# Planet Neptune travels around the sun with a period of 165 years. Find the ratio of $\large\frac{R_2}{R_1}$ where $R_2$ radius of Neptune orbit and $R_1$ radius of earth , both being considerd circular.

$(a)\;20 \quad (b)\;30 \quad (c)\; 25 \quad (d)\;35$

$T_1=T_{earth}=1 year$
$T_2=T_{neptune}=165 years$
$\large\frac{{T_1}^2}{{T_2}^2}=\frac{{R_1}^3}{{R_2}^3}$
=> ${R_2}^3=\large\frac{{R_1}^3{T_2}^2}{{T_1}^2}$
=>${R_2}^3=165^2{R_1}^3$
$R_2 \approx 30 \;R_1$
hence b is the correct answer.

edited Feb 17, 2014 by meena.p