Planetary perturbations for Oort Cloud comets. I. Distributions and dynamics

This paper is the first in a series, where we aim to model the injection of comets from the Oort Cloud so well that the shape of the energy distribution of long-period comets (i.e., the distribution of reciprocal semi-major axis) together with the observed rate of perihelion passages can be used to make serious inferences about the population size and energy distribution of the cloud. Here we explore the energy perturbations caused by the giant planets on long-period comets with perihelia inside or near the planetary system. We use a simplified dynamical model to integrate such perturbations for large samples of fictitious comets and analyse the statistics of the outcomes. After demonstrating the sensitivity of derived parameters to the sample size, when close encounters are involved, we derive a map of the RMS energy perturbation as a function of perihelion distance (q) and the cosine of the inclination (i), which compares well with the results of previous papers. We perform a critical analysis of the loss cone concept by deriving the “opacity” (chance of leaving the Oort spike by planetary perturbations per perihelion passage) as a function of q and cos i, concluding that the often made assumption of full opacity for q < 15 AU is seriously in error. While such a conclusion may also have been drawn from earlier studies, we provide the first full, quantitative picture. Moreover, we make a preliminary investigation of the long-term evolution of long-period comet orbits under the influence of planetary perturbations, neglecting the external effects of Galactic tides and stellar encounters. This allows us to make predictions about the production of decoupled objects like Halley-type comets and Centaurs from the injection of Oort Cloud comets, as well as of a related population of transneptunians deriving from the Oort Cloud with perihelia well detached from the planets.