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

Answer: (D)

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

Answer 2

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