Question

A spaceship is released in a circular orbit near the Earth's surface. How much additional velocity will have to be given to the spaceship in order to escape out of this orbit?

• A. $3.28m/s$
• B. $3.28\times {10}^{3}m/s$
• C. $3.28\times {10}^{7}m/s$
• D. $3.28\times {10}^{-3}m/s$

Answer 1

Answer: (B)

$3.28\times {10}^{3}m/s$

Here, orbital velocity and escape velocity are
$v_0=\sqrt{gR}$
$v_e=\sqrt{2gR}$
Hence, required additional velocity will be,
$v=v_e-v_o$
$v=\sqrt{2gR}-\sqrt{gR}$
$v=(\sqrt{2}-1)\sqrt{gR}$
$v=(1.414-1)\sqrt{\left(10\right)(6400\times {10}^3)}$..........$($since, $g=10m{s}^{-2}$ and $R=6400\times {10}^{3}m)$
$v=\left(0.414\right)\left(8\right)\times {10}^3$
$v=3.3\times {10}^{3}m{s}^{-1}$