Question

The earth revolves around the sun in one year. If distance between them becomes double, the new time period of revolution will be

• A. $4 \sqrt 2$ years
• B. $2 \sqrt 2$ years
• C. 4 years
• D. 8 years

Answer 1

Answer: (B)

$2 \sqrt 2$ years

Answer 2

Given : $T_1 = 1\, year, R_1 = R, R_2 = 2R$ According to Kepler's third law of planetary motion \hspace40mm T^2 \propto R^3 where R is the distance between earth and sun. \therefore \hspace20mm \bigg(\frac{T_1}{T_2}\bigg)^2 = \bigg(\frac{R_1}{R_2}\bigg)^3 \hspace35mm = \bigg(\frac{R}{2R}\bigg)^3 = \frac{1}{8} \Rightarrow \hspace25mm \frac{T_1}{T_2} = \frac{1}{2 \sqrt 2} \Rightarrow \hspace25mm T_2 = 2 \sqrt 2 T_1 \hspace35mm = 2 \sqrt 2 \, years