LinkAnother challenge would be trying to alter the ‘course’ of an asteroid. Although possible, it would take a really, really, really, long time.The Dawn spacecraft uses ion propulsion to get the additional velocity needed to reach Vesta once it leaves the Delta rocket. It also uses ion propulsion to spiral to lower altitudes on Vesta, to leave Vesta and cruise to Ceres and to spiral to a low altitude orbit at Ceres. Ion propulsion makes efficient use of the onboard fuel by accelerating it to a velocity ten times that of chemical rockets. This efficiency is measured in terms of the specific impulse of the fuel
Given enough time (probably millions of years) and using ever more massive bodies for slingshot maneuvers, we can move planets.