Question

The period of a planet around sun is 27 times that of earth. The ratio of radius of planets orbit to the radius of earths orbit is

• A. 4
• B. 9
• C. 64
• D. 27

Answer 1

Answer: (B)

From Keplers third law of planetary motion. The square of the period of revolution $ (T) $ of any planet around the sun is directly proportional to the cube of the semi major axis $ (X) $ of its elliptical orbit $ ie, $
$ {{T}^{2}}\propto {{R}^{3}} $
Given, $ {{T}_{p}}=27{{T}_{e}}, $
$ \frac{T_{e}^{2}}{T_{p}^{2}}=\frac{R_{e}^{3}}{R_{p}^{3}} $
$ \frac{T_{e}^{2}}{{{(27{{T}_{e}})}^{2}}}=\frac{R_{e}^{3}}{R_{p}^{3}} $
$ \frac{{{R}_{p}}}{{{R}_{e}}}={{(27)}^{2/3}} $
$ \frac{{{R}_{p}}}{{{R}_{e}}}={{3}^{2}} $ $ {{R}_{p}}=9{{R}_{e}} $