**If the distance between the earth and the sun were half its present value, the number of days in a year would have been**

(a) 64.5

(b) 129

(c) 182.5

(d) 730

**The correct answer is 129 days option b **

**Explaination :**

BY keplers third law \(T^2 \propto R^3\)

\(\therefore { ({ T_2\over T_1})^2=({ R_2\over R_1})^3}\)

T_{1 }= 365 days , R_{1} =R , R_{2} = R/2

\({ ({ T_2\over 365})^2=({{ R_2/2}\over R_1})^3}\)

\(T_2^2={(365)^2\over8}\)

\(T_2^2=16653 \) ----{note: \(129^2=16641 \) but 16653 is nearby 129 hence due to option answer is 129}

\(T_2=129 \space days\)