Question

A satellite is orbiting around the earth. By what percent age should increase its velocity so as to enable it escape away from earth:

• A. $41.4\%$
• B. $50\%$
• C. $82.8\%$
• D. $100\%$

Answer 1

The correct option is A $41.4\%$

We know that orbital velocity $v_0=\sqrt{gr}$

Escape velocity $v_e=\sqrt{2gr}$

Thus, the increase in velocity would be

$dv=v_e-v_0=\sqrt{2gr}-\sqrt{gr}$

$\Rightarrow dv=(\sqrt{2}-1)\sqrt{gr}$

$\Rightarrow dv=0.414\sqrt{gr}$

Now, the percentage increase would be

$\%dv=\frac{v_e-v_0}{v_0}\times 100$

$\%dv=0.414\frac{\sqrt{gr}}{\sqrt{gr}}\times 100=41.4\%$