Question

Find $\frac{v_e}{v_o}$ where
$v_e:$ Escape velocity of satellite at the surface of earth.
$v_o:$ Orbital velocity of satellite orbiting at the surface of earth.

• A. $2$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\sqrt{3}$

Answer 1

The correct option is B

$\sqrt{2}$

Escape velocity at surface of earth is given by:
$v_e=\sqrt{\frac{2GM}{R}}$

Orbital velocity of satellite at height h above the surface of earth is given by:
$v_o=\sqrt{\frac{GM}{R+h}}$
At surface of earth, $h=0$
$\therefore v_o=\sqrt{\frac{GM}{R}}$

From above,
$\frac{v_e}{v_o}=\frac{\sqrt{\frac{2GM}{R}}}{\sqrt{\frac{GM}{R}}}=\sqrt{2}$