Question

A satellite is geostationary in a particular orbit. It is allowed to go to another orbit having an orbital radius $2$ times that of the earlier orbit from the centre of the earth. The time period in the second orbit is

• A. $48$ hrs
• B. $24$ hrs
• C. $48\sqrt{2}$ hrs
• D. $24\sqrt{2}$ hrs

Answer 1

Answer: (C)

$48\sqrt{2}$ hrs

Time period is related to orbit radius as
$T^2\propto R^3$
$\Rightarrow \frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}$
Given $R_1=R$ and $R_2=2R$
$\frac{T_1^2}{T_2^2}={\left(\frac{R}{2R}\right)}^3=\frac{1}{8}$
$\Rightarrow T_2=T_1\sqrt{8}=24\times 2\sqrt{2}=48\sqrt{2}$ hours