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Q.
The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to
Given,
Semi-major axis of the orbit of saturn $=g r_{E}$
Where, $r_{E}=$ semi major axis of earth
According to Kepler's law,
$T^{2} \propto r^{3}$
Let the time period of revolution of saturn around the sun is $T_{s}$
$\therefore \frac{T_{S}^{2}}{T_{E}^{2}}=\left(\frac{9 r_{E}}{r_{E}}\right)^{3} $
$T_{S}^{2} =T_{E}^{2}(9)^{3} $
$T_{S} =\sqrt{T_{E}^{2}(9)^{3}} $
$=9^{3 / 2} \times 1 $ year
$\approx 27$ years