The Voyager missions have revealed that jovian kilometric radiation (emanating from Jupiter's magnetosphere) is beamed away from the zenomagnetic equator. Results from GEOS 1 show that terrestrial non-thermal continuum or myriametric radiation is similarly beamed away from the geomagnetic equator. A mode-coupling mechanism is proposed such that measurements of the direction of propagation of the escaping O-mode radiations may allow the construction of the first high-resolution maps of the shapes of the equatorial plasmapause and Io torus.