Question

Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also moves around the sun in circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is

• A. $2-\frac{2}{3}R$
• B. $2\frac{2}{3}R$
• C. $2\frac{-1}{3}R$
• D. $\frac{R}{\sqrt{2}}$

Answer 1

Answer: (A)

$2-\frac{2}{3}R$

Answer 2

$T^{2} \propto r^{3},\frac{rE}{rP}=\left(\frac{T_{E}}{T_{P}}\right)^{\frac{2}{3}} =\left(\frac{\omega_{P}}{\omega_{E}}\right)^{\frac{2}{3}}$ $\frac{R}{r_{p}} = \left(2\right)^{\frac{2}{3}} , r_{p} =2^{-\frac{2}{3}R}$