The present trend in satellite communication systems is towards large geostationary satellites which are accurately maintained on station. A fixed, offset, spherical reflector with a mechanically steered line feed is proposed as an economic design for a ground-station aerial. The distribution of electric field along the axis of the reflector is calculated for the case of an incident circularly polarised wave, and it is shown that the optimum distribution for a transmitting feed follows closely the axial field in the receiving case. Because of the asymmetry of the system, an entirely numerical technique has been developed, using a digital computer to calculate the axial field. A similar technique is used to compute the performance of an aerial using an offset spherical reflector and a line feed of crossed current elements. The aerial is shown to have a high theoretical efficiency (81%), with low spillover and a good sidelobe structure. The limitation of bandwidth with this type of feed is discussed, and proposals are made for an improved, design of line feed.