The terrestrial coverage of the geostationary satellite beam

A vector method is developed for both shaping a broadcast beam from a GEO satellite to cover the service area and expanding the beam to compensate for attitude and position errors of the satellite. The model is confined to second power error terms or lower, with the assumption that the satellite orbital angular velocity approximates the rotation velocity of the earth. A coordinate system is devised for analyzing the positions of intersection points of any rays of the antenna beam on the ground. The orbital position error is formulated, as are the attitude error and the elliptical beam. Sample calculations are provided for an expanded ideal beam, with consideration given to possible displacement regions for all rays at the borders of the ideal beam.