AbstractThe observed frequency of passages of Earth-crossing long-period (LP) comets (P > 200 yr) is about three per year for comets brighter than absolute magnitude H10 ∼ 10.5. About one out of six LP comets is estimated to be new, i.e., making its first passage through the inner planetary region. The sample of observed LP comets shows an excess of retrograde orbits that may be accounted for by the shorter dynamical lifetimes of comets on direct orbits due to planetary perturbations. The original semimajor axes of new comets concentrate in the range 7 × 103 ≳ aorig ≳ 4 × 104 AU, which tells us about the region of the Oort cloud where forces other than planetary perturbations act with the greatest efficiency. Yet the distribution of original semimajor axes cannot tell us anything about the existence of a dense inner core of the Oort cloud. Besides planetary perturbations, passing stars, molecular clouds and the galactic tidal force also influence the dynamical evolution of Oort cloud comets. The observed distribution of the aphelion points of near-parabolic comets shows such a dependence on the galactic latitude. Molecular clouds and stars penetrating very deeply in the Oort cloud are found to give rise to major enhancements in the influx rate of new comets, known as comet showers, at average intervals of a few 107 yr.An important issue to solve concerns how the frequency of comet passages varies with time, in particular as regards to the current level of comet appearances. Should we be passing through a highly intense phase, most aphelia of the incoming Oort comets would concentrate on the sky area where the strong perturber exerted its greatest effect. By contrast, the observed galactic latitude dependence of the aphelia suggests a dominant influence of the vertical galactic tidal force as compared with random strong perturbers. This seems to indicate that the frequency of comet passages is currently at, or near, its quiescent level. Whether intense comet showers are reflected in the impact cratering record is still a debatable issue. A periodicity of ∼ 26-30 Myr in the impact cratering rate is quite uncertain, owing to the small size of the sample of well-dated craters and the noise from background impact craters from asteroids.The family of short-period (SP) comets (orbital periods P < 20 yr) has long been regarded as the dynamical end-state of new comets on low-inclination orbits captured by Jupiter. However, if SP comets came from a spherical population of comets (e.g., incoming new comets), we should expect to find a percentage of them on retrograde orbits, which contradicts the observations. An alternative hypothesis for the origin of most SP comets is that they come from a trans-Neptunian comet belt. Extensive searches aimed at detecting faint slow-moving objects are required to assess the size of the comet population in the outer planetary region. Modeling of the transfer rate of comets from an outer belt to SP orbits gives transient populations between Saturn and Neptune on the order of 106 – 107 bodies. This is roughly comparable to the upper limit set by the most recent searches of outer solar system bodies.The impact crater production rate of comets, at the present time, can be estimated to be on the order of 10% of the value corresponding to asteroidal impacts. These estimates, however, are subject to large uncertainties in the brightness-mass relation of comets and crater scaling law. The Earth could have received about 2 × 1020 g of cometary material over the last 4 billion years — if the injection rate of new comets remained constant in the time interval. Within the context of H2O inventory, the cometary influx should have rather minor effects. On the other hand, because of the paucity of H2O content in the atmospheres of Venus and Mars, cometary impact could strongly modulate their water contents.
A Theory on the Slope of the IMF