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Insights into the history of the inner solar system can be derived from the impact cratering record of the Moon, Mars, Venus, and Mercury and from the size distributions of asteroid populations. Old craters from a unique period of heavy bombardment that ended approximately 3.8 billion years ago were made by asteroids that were dynamically ejected from the main asteroid belt, possibly due to the orbital migration of the giant planets. The impactors of the past approximately 3.8 billion years have a size distribution quite different from that of the main belt asteroids but very similar to that of near-Earth asteroids.
Strom et al. (2005) studied this question.