Published online by Cambridge University Press: 12 April 2016
All the known short-period comets have been followed by numerical integration over a time span of 821 years, from 1585 to 2406. A preliminary survey of the results of these integrations has shown some interesting features, which become recognizable thanks to the length of the time interval covered, not negligible if compared with the typical evolutionary time scale of comets moving in short-period orbits. Interesting phenomena that have been recognized include: (1) captures from, or ejections into, very elongated ellipses, with perihelia of the parking orbits close to the orbit of Jupiter and aphelia within or beyond the region of outer planets; (2) passages of comets from the control of Saturn to that of Jupiter; (3) orbital evolutions controlled mainly by Saturn; (4) librations of comets around low-order resonances; (5) repeated close approaches of comets to Jupiter, often with the comet being captured as a temporary satellite; (6) an almost perfect coincidence of two comet orbits just before a close approach to Jupiter, suggesting their genetic relationship.