question_answer

The mean distance of sun from a planet is four times the distance of the sun from the earth. In how many years will planet complete one revolution around the sun?

Answer:

From Sun to Earth: \[{{R}_{1}}=R{{T}_{1}}=1yr\] From Sun to Planet: \[{{R}_{2}}=4R{{T}_{2}}=?\] We know,\[{{T}^{2}}\propto {{R}^{3}}\Rightarrow \frac{T_{2}^{2}}{T_{1}^{2}}\,\,or\,\,\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{R_{2}^{3/2}}{R_{1}^{3/2}}{{T}_{2}}\] \[={{T}_{1}}{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{3/2}}=1\times {{\left( \frac{4R}{R} \right)}^{3/2}}=8\,\,years.\]