the first discovered on an unstable planet-crossing orbit that lies entirely in the outer Solar System. Since that time,
We present numerical orbital integrations of thousands of massless particles as they evolve from Neptune-encountering a total of six objects on similar giant plant-crossing orbits orbits in the Kuiper belt for up to 1 Gyr or until they either have been discovered. These objects have come to be impact a massive body or are ejected from the Solar System. known as ''Centaurs'' and, as many have suggested, proba-
The median dynamical lifetime of these objects is 4.5 ؋ 10 7 bly represent the observational connection between the years. We found that about 30% of these objects became visible recently discovered trans-neptunian Kuiper belt objects comets. (We refer to a comet with perihelion distance Ͻ2.5 AU (Jewitt and Luu 1995, Cochran et al. 1995) and visible as a ''visible'' comet.) Of those, 99.7% were Jupiter-family Jupiter-family comets. comets (as defined by their Tisserand parameter, hereafter Ferna ´ndez (1980) first suggested that a belt of distant ''JFCs'') when they first became visible, although some evolved icy planetesimals could serve as the source of comets with out of the Jupiter family as time progressed. By comparing the observed orbital element distribution of JFCs to that produced periods less than 200 years. Duncan et al. (1988) strengthby our simulations we deduce that JFCs are statistically most ened this argument by performing dynamical simulations likely to have physical lifetimes of ȁ12,000 years. Based on which showed that a cometary source beyond Neptune this estimate of physical lifetimes and the fact that there are with a low initial inclination distribution (which they ȁ110 active, visible JFCs with H T Ͻ 9, we conclude that there named the Kuiper belt) was far more consistent with the are currently ȁ1.2 ؋ 10 7 ecliptic comets (those with T Ͼ 2), observed orbits of most of these comets than the randomly of sizes consistent with this absolute magnitude, that originated distributed inclinations of comets in the Oort cloud (see in the Kuiper belt. This conclusion assumes that the rate of also Quinn et al. 1990). However, Duncan et al. (1988) and objects leaving the Kuiper belt has remained approximately Quinn et al. (1990) started their simulations with objects
constant over the history of the Solar System. We calculate the orbital distribution of this population and show that ȁ90% are that were already on unstable Neptune-encountering orbeyond the orbit of Neptune at any given time. In addition, we bits. Torbett (1989) showed that chaos induced by planecalculate the impact rates of these objects onto the planets. We tary perturbations might transform some nearly circular find that a JFC impact onto Jupiter happens approximately orbits beyond Neptune into trajectories which can encounonce every 400 years and one on the Earth should occur once ter Neptune-a suggestion which was later strengthened every 13 million years.