# A geo stationary satellite orbits around the earth in a circular orbit of radius $36000km$. Then the time period of a spy satellite orbiting a few Kilometers above the earth's surface $(R_{earth}=6400 Km)$ will be approximately

$(a)\;\frac{1}{2}\;hour \quad (b)\;2\;hour \quad (c)\;1\;hour \quad (d)\;4\;hour$

We know time period of geostationary satellite is $24 hrs$
Also $T^2 \;\alpha\; R^3$
$\large\frac{T_2}{T_1}=\bigg (\large\frac{R_2}{R_1}\bigg)^{\large\frac{3}{2}}$
$\large\frac{T_2}{24}=\bigg (\large\frac{6400}{36000}\bigg)^{\large\frac{3}{2}}$
$T_2=24 \times \bigg (\large\frac{6400}{36000}\bigg)^{\large\frac{3}{2}}$
$\quad=2\;hours$
Hence b is the correct answer.

edited Feb 17, 2014 by meena.p