Orientation—dependent effects in Oort's theory of comet origin: I. Evolution of the orbital orientations and perihelion distances of long-period comets

Abstract

The orbital orientations and perihelion distances of long-period comets undergo appreciable systematic evolution due to planetary perturbations over many perihelion passages, and such evolution should have a significant bearing upon Oort's theory of comet origin. Once a comet has been captured into a long-period orbit, the effects of stellar perturbations upon its orbital orientation are generally small and random, so that the orientation is well defined from one perihelion passage to the next. The direct perturbation of Jupiter dominates the planetary perturbations; the indirect perturbations are small and random, while the principal effect of the combined direct perturbations of the other planets is to increase the rate of evolution by a factor of about 1.6. A method has been developed to calculate the mean evolution of a long-period orbit over many perihelion passages; the method is applicable to orbits with perihelion distances less than or on the order of 1 a.u. This technique has been applied to the numerical calculation of the evolution of 100 orbits with initially isotropic orientations and initial perihelion distances of 0.1 a.u. The results of these calculations are summarized in Table II. In this table, n is the number of perihelion passages since the injection of each hypothetical comet into a long-period orbit; A, B, and C are direction cosines which fix the orientation of the cometary orbit with respect to the plane of Jupiter's orbit (as defined in Section III); q is the perihelion distance; and Δ m a 0 is the minimum possible distance of approach of the comet to Jupiter, in units of Jupiter's semi-major axis. The more common orbital parameters are expressed in terms of the direction cosines in Eqs. (26), (27), and (28). In these calculations, the typical time scale of evolution was on the order of 100 perihelion passages. Long-period comets with larger perihelion distances will undergo similar evolution, but the mean evolution rate will be slower by a factor of about q −1 2 . The existence of an anamalously high correlation between the observed inclinations and latitudes of perihelion of the long-period comets can be explained at least qualitatively by this evolution.