Earth-fixed cell beam management methods which may be employed to allocate beams generated by a constellation of low Earth orbit satellites (12) flying in orbits below geosynchronous altitudes are disclosed. These beams (19) are electronically steered so that they illuminate "Earth-fixed cells" (26) as opposed to "satellite-fixed cells." Beam steering apparatus using a spherical dielectric lens (106) is disclosed. In a system that employs satellite-fixed cells, the "footprint" of the beams propagated by a spacecraft defines the zone on the ground called a "cell" which is illuminated by the spacecraft. This satellite-fixed cell moves constantly as the spacecraft moves around the globe. In sharp contrast, an "Earth-fixed cell" (26) is a stationary region mapped onto the surface of the Earth (E) that has permanent fixed boundaries, just like a city or a state. Although the rapidly moving satellites (12) still shine their beams over the ground in rapidly moving footprints (16), the locations of the footprints at any given time do not determine the location of the unchanging Earth-fixed cells (26). The great advantage provided by using cells having boundaries that are fixed to an Earth-fixed grid (20) is realized when a subscriber being served by one satellite must switch to another beam in the same satellite or to a second satellite because the first is moving out of range below the local horizon. With satellite-fixed cells, this "hand-off" involves the assignment to the terminal of a new communication channel within the new beam or new satellite. This assignment process takes time and consumes processing capacity at both the terminal and the satellite. It is also subject to blocking, call interruption, and call dropping if there is not an idle communication channel in the next serving beam or satellite. The Earth-fixed cell method avoids these problems by allocating communication channels (frequency, code, and/or time slot) on an Earth-fixed cell basis rather than on a satellite-fixed cell basis. Regardless of which satellite/beam is currently serving a particular cell, the terminal maintains the same channel assignment, thus ameliorating the "hand-off" problem.