Question

Calculate the period of revolution of jupiter around the sun. The ratio of the radius of jupiter's orbit to that of the earth's orbit is $5$

Answer 1

Given, $\frac{R_j}{R_e}=5$

Using Kepler's $3rd$ Law;

where

$T^2\propto R^3$

$\Rightarrow \frac{T_j^2}{T_e^2}={\left(\frac{R_j}{R_e}\right)}^3$

$\Rightarrow \frac{T_j}{T_e}={\left(\frac{R_j}{R_e}\right)}^{3/2}=(5{)}^{3/2}$

$=11.18year$ (as $T_e=1year$)

$\therefore T_j=11.8years$