The Long-Term Dynamical Behavior of Short-Period Comets

We have developed and carefully tested a new computer code to follow the long-term dynamical evolution of a swarm of test particles in the solar system. This new integrator is approximately an order of magnitude faster than previously existing codes. The technique efficiently and accurately handles close approaches between test particles and planets while retaining the powerful features of recently developed mixed variable symplectic integrators. We use the new code to numerically integrate the orbits of the known short-period comets (those with periods P < 200 years) under the influence of the Sun and all the planets except Mercury and Pluto, for times up to 10 ⁷ years. It is found under a classification based on period that most comets move between Jupiter-family ( P < 20 yr) and Halley-family ( P > 20 yr) orbits many times in their dynamical lifetimes. However, it is found that the Tisserand parameter, T, does not vary substantially for most comets. Therefore, we adopt a classification originally suggested by Carusi et al. (1987) that defines Jupiter-family comets (JFCs) as comets with T > 2 and Halley-family comets (HFCs) as those with T < 2. In this scheme, less than 8% of comets change families during the integration and most of those that change tend to remain near the Tisserand dividing line throughout. Thus, the JFCs (as defined by the Tisserand parameter) are dynamically distinct from the HFCs. We find that in our forward integration, 92% of comets are ejected from the solar system, and that ≈6% are destroyed by becoming sun-grazers. The number of sun-grazers is far more than would be expected from the existing analytic theories. The median lifetime of all known short-period comets from the current time to ultimate destruction or ejection is approximately 4.5 × 10 ⁵ years. The very flat inclination distribution of Jupiter-family comets is found to become more distended as it ages. Since JFCs are dynamically distinct from HFCs, they must have an inclination distribution, when they first become visible, that is even flatter than that currently observed. For reasonable values of the physical lifetime before fading, we calculate that there should be roughly 5-20 times as many extinct JFCs as currently known JFCs. Our prediction for the mean cos ( i) of the extinct JFCs is consistent with the existing data on these objects.