Question

A Saturn year is 29.5 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

Distance of earth from sun is the Earth’s orbital radius;

r_e = 1.5 × 10⁸ km

= 1.5 × 10¹¹ m

Time period of Earth = T_e

Time period of Saturn = (29.5 × T_e)

From Kepler’s 3^rd Law of planetary motion

T² ∝ R³

= (29.5)² × (1.5 × 10¹¹)³

r_s = (29.5)^2/3 × 1.5 × 10¹¹

= 1.432 × 10¹² m.