For two planets 1 and 2 orbiting the same star with orbital periods and orbital radii

PHYSICS · Single correct · CBSE · Physics · Gravitation · Gravitation

Problem

For two planets 1 and 2 orbiting the same star with orbital periods

T_1, T_2

and orbital radii

r_1, r_2

, which of the following relations represents Kepler’s third law? (a)

\displaystyle \frac{T_1^{2}}{T_2^{2}} = \frac{r_2^{3}}{r_1^{3}}

(b)

\displaystyle \frac{T_1^{3}}{T_2^{3}} = \frac{r_1^{2}}{r_2^{2}}

(c)

\displaystyle \frac{T_1^{2}}{T_2^{2}} = \frac{r_1^{3}}{r_2^{3}}

(d)

\displaystyle \frac{T_1}{T_2} = \frac{r_1^{3}}{r_2^{3}}