Question

If $v_e$ is the escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the earths surface. Then these are related by

• A. $v_o=\sqrt{2}{v}_e$
• B. $v_o=v_e$
• C. $v_e=\frac{v_o}{2}$
• D. $v_e=\sqrt{2}{v}_o$

Answer 1

Answer: (D)

Escape velocity,
$v_e=\sqrt{\frac{2G{M}_E}{R_E}}\dots \left(i\right)$
where $M_E$ and $R_E$ be the mass and radius of the earth respectively.
The orbital velocity of a satellite close to the earth's surface is
$v_o=\sqrt{\frac{G{M}_E}{R_E}}\dots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, we get $v_e=\sqrt{2}{v}_o$