Question

How long will a satellite, placed in a circular orbit of radius that is $\left(\frac{1}{4}\right)^{\text {th }}$ the radius of a geostationary satellite, take to complete one revolution around the earth?

• A. 12 hours
• B. 6 hours
• C. 3 hours
• D. 4 days

Answer 1

Answer: (C)

From Kepler's third law
$T^{2} \propto R^{3}$
or $T \propto R^{3 / 2}$
$\therefore \frac{T_{1}}{T_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{3 / 2}$
$\frac{T_{1}}{T_{2}}=\left(\frac{4 R_{1}}{R_{1}}\right)^{3 / 2}$
$T_{2}=\frac{T_{1}}{8}=\frac{29}{8}=3 h$