The long-term dynamical evolution of comet Swift-Tuttle.

Abstract

Periodic comet Swift-Tuttle is the largest known object in the Solar System whose current orbit allows it to make repeated close approaches to the Earth. As such it poses a significant impact hazard. In addition, P/Swift-Tuttle possesses the second longest observing are of any comet, with recorded observations spanning two millennia. These data place extremely tight constraints on the current orbit. This paper analyzes the likely dynamical evolution of P/Swift-Tuttle for 40,000 years centered on the present. The evolution is uncertain prior to the earliest observations in 69 BC; however, given that nongravitational forces appear to be negligible, the future evolution is clear until an exceptionally close encounter with Earth in 4479 AD. Beyond this date, the current librations about the 1:11 mean-motion resonance with Jupiter will continue until at least 7000 AD, while the orbital descending node is likely to remain within 0.1 AU of Earth's orbit for the next 20,000 years. The resonant librations increase the orbit's Lyapunov time by a factor of two in the future and strongly influence the movement of the orbital nodes. The librations are maintained by indirect rather than direct planetary perturbations, which explains why a retrograde comet of such long orbital period is located in a resonance, and why Jupiter is the resonant planet. After 4479 the probability of impacting Earth is roughly 2 × 10 ^-8 per revolution until 12,000 AD, while the chance of a collision in 4479 is of order 1 in 10 ⁶.