Two planets move around the sun. The periodic times and the mean radii of the orbits are $T_{1}, T_{2} a n d r_{1}, r_{2}$ respectively. The ratio $\frac{T_{1}}{T_{2}}$ is equal to

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Solution

The correct option is D

From Kepler's third law, the relation between time period and radius of the orbit is given as
$T^{2} \propto r^{3} \Rightarrow \frac{T_{1}}{T_{2}} = (\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$

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$T^{2} \propto r^{3} \Rightarrow \frac{T_{1}}{T_{2}} = (\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$