Example:

A satellite on circular orbit, has a period of 90 min. What is radius of the orbit and the altitude of the satellite. From (7) we get:

$$r=\sqrt[3]{\frac{G M_E T^2}{4\pi^2}}=6652555.5 {\rm m}=6652.6 {\rm km}.$$

The radius of the Earth is about 6360 km, hence the altitude is about 292 km.