Question

A Saturn year is 30 times the earth year. How far is the Saturn from the sun if the earth is 1.50 × 10⁸ km away from the sun?

Answer 1

According to Kepler's third law, T² ∝ R³ 

where T_S and T_E are the period of revolution of Saturn and the earth and R_S and R_E are the distances of Saturn and the earth from the sun respectively.

Given R_E = 1.50 × 10¹¹m

T_S = 30 × T_E

∴ RS = 1.50 × 10¹¹ × \((\frac {30T_E}{T_E})^{2/3}\)

= 1.50 × 10¹¹ x 30^2/3

= 1.448 × 10¹² m

= 1.448 × 10⁹ km.