Question

Two small satellite move in circular orbits around the earth, at distance $r$ and $r+\Delta r$ from the centre of earth. Their period of rotations are $T$ and $T+\Delta T,$ respectively. If $\Delta r<<r,$ then $\frac{\Delta T}{T}$ is equal to

• A. $\frac{\Delta r}{r}$
• B. $\frac{3}{2}\frac{\Delta r}{r}$
• C. $-\frac{3}{2}\frac{\Delta r}{r}$
• D. $2\frac{\Delta r}{r}$

Answer 1

The correct option is B $\frac{3}{2}\frac{\Delta r}{r}$

As $T^2\propto r^3$ or $T^2=c{r}^3$.........1
$\therefore 2T△T=3c{r}^2△r$...................2
Dividing 2 by 1.
$\frac{2T△T}{T^2}=\frac{3c{r}^2△r}{c{r}^3}$
$\frac{△T}{T}=\frac{3}{2}\frac{△r}{r}$