Space-based solar power systems (SSPS) offer a renewable source of energy generation that features higher power production than terrestrial photovoltaics (PV) systems with visibly unobstructed access to direct sunlight. Because of the high launch and deployment costs for SSPS, PV arrays intended for such applications are designed so as to maximize the specific power (W/kg) of the array. Here we present a first analysis for a luminescent solar concentrator (LSC) module designed for SSPS. LSC devices absorb and trap incident sunlight in a planar dielectric waveguide through photon downshifting via absorption and Stokes-shifted emission from embedded luminophores. Emitted photons are trapped within the waveguide and concentrated onto small area solar cells, spectrally matched to the luminophore band edge. Here we investigate the influence of luminophore material and concentration factor on the LSC specific power. We develop an LSC system design that can achieve up to 1.8 kW/kg.