Satellites that orbit the Earth at a distance of 35 800 km above the Earth's equator, and travel at a speed that matches the speed of the Earth's rotation, are said to be in geostationary orbit. In this orbit, a satellite's distance above the Earth's surface is fixed, and it maintains a fixed position above a certain point on the Earth's surface as it rotates. A telecommunications company owns satellites A, B and C, which are in geostationary orbit. Satellite A is diametrically opposite satellite C (i.e. AC is the diameter of the geostationary orbit). Satellite B is 51 000 km from satellite A, and ZABC is 90. Assume that the Earth is spherical, with diameter 12700 km. A diagram of the satellites in orbit is given in Figure 2. Figure 2 Orbit B 51 000 km Earth 35 800 km 12 700 km (a) (i) Find the length AC. (ii) Find the circumference of the geostationary orbit. (iii) Use Pythagoras' Theorem to calculate the length BC. (iv) Using trigonometry, calculate BAC. [1] [2] [2] [3]