Question

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

Answer 1

The correct answer is  129 days option b 

Explaination :

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

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

T₁ = 365 days , R₁ =R , R₂ = 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}

\(T_2=129 \space days\)