Migration of comets to the terrestrial planets

The orbital evolution of 30,000 objects with initial orbits close to those of Jupiter-family comets (JFCs) and also of 15,000 dust particles was integrated [1-3]. For initial orbital elements close to those of Comets 2P, 10P, 44P, and 113P, a few objects got Earth-crossing orbits with semi-major axes a<2 AU and aphelion distances Q<4.2 AU, or even got inner-Earth (Q<0.983 AU), Aten, or typical asteroidal orbits, and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myrs). Most of former trans-Neptunian objects that have typical near-Earth object (NEO) orbits moved in such orbits for Myrs, so during most of this time they were extinct comets. From a dynamical point of view, the fraction of extinct comets among NEOs can exceed several tens of percent, but, probably, many extinct comets disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes if these lifetimes were large. The probability of the collision of Comet 10P with the Earth during a dynamical lifetime of the comet was P[E]≈1.4∙10^-4, but 80% of this mean probability was due only to one object among 2600 considered objects with orbits close to that of Comet 10P. For runs for Comet 2P, P[E]≈(1-5)∙10^-4. For most other considered JFCs, 10^-6 < P[E] < 10^-5. For Comets 22P and 39P, P[E]≈ (1-2)∙10^-6; and for Comets 9P, 28P and 44P, P[E]≈(2-5)∙10^-6. For all considered JFCs, P[E]>4∙10^-6. The Bulirsh-Stoer method of integration and a symplectic method gave similar results. In our runs the probability of a collision of one object with the Earth could be greater than the sum of probabilities for thousands of other objects. The ratios of probabilities of collisions of JFCs with Venus and Mars to the mass of a planet usually were not smaller than that for Earth. For dust particles started from comets and asteroids, P[E ]was maximum for diameters d~100 μm. These maximum values of P [E] were usually (exclusive for 2P) greater at least by an order of magnitude than the values for parent comets. [1] Ipatov S.I. and Mather J.C. (2004) Annals of the New York Acad. of Sci., v. 1017, 46-65. [2] Ipatov S.I. et al. (2004) Annals of the New York Acad. of Sci., v. 1017, 66-80. [3] Ipatov S.I. and Mather J.C. (2006) Adv. in Space Res., v. 37, N 1, 126-137.