Anisotropy of Long-period Comets Explained by Their Formation Process
  Long-period comets coming from the Oort cloud are thought to be planetesimals
formed in the planetary region on the ecliptic plane. We have investigated the
orbital evolution of these bodies due to the Galactic tide. We extended Higuchi
et al. (2007) and derived the analytical solutions to the Galactic longitude
and latitude of the direction of aphelion, $L$ and $B$. Using the analytical
solutions, we show that the ratio of the periods of the evolution of $L$ and
$B$ is very close to either 2 or $\infty$ for initial eccentricities $e_i\simeq
1$, as is true for the Oort cloud comets. From the relation between $L$ and
$B$, we predict that Oort cloud comets returning to the planetary region are
concentrated on the ecliptic plane and a second plane, which we call the "empty
ecliptic." This consists in a rotation of the ecliptic around the Galactic pole
by 180$^\circ$. Our numerical integrations confirm that the radial component of
the Galactic tide, which is neglected in the derivation of the analytical
solutions, is not strong enough to break the relation between $L$ and $B$
derived analytically. Brief examination of observational data shows that there
are concentrations near both the ecliptic and the empty ecliptic. We also show
that the anomalies of the distribution of $B$ of long-period comets mentioned
by several authors are explained by the concentrations on the two planes more
consistently than by previous explanations.
