The capture of comets by swing-by

Abstract

In this paper, numerical simulations are made, using the restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Jupiter in the orbit of a comet. In particular, the orbital elements of the comets are calculated after the passage by Jupiter, the distribution obtained is shown and the probability of capture is calculated as a function of the Jacobian constant of the comet. The results showthat the probability of capture goes from 0.2% to 3.6%, depending on the value of the Jacobian constant of the comet. The details of this mechanism and some trajectories are shown. It is also concluded that more than 95% of the captured comets have pericenter distance less than 5 AU (what makes them visible) and that about 70% of them are short-period comets.