Short-period comet production in close encounters with Jupiter

A method for calculating the resultant probability distributions of orbital elements for a small body (a comet, asteroid or meteoroid) after a gravitational encounter with a planet is described. This technique incorporates the frequency of such encounters so that the chance of attaining a certain new orbit per unit time is derived. The use of this technique is then illustrated by considering the effect of Jupiter upon the orbits of near-parabolic comets with perihelia near the planet (q = 5.2 AU) and in the inner solar system (q = 1.0 AU), with prograde (i = 10 deg) and retrograde (i = 170 deg) paths. As indicated by previous authors the prograde comets are more easily captured into short-period (P less than 20 yr) and intermediate-period (P between 20 and 200 yr) orbits; it is found that the comets with smaller perihelia, rather than those with perihelia near Juptier, have higher capture probabilities. This is apparently due to the fact that a small deflection only is needed to sufficiently decelerate a comet onto a smaller orbit if it makes a near-perpendicular crossing of Jupiter's path, whereas a larger deflection (to achieve a large orbital change) is needed if the paths are near-parallel.