Asteroid deflection through explosive blasting provides an avenue to achieve significant changes in velocity for a given explosive yield, enabling deflection of bodies on a collision course with Earth much closer to time of impact. In this analysis, a number of computational numerical methods have been applied to outstanding problems of determining the change of velocity induced to an asteroid, the uncertainty distribution within the model, and the impact deflection that a modeled change in velocity would induce in a hypothetical test case. The results from this modeling support the utility of further research and small-scale testing, and suggest that blasting has the capacity to redirect asteroids less than a year before the time of impact in many cases. Filling this capacity is essential, considering the potentially short detection interval compared to the times necessary for many other deflection strategies.