Q. The period of a planet around sun is 27 times that of earth. The ratio of radius of planet’s orbit to the radius of earth’s orbit is
A) 4
B) 9
C) 64
D) 27
Explanation
(b) From kepler’s third law of planetary motion:
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto R^{3}$
$Given,\ \ \ \ \ \ \ \ \ T_{p} = 27T_{e^{'}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{e}^{2}}{T_{p}^{2}} = \frac{R_{e}^{3}}{R_{p}^{3}}$
$\ \ \ \ \ \ \ \ \ \ \frac{T_{e}^{2}}{(27T_{e})^{2}} = \frac{R_{e}^{3}}{R_{p}^{3}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{R_{p}}{R_{e}} = (27)^{1/2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{R_{p}}{R_{e}} = 3^{2}$
${\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R}_{p} = {9R}_{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.