http://neo.jpl.nasa.gov/

The Moon evidently has had its share of meteorite hits; it’s carpeted in craters.

The likelihood depends first on the close passage of a potential impactor. Second is the Moon’s diameter. This presents a circular cross-section through which an asteroid’s path may pass. The larger the cross-section, the larger the chance that a path may pass through it. And of course, the Moon’s gravity plays a role, because it bends the paths of passing rocks toward it. So as you are aware, the stronger the gravitational field, the more that an asteroid will be attracted and the greater the chance that it’ll collide.

So from this it’s obvious that, for a population of asteroids with paths that come near the Earth-Moon system, Earth will get more hits on average. (But then again, most meteors are small and disintegrate as they plow through our atmosphere. The Moon has more large craters because it has no air and very slow erosion processes.)

Such an asteroid impact could easily eject some smallish fragments at escape velocity.

They could also be put on an elliptical orbit. However, with this is scenario the elliptical path, intersecting the planetary surface, would necessarily bring the ejecta right back into the surface. (If a chunk of ejecta could be made to explode in-two at just the right place on its trajectory, with just the right energy, with the fragments separating in just the right direction, then one piece’s path could be adjusted to put it on a non-intersecting ellipse. This is essentially a two-stage rocket, with the first stage being the initial asteroid impact.)

Dan