A satellite $S_1$ of mass $m$ is moving in an orbit of radius $r$. Another satellite $S_2$ of mass $2…
A satellite $S_1$ of mass $m$ is moving in an orbit of radius $r$. Another satellite $S_2$ of mass $2 \mathrm{~m}$ is moving in an orbit of radius $2 r$. The ratio of time period of satellite $S_2$ to that of $S_1$ is
2:1
1:8
1:4
$2 \sqrt{2}: 1$
Solution
According to Kepler's Law of periods:
$T^2 \propto R^3$
Therefore,
$\frac{T_2}{T_1}=\left(\frac{2 r}{r}\right)^{\frac{3}{2}}=\frac{2 \sqrt{2}}{1}$