Per la terra

$$n=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

Per la luna

$$n'=\frac{1}{2\pi}\sqrt{\frac{k}{6m}}\perché g_{moon}=\frac{g}{6}$$

$$\frac{n'}{n}=\frac{1}{\sqrt{6}}\quindi n':n=1:\sqrt6$$