Dynamical evolution of Halley-type comets

The dynamical evolution of Halley-type comets is studied by numerically integrating 10 variational orbits for each of 10 observed Halley-type comets for +/- 1 Myr or more. The principal features of the orbital evolution are determined by complex interactions between mean-motion resonances, secular perturbations and close encounters with planets. We find that high-order mean-motion resonances with respect to the motion of Jupiter occur frequently and with long duration, and also occasionally involve exceptionally high orders ranging up to 1/18. The median lifetime of Halley-type comets against dynamical ejection on to a hyperbolic orbit slightly exceeds 1 Myr, during which time the evolution is dominated by a variety of secular effects, including Kozai librations, secular resonances and Sun-grazing states. It is notable that strong secular resonances are the dominant process driving the long-term evolution of the perihelion distance, and that effects due to secular evolution are frequently present despite close encounters with planets. Although secular resonances associated with Jupiter's non-zero orbital eccentricity are dominant, examples of similar effects associated with both Uranus and Neptune are also found. Secular perturbations can also cause evolution of orbits from retrograde to prograde, and allow the perihelion distance to evolve from outside Saturn's orbit to within the orbit of the Earth. The connection between the evolution of Halley-type comets and related objects such as 96P/Machholz 1, (944) Hidalgo and (5335) Damocles is briefly discussed.