Collisions in the Solar system - V. Terrestrial impact probabilities for parabolic comets

For a theoretical distribution of parabolic comets arriving from a spherical source, the terrestrial impact probability is determined numerically. If the distribution of perihelion distances is uniform, as would occur for Oort cloud comets whose velocity vectors are random, the mean impact probability is $$2.2\times {10}^{-9}$$ per perihelion passage, with a mean impact speed of 55 km s^–1. If the distribution varies as q^1/2, as suggested by the analysis of observed long-period comets, the mean impact probability is $$2.6\times {10}^{-9}$$ per perihelion passage, with a slightly higher mean impact speed. These probabilities are both lower than that obtained for the observed set of long-period comets. It is suggested that, in view of our lack of knowledge about how the observed population relates to the actual population of long-period and parabolic comets, $$(3\pm 1)\times {10}^{-9}$$ per perihelion passage should be adopted as an appropriate mean value and uncertainty for the terrestrial impact probability for such bodies.