Question:
A body is moving in a low circular orbit about a planet of mass $M$ and radius $R$. The radius of the orbit can be taken to be $R$ itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :
Correct Option: 1
Solution:
(1) Orbital speed of the body when it revolves very close to the surface of planet
$V_{0}=\sqrt{\frac{G M}{R}}$ ....(1)
Here, $G=$ gravitational constant
Escape speed from the surface of planet
$V_{e}=\sqrt{\frac{2 G M}{R}}$ ....(2)
Dividing (i) by (ii), we have
$\frac{V_{0}}{V_{e}}=\frac{\sqrt{\frac{G M}{R}}}{\sqrt{\frac{2 G M}{R}}}=\frac{1}{\sqrt{2}}$