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

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

Tardigrade Admin · Accepted Answer

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

i e,

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}

Q. 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

4

9

64

27