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Capture Statistics of Short-Period Comets: Implications for Comet D/Shoemaker–Levy 9

Abstract Comet D/Shoemaker–Levy 9 orbited Jupiter for decades (P. W. Chodas and D. K. Yeomans 1995, Bull. Am. Astron. Soc. 27, 1111–1112; L. A. M. Benner and W. B. McKinnon 1995, Icarus 118, 155–168) and was tidally disrupted during the orbit before impact. To estimate the rate of such events and to infer the implications for the comet's previous orbit, we have performed numerical integrations of test particles with orbits similar to those of Jupiter-family comets. We follow the dynamical evolution of 49,000 synthetic comets for ∼10 5 years and find 10,089 captures in which a comet completed more than one full orbit around Jupiter. Of these Jupiter-orbiting comets (“orbiters”), one in 112 undergoes a long capture, an event in which the comet orbits Jupiter for over 50 years. Captured bodies with mean orbital periods >3.5 years generally have jovicentric inclinations >120° and large perijove distances, while bodies with shorter orbital periods have smaller inclinations and are more likely to approach Jupiter closely. Long captures are more likely to include very close approaches to Jupiter. For example, long captures make up roughly one event in 15 in which an orbiter passes within 2.4 R J (Jupiter radii) of Jupiter's center (without immediately impacting the planet). Thus, if passage within ∼2.4 R J makes a comet observable by causing mass loss, the bias in favor of long capture events is a factor of eight over the general population of Jupiter-orbiting comets. About 15% of the comets that hit Jupiter are orbiting the planet at impact; approximately 1% impact after orbiting for more than 50 years. We infer that a 1-km comet impacts Jupiter once every 30–500 years, with a most probable interval of 240 years. Comets in orbit about Jupiter impact once every (0.2–3.5) × 10 3 years; orbiting comets impact one orbit after tidal disruption once every (0.1–2) × 10 5 years.