Why Halley-types resonate but long-period comets don't: a dynamical distinction between short- and long-period comets

Several recent studies have noted that the orbital evolution of many comets is influenced by mean-motion resonances with Jupiter. However, the distribution and relative importance of these resonances and the orbital characteristics of the comets affected have not been addressed to date. Here I show analytically that cometary orbits with periods greater than a critical value, [P.sub.c], (which depends upon the orbital inclination) are prevented from undergoing librations about a mean-motion resonance. Conversely, numerical integrations indicate that resonances play an important role in the dynamics of comets with P [less than] [P.sub.c]. The inclination-averaged value of [P.sub.c] approximately coincides with the traditional and arbitrary dividing line between Halley-type and long-period comets, which explains why many of the former are currently observed to be in resonance, whereas the latter are not. Thus, we now have a dynamical justification for separating comets into those of short and long period.