The threat of collision between an asteroid or a comet and the Earth has been well documented. Mitigation of such a threat can be accomplished by destruction of the threat or by perturbing the threat object into a safe orbit. Following a summary of proposed mitigation techniques, this thesis investigates the impulse required to safely perturb a threatening Earth Crossing Asteroid (ECA). While previously published analysis included only two body approximations to the impact geometry, this thesis adds the effect of the Earth's gravitational field to more closely approximate reality. The results indicate that third body effects are strongest on ECA's in a nearly circular heliocentric orbit, where the minimum required delta V can be several times larger than that calculated using two body approximations. To determine the minimum delta V required for mitigation, MATLABs sequential quadratic programming (SQP) algorithm is applied to a constrained optimization problem. Third body effects were added to a previously published two body optimization by modifying the boundary conditions. With knowledge of the minimum delta V requirements, the capability of current impulsive mitigation technology is analyzed. For asteroids of median density in co-planar orbits, a single 24 Mt nuclear explosive impulse applied earlier than 3 years before impact can effectively mitigate a threat with a diameter of 6 km. The capability significantly decreases with shorter warning times.