Specifics of the Distribution of Orbits of Long-Period Comets in the Inner Part of the Oort Cloud

We investigate statistical patterns in the distribution of the orbits of long-period comets that belong to the inner region of the Oort cloud (with aphelion distances, Q, lying in the 50-2000 AU interval). We show that the distribution of aphelia is not random and such patterns can be due, in particular, to the presence of hypothetical massive bodies in the region considered. We varied the orbital parameters of such bodies to obtain two orbits such that each of them has the aphelia of 40 comets located within the 20-degree neighborhood of the orbit. This number is statistically significant. The orbits have the following parameters in the ecliptic coordinate system: P-1: Omega(P) = 297 degrees, i(P) = 24 degrees, Omega(P) = 322 degrees, e(P) = 0.6, a(P) = 510 AU; P-2: Omega(P) =92 degrees, i(P) = 80 degrees, Omega(P) =327 degrees, e(P) = 0.3, a(P) =1000 AU. For the adopted masses of these bodies we determined the minimum distances between their orbits and the orbits of the comets and estimated the number of aphelia located within the spheres of influence of these bodies. We found that the greatest number of aphelia are located near orbit P-1. However, their number is insufficient to conclude that massive bodies actually move in the inferred orbits. It is remarkable that the planes of orbits P-1 and P-2 in the Galactic coordinate system have the same inclinations (40 degrees) and longitudes of their ascending nodes are equal to 10 degrees and 170 degrees, i.e., the orbital planes are almost symmetric with respect to the direction toward the Galactic center. The concentration of orbital aphelia of the comets considered found in this study can therefore be due to the attraction from the Galactic center and/or complex motion of the Solar system.