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?
Answer & explanation
Correct answer: option 1
It is given that
Ts = 29.5 Te ; Re = 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