Question

ESCAPE SPEED
If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the earth's 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

The correct option is D $v_e=\sqrt{2}{v}_o$

Escape velocity, $v_e=\sqrt{\frac{2G{M}_E}{R_E}}$ ...(i)
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 $v_o=\sqrt{\frac{G{M}_E}{R}}$ ....(ii)
From (i) and (ii), we get $v_e=\sqrt{2}{v}_o$