The National Aeronautics and Space Administration is considering nuclear power sources for space exploration. A series of critical mass experiments was designed to address the development, performance, and design of a space nuclear reactor being considered to support the Prometheus project. These experiments consisted of interlacing the refractory metals rhenium (Re), molybdenum (Mo), tantalum-2.5 wt% tungsten (Ta-2.5W), and niobium-1 wt% zirconium (Nb-1Zr) with moderating materials (graphite or polyethylene) and were fueled by highly enriched uranium plates. These experiments are designed to assess the adequacy of and uncertainty in refractory metal neutron cross-section evaluations for use in Prometheus nuclear reactor design work. The critical experiments were designed in the energy spectrum closely resembling or bracketing that in the proposed space reactor. For each material (Re, Mo, Ta-2.5W and Nb-1Zr), four critical configurations were designed and performed to measure the sensitivity of keff to the material under four different and progressively softer neutron spectra (core center spectrum, harder than core average spectrum, softer than core average spectrum, and accident flooded spectrum). The thicknesses of the graphite or polyethylene moderator and reflector plates were adjusted to achieve the desired neutron spectrum. One critical and 18 subcritical experiments provided for measurements of material neutronic behavior in a simple cylindrical geometry configuration that was modeled in MCNP with ENDF/B-VI.6 cross-section data and compared to the extrapolated or predicted critical mass for all the experiments. These experiments were performed at the Los Alamos National Laboratory using the Planet vertical lift critical assembly at the Los Alamos Critical Experiment Facility.