question_answer

If the earth be one half its present distance from the sun, how many days will the present one year on the surface of earth will change?

Answer:

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

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

The formula above terms is. \[{{T}^{2}}\propto {{R}^{3}}\] \[\Rightarrow \frac{{{T}_{2}}}{{{T}_{1}}}=\left[ \frac{{{R}_{2}}}{{{R}_{1}}} \right]={{\left[ \frac{\frac{R}{2}}{R} \right]}^{\frac{3}{2}}}={{\left[ \frac{1}{2} \right]}^{\frac{3}{2}}}\] \[\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{1}{2\sqrt{a}}\Rightarrow {{T}_{2}}=\frac{{{T}_{1}}}{2\sqrt{2}}=\frac{T}{2\sqrt{2}}\] \[{{T}_{2}}=\frac{365}{2\sqrt{2}}=125\] \[{{T}_{2}}=129\,\,days\] \[\therefore \]Decrease in no. of days\[=365-129\] \[=236\,days\]