Show that the period $T$ of the satellite’s orbit is given by $T^2 = \frac{4\pi^2 r^3}{GM}$, where $G$ is the gravitational constant. Explain your working.
A satellite in geostationary orbit seems to stay above the same point on the Earth and has a period of 24 hours. State two other characteristics of a geostationary orbit.
The Earth’s mass $M$ is $6.0 \times 10^{24}\,\text{kg}$. Use the relation in (a) to find the radius of a geostationary orbit.
A global positioning system (GPS) satellite orbits the Earth at a height of $2.0 \times 10^4\,\text{km}$ above the Earth’s surface. The Earth’s radius is $6.4 \times 10^3\,\text{km}$. Use your answer in (b)(ii) together with the expression $T^2 \propto r^3$ to calculate, in hours, the period of the orbit of this satellite.