Question

A satellite is launched into a circular orbit of radius $R$ around earth, while a second satellite is launched into a circular orbit of radius $1.02R$. The percentage difference in the time periods of the two satellites is :

• A. $3.0$
• B. $2.0$
• C. $0.7$
• D. $1.5$

Answer 1

The correct option is A $3.0$

Given:
$\Delta R=1.02R-R=0.02R$

Using Kepler's third law,

$T^2\propto R^3$

$T=k{R}^{3/2}(k=\text{constant})$

$\frac{\Delta T}{T}=\frac{3}{2}\frac{\Delta R}{R}$

$\Rightarrow \frac{\Delta T}{T}=\frac{3}{2}\times 0.02=0.03$

$\text{\% Change in time period}=\frac{\Delta T}{T}\times 100=3\%$

Hence, option $\left(\text{D}\right)$ is correct.