We propose to develop a Fortran computer program to determine the thermal radiant interchange factors among real, non-diffuse, non-specular surfaces. The innovation lies in our solution procedure, which yields, in one step, an exact solution to the computational problem. Previous methods for real surfaces are based on ray-trace, monte carlo simulations, which are costly and inaccurate for non-ideal surfaces; or on an adaption of stray-light methods found in optics technologies, a costly and cumbersome method that is inaccurate for highly specular surfaces. The costliness, awkwardness and inaccuracy of these previous methods causes spacecraft designers to design with the simpler pure-diffuse/pure-specular models which incur currently unknowable inaccuracies. Therefore, today's designers cannot ascertain the adequacy of many of their designs. The result of our development, which will be completed in phase ii, is of great importance to current and future NASA missions. For example, a radiator on the moon that uses non-diffuse reflectors to divert sunlight can achieve end-of-life sink temperatures of 2 F; today's flat-plate radiator designs can achieve only 94 F -- so high that a costly and relatively unreliable heat pump is needed. Similar performance improvements are possible with non-diffuse reflectors for space radiators operating at 80 K. The proposed computer program will provide the tool necessary for the design of such radiators.