Mathematical modelling of antenna look angles of geostationary communications satellite using two models of control stations

Antenna look angles of geostationary communications satellite provide the information required to ensure that control station antenna is directed towards the satellite; more specifically to ensure that the main lobe of the antenna is aligned with the main lobe of the satellite´s antenna, and to ensure that the largest amount of energy is captured from the satellite. To optimize the performance of a satellite communications system, the directions of maximum gain of a satellite ground control station antenna (referred to as boresight) must be pointed directly at the satellite. To ensure that the earth station antenna is aligned, two angles must be determined: the azimuth and the elevation angle. Azimuth angle and elevation angle are jointly referred to as the antenna look angles. This paper describes in detail, the mathematical modelling of antenna look angles of two models of satellite ground control station. The mathematical models developed are abstract models that use mathematical equations to describe the antenna look angles. The mathematical representations presented takes into consideration the redundancy of the control stations. Two models are used in order to pave way for redundancy so that if one fails the other takes over. Mathematical model of antenna look angles is a mathematical representations of the equations governing them.