The design of aerospace vehicles has required the solution of radically new scientific and technological problems. One of the important problems has been to create reusable heat shield materials. In [1, 2] information concerning the methods and results of solving these problems, including the development of composites from ultrathin quartz fibers and carbon-carbon materials for the "Buran" orbital vehicle heat shield, was presented. The basic thermophysical characteristics of these materials include both the rate or probability coefficients of heterogeneous nitrogen and oxygen atom recombination and the accommodation coefficients of energy recombination at high surface temperatures. In the present paper the experimental and computational aspects of determining these parameters, which are also of interest for new heat shield materials for future space transport systems, are discussed.