Question

According to Kepler's law of planetary motion if $ T $ represents time period and $ r $ is orbital radius, then for two planets these are related as :

• A. $ {{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{3}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}} $
• B. $ {{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{\frac{3}{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}} $
• C. $ {{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}} $
• D. $ \left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{\frac{3}{2}}} $

Answer 1

The Correct Option is D

$ {{T}^{2}}\propto {{r}^{3}} $ $ \Rightarrow $ $ {{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}} $