The idea is that you catch them far enough away in time so that a small nudge pushes them enough to miss. Far away in time doesn’t even need to mean far away i

The idea is that you catch them far enough away in time so that a small nudge pushes them enough to miss. Far away in time doesn’t even need to mean far away in space, since many of the objects of concern are orbiting the Sun along with us. They may even have multiple close passes before being perturbed enough to become a threat. Also, the masses involved don’t have to be huge. Two rocks intersecting in space are likely to be doing so with very different velocities. Kinetic energy is mass times velocity squared, so velocity rapidly overtakes mass as the dominant factor.