Question

The orbital speed for an Earth satellite near the surface of the Earth is 7 km/sec. If the radius of the orbit is 4 times the radius of the Earth, the orbital speed would be

• A. $3.5$ km/sec
• B. $7$ km/sec
• C. $7\sqrt{2}$ km/sec
• D. $14$ km/sec

Answer 1

The correct option is A $3.5$ km/sec

Orbital speed is $v=\sqrt{\frac{G{M}_e}{r}}$ for a satellite at a distance $r$ from the Earth's centre.
Firstly, the satellite is said to be near the earth's surface, we take the radius as Earth's radius, '$R$'.
$\Rightarrow v=\sqrt{\frac{G{M}_e}{R}}=7km/s$
Now, the radius of the orbit is $4$ times the radius of the earth$\left(R\right)$, the orbital speed $\left(v^{{}^{\prime }}\right)$ is given by:
$v^{{}^{\prime }}=\sqrt{\frac{G{M}_e}{4R}}=\frac{1}{\sqrt{4}}\sqrt{\frac{G{M}_e}{R}}=0.5\times 7=3.5$ $km/s$