A) \[{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{3/2}}=\frac{{{r}_{1}}}{{{r}_{2}}}\]
B) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\left[ \frac{{{r}_{1}}}{{{r}_{2}}} \right]\]
C) \[{{\left[ \frac{{{T}_{1}}}{{{T}_{2}}} \right]}^{2}}={{\left[ \frac{{{r}_{1}}}{{{r}_{2}}} \right]}^{3}}\]
D) \[\frac{T_{1}^{2}}{{{T}_{2}}}=\frac{r_{1}^{3}}{{{r}_{1}}}\]
Correct Answer: C
Solution :
By Kepler's third law of planetary motion, \[{{T}^{2}}\propto {{R}^{3}}\] \[{{\left[ \frac{{{T}_{1}}}{{{T}_{2}}} \right]}^{2}}={{\left[ \frac{{{r}_{1}}}{{{r}_{2}}} \right]}^{3}}\]
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