Space radiation presents significant health risks to astronauts on the International Space Station and for future missions to the Earth's moon or Mars. Risks of concern are carcinogenesis, degenerative tissue effects including early and late responses to the central nervous system, heart disease and cataracts, and acute risks. Methods used to project risks on Earth need to be modified because of the large uncertainties in projection models for space radiation risks, and thus impact safety factors and mission costs. We describe NASA's unique approach to radiation safety that applies uncertainty based criteria within the occupational health program for astronauts. The terrestrial criteria of the "point estimate" of the maximum acceptable level of risk is supplemented by a requirement that protects against risk projection uncertainties using the upper 95% confidence level (CL) in the radiation cancer projection model. NASA's 95% CL criteria links space flight safety to a vibrant ground based radiobiology program investigating the radiobiology of high-energy protons and heavy ions using the NASA Space Radiation Laboratory (NSRL) at the Brookhaven National Lab. The near-term goal of this research is new knowledge leading to the reduction of uncertainties in projection models. Long-term goals include the development of biomarkers and countermeasures of space radiation risk. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. The current model for projecting space radiation cancer risk relies on the three assumptions of linearity, additivity, and scaling along with the use of population averages. We describe mechanistic research that will reduce uncertainty estimates for this model by testing these underlying assumptions.