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  4. The distance of Neptune and Saturn from the Sun are nearly 1013 m and 1012 m respectively. Ratio of their time period will be

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Q. The distance of Neptune and Saturn from the Sun are nearly $10^{13} \, m$ and $10^{12} \, m$ respectively. Ratio of their time period will be

NTA AbhyasNTA Abhyas 2020Gravitation

Solution:

Using Kepler's Third law of gravitation, we get
$\frac{T_{n}^{2}}{T_{s}^{2}}=\frac{R_{n}^{3}}{R_{s}^{3}}$
$\frac{T_{n}^{ \, }}{T_{s}^{ \, }}=\left[\frac{1 0_{ \, }^{13}}{1 0_{ \, }^{12}}\right]^{3 / 2}$
$=\left(\sqrt{10}\right)^{3}=10\sqrt{10}$