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,
$v_{e} = \sqrt{\frac{2GM_{E}}{R_{E}}}\quad\ldots\left(i\right)$
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
$v_{o} = \sqrt{\frac{GM_{E}}{R_{E}}}\quad \ldots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, we get $v_{e} = \sqrt{2}v_{o}$