Earth Footprints of Satellite Antennas

This paper develops the expressions for computing the footprint on Earth (i.e., power density contours) of a satellite antenna. The expression for determining the antenna pattern coordinate as a function of the Earth coordinates is derived. The antenna pattern operator which converts the pattern function into the available power density is obtained. In this case it is assumed that the Earth-based antenna is directed towards the satellite. The radar operator is also derived; this operator yields the power density intercepted by the Earth.