Question

A Saturn year is 29.5 times the earth year how far is the Saturn from the sun if the earth is 1.5×10^8km 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

Answer 2

answer is Distance of the Earth from the Sun, re = 1.5 × 108km = 1.5 × 1011 m
Time period of the Earth = T­e
Time period of Saturn, Ts = 29. 5 Te
Distance of Saturn from the Sun = rs 
From Kepler’s third law of planetary motion, we have
T = (4π2r3 / GM)1/2
For Saturn and Sun, we can write
rs3 / re3  =  Ts2 / Te2
rs = re(Ts / Te)2/3
= 1.5 × 1011 (29.5 Te / Te)2/3
= 1.5 × 1011 (29.5)2/3
= 14.32 × 1011 m
Hence, the distance between Saturn and the Sun is 1.43 × 1012 m.