(a)[3]
Show that the satellite’s orbital period $T$ is described by $T^2 = \frac{4\pi^2 r^3}{GM}$, where $G$ denotes the gravitational constant. Show your working.
(b(i))[2]
A geostationary satellite seems to stay above one fixed point on the Earth and takes 24 hours to complete an orbit. State two further characteristics of a geostationary orbit.
(b(ii))[2]
The Earth has mass $M=6.0 \times 10^{24}\,\text{kg}$. Apply the relation in (a) to find the radius of a geostationary orbit.
(c)[2]
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) and $T^2 \propto r^3$ to calculate the orbital period of this satellite, in hours.