An analytical approach is outlined to obtain the fields near the earth's surface for a long wave transmitting antenna on a satellite. The medium is divided into slabs, each of which is characterized by a dielectric tensor. To simplify the calculations, a planar model is considered in which the d.c. magnetic field is vertical. An explicit derivation is given for a three-layer planar model: the lowest layer, up to ca. 70 km, represents the earth–ionosphere waveguide, the second layer may represent the D region; and the third layer is the one containing the satellite, which is idealized by a vertical electric dipole. Emphasis is placed on the relative launching efficiency of a satellite-borne antenna as compared with a ground-based antenna of the same strength. For sake of simplicity the antenna is idealized as an electric dipole and all sheath effects are neglected.