The Earth may be considered to be a uniform sphere of radius 
, with its mass concentrated at its centre. By considering the gravitational field strength at the surface of the Earth, show that the mass of the Earth is 
.
The Global Positioning System (GPS) is a navigation system that can be used anywhere on Earth. It uses a number of satellites that orbit the Earth in circular orbits at a distance of 
above its surface. Use data from (a) to calculate the angular speed of a GPS satellite in its orbit.
.
