A satellite launched into a circular orbit of radius ‘R’ around the earth while a second satellite is launched into an orbit of radius $1.06R$ . The percentage change in the time periods of the two satellite is

$\frac{T_2}{T_1}={\left(\frac{R_2}{R_1}\right)}^{3/2}={\left(\frac{1+0.06}{1}\right)}^{3/2}$      $\frac{\Delta T}{T}\times 100=\frac{3}{2}\frac{\Delta R}{R}\times 100$ 

$\frac{T_2}{T_1}-1=\left(1+0.09\right)-1$                     $=\frac{3}{2}\times \frac{1.06R-R}{R}\times 100$

$100\times \frac{\Delta T}{T}=9$                                      $=\frac{3}{2}\times 0.06\times 100$

                                                                     $=9\%$