Question

A saturn year is 29.5 times the earth's year. How far is the saturn from the sun if the earth is 1.50*10^8 km away from the sun?

Answer 1

“A Saturn year is 29.5 times the earth year”
It means time period of Saturn is 29.5 times that of earth
T’ = 29.5T

According to Kepler’s law
T^2 ∝ r^3

(T / T’)^2 = (r / r’)^3
(T / (29.5T))^2 = (1.5 × 10^8 / r)^3
1 / 870.25 = (1.5 × 10^8 / r)^3
r = 1.5 × 10^8 × (870.25)^(1/3)
r = 1.43 × 10^9 km

Distance between Saturn and sun is 1.43 × 10^9 km