Question

The distance of the two planets from the Sun are ${10}^{13}$m and ${10}^{12}$m, respectively. Find the ratio of time periods and speeds of the two planets.

Answer 1

We have $T^2\propto r^3$

$\frac{T_1}{T_2}={\left(\frac{r_1}{r_2}\right)}^{\frac{3}{2}}={\left(\frac{{10}^{13}}{{10}^{12}}\right)}^{\frac{3}{2}}\Rightarrow \frac{T_1}{T_2}=31.62$

Since $T\propto \frac{1}{\omega }$

$\frac{{\omega }_1}{{\omega }_2}=\frac{T_2}{T_1}=0.0316$