A Saturn year is $29.5$ times the Earth year. If the Earth is $1.5 imes 10^8 ext{ km}$ away from

Question

A Saturn year is $29.5$ times the Earth year. If the Earth is $1.5 	imes 10^8	ext{ km}$ away from the Sun, approximately how far is Saturn from the Sun?

Professor PC Thomas Classes · Answer

Using Kepler's third law, $T^2 \propto R^3$. The ratio of the distances is $\frac{R_S}{R_E} = (\frac{T_S}{T_E})^{2/3}$. Therefore, $R_S = 1.5 	imes 10^8 	imes (29.5)^{2/3} \approx 1.5 	imes 10^8 	imes 9.55 \approx 1.43 	imes 10^9	ext{ km}$.