A Saturn year is 29.5 times the earth year. How far is the Saturn from the Sun if the Earth is $1.5 \times {10}^8$ away from the Sun?

Here, ${\mathrm{T}}_{\mathrm{S}} = 29.5 {\mathrm{T}}_{\mathrm{E}}, {\mathrm{R}}_{\mathrm{E}} = 1.5 \times {10}^8 \mathrm{km}, {\mathrm{R}}_{\mathrm{s}} = ?$

According to Kepler's third law, ${\mathrm{T}}^2\infty {\mathrm{R}}^3$

$\frac{{{\mathrm{T}}_{\mathrm{S}}}^2}{{{\mathrm{T}}_{\mathrm{E}}}^2} = \frac{{{\mathrm{R}}_{\mathrm{S}}}^3}{{{\mathrm{R}}_{\mathrm{E}}}^3}$

${\mathrm{R}}_{\mathrm{S}} = {\mathrm{R}}_{\mathrm{E}}{\left(\frac{{\mathrm{T}}_{\mathrm{S}}}{{\mathrm{T}}_{\mathrm{E}}}\right)}^{\frac{2}{3}}$

${\mathrm{R}}_{\mathrm{S}} = 1.5 \times {10}^8{\left(\frac{29.5{\mathrm{T}}_{\mathrm{E}}}{{\mathrm{T}}_{\mathrm{E}}}\right)}^{\frac{2}{3}} = 1.4 \times {10}^9 \mathrm{km}$