Question

A satellite is moving around the with speed v in a circular orbit of radius r. If the orbit radius is decreased by $1\%$, its speed will

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Orbital velocity $v=\sqrt{\frac{Gm}{r}}\therefore v\propto \frac{1}{\sqrt{r}}$ [If r decreases then v increases]

Percentage change in $v=\frac{1}{2}$ (Percentage change in r) $=\frac{1}{2}\left(1\%\right)=0.5\%$

$\therefore$ orbital velocity increases by $0.5\%$.