Answer:
Earth Saturn \[{{T}_{1}}=T\] \[{{T}_{2}}=29.5\,T\] \[{{R}_{1}}=1.5\times {{10}^{8}}km\] \[{{R}_{2}}=?\]
We know \[\frac{{{T}^{2}}}{{{R}^{3}}}=const\] \[\Rightarrow {{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{3}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}\] \[\frac{{{R}_{2}}}{{{R}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{\frac{2}{3}}}\] On substitution, we get \[{{R}_{2}}=1.5\times {{10}^{8}}\times {{\left( \frac{29.5}{1} \right)}^{\frac{2}{3}}}\] \[=14.32\times {{10}^{11}}km\]
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