Question

The mean distance from Saturn to the sun is 9 times greater than the mean distance from Earth to the sun. Calculate the time period of Saturn in terms of Earth's time period.

• A. 18 Earth years
• B. 27 Earth years
• C. 81 Earth years
• D. 243 Earth years
• E. 729 Earth years

Answer 1

Answer: (B)

27 Earth years

Using Kepler's third law, $T^2\propto R^3$ where T be the time period and R be the orbital distance.

So, $\frac{T_2^2}{T_1^2}=\frac{R_2^3}{R_1^3}=\frac{(9R_1{)}^3}{R_1^3}$

or $T_2=(3^2{)}^{3/2}{T}_1=27T_1$