Question

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

• A. $0.7$
• B. $1.0$
• C. $1.5$
• D. $3$

Answer 1

Answer: (D)

$3$

According to Kepler's Law: $T^2\propto R^3$

Differentiating $2T\Delta T=3R^2\Delta R$

Dividing the LHS by $T^2$ and RHS by $R^3$

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

$\Rightarrow \frac{\Delta T}{T}=\frac{3}{2}\frac{1.02R-R}{R}=\frac{3}{2}\times 0.02=0.03$

The percentage of increase is $0.03\times 100=3\%$