Question

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

• A. 81 years
• B. 27 years
• C. 729 years
• D. $\sqrt[3]{81}$ years

Answer 1

Answer: (B)

27 years

Answer 2

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