Keplerian consequences of an impact on an asteroid and their relevance for a deflection demonstration mission

We investigate upon the change of an asteroid orbit caused by an impact. We find that, given the assumption of two dimensional motion, the asteroid displacement may be described by an analytic and explicit expression that is the vectorial sum of a radial component and a component along the asteroid velocity. The new formulation bridges the gap between the study of short-term effects, using numerical methods and the analytic study of secular changes of the asteroid orbit. The relation of the method to the established formulations is described and the known results are derived as limiting cases.