if the distance between the earth nad the sun is reduced to half of its present value, what would be the number of days inone year?

From Kepler's 3rd laws of planetary motion we know that
$T^2= k{R}^3$
Where
K is a constant
T is orbital period = 365 days for earth
R is semi-major axis of orbit
$$\begin{gathered} \Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3 \\ Putting \\ {T}_1 = 365 days \\ {R}_1=R \\ {R}_2 =\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ We get \\ {\left(\frac{365}{T_2}\right)}^2={\left(\frac{R}{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^3=8 \\ \Rightarrow T_2^2=\frac{{365}^2}{8}\Rightarrow T_2=129.04 Days \end{gathered}$$
Therefore, Number of days in one year will be about 129 days