Abstract
An explanation is proposed for the observed and often discussed clustering of long-period comet aphelia on the sky. Poisson and several multinomial distributions are applied to the most conspicuous cluster, considering only the 80 "new" and 59 "intermediate" comets with the best-determined orbits. The observed number of aphelion points in adjacent areas in two tests with 24 and 36 equal sky areas, respectively, shows a large deviation from a random distribution. The expected probability frequency for this to happen by chance is <0.1% for the "new" comets alone; it is further reduced when "new" and "intermediate" comets are combined. When these comets are analyzed separately from others, it is found that the clustering is the result of perturbations of their original orbits by the passage of a star, or a stellar system, through Oort's cloud a few million years ago. Because the statistical effect on the change of a comet's angular momentum about the sun is proportional to the square of the ratio of the mass to the velocity of a star relative to the sun, it is a priori probable that passages by a few stars should produce clustering of the aphelia, as is discussed in detail.