A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.5 × 10⁸ km away from the sun?

1.43 × 10⁹ km

It is given that

T_s = 29.5 T_e ;  R_e = 1.5 × 10¹¹ m

Now, according to Kepler’s third law

$\frac{T_{S}^2}{T_{e}^2}=\frac{R_{S}^3}{R_{e}^3} \Rightarrow R_{s} = R_{e}\left(\frac{T_{S}}{T_{e}}\right)^{\frac{2}{3}}$

$=1.5 \times 10^{11}\left(\frac{29.5 T_{e}}{T_{e}}\right)^{\frac{2}{3}}$ = 1.43 × 10¹² m = 1.43 × 10⁹ km