This paper proposes a geometry for the coverage of the whole Earth surface by a non-geo Earth fixed cell satellite constellation, where each cell on the Earth is illuminated by a steered beam as the satellite proceeds along its orbit. The relevant parameters are identified and frequency reuse patterns are proposed. The variation of the frequency reuse pattern parameter, defined as the number of sub-bands to be reused in the system, is analysed as a function of the beam coverage radius and the co-channel cell minimum distance. It is shown that the frequency reuse pattern parameter increases both with the beam coverage radius and with the minimum distance between co-channel cells. The frequency reuse pattern parameter must be increased at high latitudes, in order to maintain a specified carrier to interference power ratio, C/I.