From the Oort cloud to observable short-period comets - I. The initial stage of cometary capture

We investigate the first stage of the dynamical evolution of Oort cloud com ets entering the planetary region for the first time. To this purpose, we i ntegrate numerically the motions of a large number of fictitious comets per taining to two samples, both with perihelion distances up to 5.7 au and ran dom inclinations; the first sample is composed of comets whose orbits have at least one node close to 5.2 au, while the second is not subject to this constraint. We examine the orbits when the comets come to aphelion after th eir first perihelion passage within the planetary region, and find that the re is a clear statistical dependence of the energy perturbations on the Tis serand parameter. There appear to be two main processes, of comparable impo rtance, governing the shortening of semimajor axes to values of less than 1 000 au, i.e. planetary close encounters, especially with Jupiter, and indir ect perturbations due to the shifting of the motion from barycentric to hel iocentric and back; the former process mostly affects comets crossing the e cliptic at about 5.2 au, or on low-inclination orbits, while the latter mos tly affects comets of small perihelion distance. This last result may help to understand the relative paucity of Halley-type comets with perihelion di stances larger than about 1.5 au.