v=\frac{\sqrt{GM}}{r}$

We know that for a satellite moving in orbit Gravitational force $=$ Centripetal force

So, $\frac{GM}{r^2}=\frac{{mv}^2}{r}$

Hence $r$ is the radius of the earth as satellite is very close to it.

So, by rearranging

$v^2=\frac{GM}{r}$

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

$g=\frac{GM}{r^2}$

$v=\sqrt{gr}$