question_answer

What would be the duration of the year if the distance between the earth and the sun gets doubled? Take the present duration of one year = 365 days.

Answer:

The duration of year is equal to the time period of a planet.

Case-I	Case-II
\[{{R}_{1}}=R\]	\[{{R}_{2}}=2R\]
\[{{T}_{1}}=T=\] (365 days)	\[{{T}_{2}}=?\]

We know \[\frac{{{T}^{2}}}{{{R}^{3}}}=const\] \[\Rightarrow \frac{T_{2}^{2}}{T_{1}^{3}}=\frac{R_{2}^{3}}{R_{1}^{3}}\] \[\Rightarrow \frac{{{T}_{2}}}{{{T}_{1}}}={{\left[ \frac{{{R}_{2}}}{{{R}_{1}}} \right]}^{\frac{3}{2}}}={{\left[ \frac{2R}{R} \right]}^{\frac{3}{2}}}=\sqrt{8}\] \[\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{2\sqrt{2}}{1}\Rightarrow {{T}_{2}}=2\sqrt{2}T\] \[{{T}_{2}}=2.83\times 365\,\,days\]