The transfer of comets from near-parabolic to short-period orbits: map approach

In the framework of the circular restricted three-body problem (the Sun-pla net-comet), we generalize the map of Liu & Sun (1994) to study the transfer of comets from near-parabolic to Halley-family ones, under the perturbatio ns of Jupiter. Numerical results show that the transfer is effective for co mets on both the direct and retrograde orbits crossing the planet's orbit, and on the direct non-crossing orbits but with the perihelion distances clo se to the semi-major axis of the planet's orbit. The dependence of the tran sfer probability and of the average transfer time on the perihelion distanc es of the cometary orbits and on the planet mass are determined. The probab ilities of comet transfer from the Oort Cloud are found to be 0.12 and 0.06 7 for comets on direct and retrograde orbits, respectively. This leads us t o expect an average flux of 0.23 new Halley-family comets per year interior to Jupiter's orbit. The calculation shows that about 86% of the flux comes from comets on the Jupiter-crossing orbits.