\(F \propto \frac{1}{r^{2}}\)

\(F=\frac{k}{r ^{2}}\)

\(\frac{K}{r^{2}}=\frac{m v^{2}}{r}\)     \(T=\frac{2 \pi r}{v}\)

\(v^{2}=\frac{k}{m r}\)

\(v=\sqrt{\frac{k}{m r}}\)

\(T=\frac{2 \pi r}{\sqrt{\frac{R}{m r}}}\)

\(\Rightarrow T=\frac{2 \pi  r^{3 / 2} m^{1 / 2}}{\sqrt{k}}\)

\(T^{2}=\frac{4 \pi^{2} r^{3} m}{ki}\)

\(T^{2} \propto r ^{3}\)