A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will :
Answer & explanation
Correct answer: option 2
Orbital velocity $V = \sqrt {\frac{Gm}{r}}$
$V' = \sqrt {\frac{Gm}{r - 0.01 r}}= \sqrt {\frac{Gm}{r}}(1 + \frac{0.01}{2}) = V + 0.005 V $
$\Rightarrow \Delta V = 0.005 V$
$\Rightarrow \text{Speed will increase by 0.5%}$