Abstract :
The basic problem considered is the relation of the shape of the beam of a geostationary satellite antenna to the area that it covers on the surface of the earth. It is envisaged that circular or elliptical beams may be used, but the beam is defined in general terms by a beam contour on a beam plane perpendicular to the beam axis by two angular co-ordinates ¿ and¿, while the earth contour in which the beam cuts the surface of the earth is defined by the latitude ¿ and the longitude ¿. Corresponding points on the two contours are linked by the direction cosines of the line from the satellite passing though them, leading to equations for finding ¿ and ¿ from ¿ and and ¿ and vice-versa. The process of finding the shape of a beam to serve a specified area on the earth with as little excess coverage as possible is discussed, with the limited possibility of compensating for the difference in clear-air attenuation in different directions from the satellite. The major problem of absorption, for example, by rain or clouds, is regarded as outside the scope of the paper.
