The stellar perturbations of orbital elements of long-period comets

Abstract

Perturbations by nearby stars on orbital elements of comets with large heliocentric distances are calculated by the impulse approximation and by accurate numerical integration using Cowell's method. It is shown that the agreement is sufficiently close for elliptic orbits but rather poor for parabolic orbits. The perturbation of inclination is a few tens of degrees while that of perihelion distance, q, is from a few to a few tens of AU depending on mutual configurations. For very close encounters, δq can be a few hundred AU. Some cases have been found where an initially direct orbit is converted into a retrograde one and vice versa. For random encounters, statistical parameters which specify the distributions of orbital elements are calculated by the Monte Carlo method. For direct orbits, the perturbations are such as to increase i, while if the initial orbit is retrograde, the tendency is for i to decrease. An almost complete randomization of inclinations will take place within a few million yr. Again, q tends to increase by a few AU but the dispersion is much greater. Although the inclination is significantly perturbed, longitude and latitude of perihelion point are hardly perturbed. This may have an implication for cometary origin.