Question

A spaceship is launched into a circular orbit close to earth's surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull? (Radius of earth = 6400 km and g = 9.8 $m/s^2$)

• A. $2.83km/s$
• B. $3.28km/sec$
• C. $6.68km/s$
• D. $8.32km/sec$

Answer 1

Answer: (B)

$3.28km/sec$

Orbital velocity of space-ship,
$v_0=\sqrt{\frac{GM}{r}}(sincer>>R)$

Since, $g=\frac{GM}{R^2}$
$\therefore GM=g{R}^2$

Now, $v_0=\sqrt{Rg}=\sqrt{6.4\times {10}^6\times 9.8}$
$=7.9195km/s$

Again, $v_e=\sqrt{2Rg}=\sqrt{2\times 7.9195}$
$=11.20km/s$

$\therefore$ Additional velocity required $=11.20-7.9195=3.28km/sec$