The distance of Neptune and Saturn from the Sun are nearly $10^{13}$ and $10^{12}$ metres respective

Question

The distance of Neptune and Saturn from the Sun are nearly $10^{13}$ and $10^{12}$ metres respectively. Assuming that they move in circular orbits their periodic times will be in the ratio\

Professor PC Thomas Classes · Answer

$\mathrm{T}_{\mathrm{n}}^{2} \propto \mathrm{r}_{\mathrm{n}}^{3} \quad \mathrm{~T}_{\mathrm{s}}^{2} \propto \mathrm{r}_{\mathrm{s}}^{3}$\ $\frac{T_{n}^{2}}{T_{s}^{2}}=\frac{r_{n}^{3}}{r_{s}^{3}}=\left(\frac{10^{13}}{10^{12}}ight)^{3}=10^{3} \quad \frac{T_{n}}{T_{s}}=10 \sqrt{10}$\