Periodic variation of Oort Cloud flux and cometary impacts on the Earth and Jupiter

Time variation in impact probability is studied by assuming that the period ic flux of the Oort Cloud comets within 15 au arises from the motion of the Sun with respect to the Galactic midplane. The periodic flux clearly shows up in the impact rate of the captured Oort Cloud cometary population, with a phase shift caused by the orbital evolution. Depending on the assumed fl ux of comets and the size distribution of comets, the impact rate of the Oo rt Cloud comets of I km in diameter or greater is from 5 to 700 impacts Myr (-1) on the Earth and from 0.5 to 70 impacts per 1000 yr on Jupiter. The re lative fractions of impacts are 0.09, 0.11, 0.26 and 0.54 for long-period c omets, Halley type comets, Jupiter family comets and near-Earth objects, re spectively. For Jupiter, the corresponding fractions in the first three cat egories are 0.18, 0.31 and 0.51. If we consider physical fading of comet ac tivity that is compatible with the observations, then the impact rates of a ctive comets are two orders of magnitude smaller than the total impact rate s by all kinds of comets and cometary asteroids of size I km or greater.