A simplified approach to uncertainty quantification for orbits in impulsive deflection scenarios

For the majority of near-Earth Asteroid (NEA) impact scenarios, optimal deflection strategies use a massive impactor or a nuclear explosive, either of which produce an impulsive change to the orbit of the object. However, uncertainties regarding the object composition and the efficiency of the deflection event lead to a non-negligible uncertainty in the deflection delta-velocity. Propagating this uncertainty through the resulting orbit will create a positional uncertainty envelope at the original impact epoch. We calculate a simplified analytic evolution for impulsively deflected NEAs and perform a full propagation of uncertainties that is nonlinear in the deflection delta-velocity vector. This provides an understanding of both the optimal deflection velocities needed for a given scenario, as well as the resulting positional uncertainty and corresponding residual impact probability. Confidence of a successful deflection attempt as a function of launch opportunities is also discussed for a specific case.