Centaurs are solar system objects with orbits situated among the orbits of Jupiter and Neptune. Centaurs represent one of the sources of Near-Earth Objects. Thus, it is crucial to understand their orbital evolution which in some cases might end in collision with terrestrial planets and produce catastrophic events. We study the orbital evolution of the Centaurs toward the inner solar system, and estimate the number of close encounters and impacts with the terrestrial planets after the Late Heavy Bombardment assuming a steady state population of Centaurs. We also estimate the possible crater sizes. We compute the approximate amount of water released: on the Earth, which is about 0.00001 the total water present now. We also found sub-regions of the Centaurs where the possible impactors originate from. While crater sizes could extend up to hundreds of kilometers in diameter given the presently known population of Centaurs the majority of the craters would be less than about 10 km. For all the planets and an average impactor size of 12 km in diameter, the average impact frequency since the Late Heavy Bombardment is one every 1.9 Gyr for the Earth and 2.1 Gyr for Venus. For smaller bodies (e.g. > 1 km), the impact frequency is one every 14.4 Myr for the Earth, 13.1 Myr for Venus and, 46.3 for Mars, in the recent solar system. Only 53% of the Centaurs can enter into the terrestrial planet region and 7% can interact with terrestrial planets.
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