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Fig. 15. The differential distribution of LPCs as a function of the inverse semimajor axis. The big spike at 1/a < 10~4 is due to the new comets and is usually called the Oort spike. From [183]

the mass distribution in the galaxy (the so-called galactic tide) and by sporadic passing stars and giant molecular clouds (GMCs).

Assuming that the galaxy has a disk-like structure and considering that the Sun is not at the center, the galactic tide has both "disk" and "radial" force components. In a coordinate system centered on the Sun, with x-axis pointing away from the galactic center, y-axis in the direction of the galactic rotation, and z-axis toward the south galactic pole, the radial component of the tide can be expressed with forces along the x and y directions, respectively:

where Q0 is the frequency of revolution of the Sun around the galaxy. The disk component of the tide can be represented with a force along the z direction:

where p0 is the mass density in the solar neighborhood [76]. The disk component dominates over the radial component by a factor 8-10, so that typically only the disk component (12) is considered.

The effect of the disk tide is analogous to the Kozai effect for the dynamics of asteroids with high inclination relative to Jupiter's orbit [101]. In the following, I denote the inclination of the comet relative to the galactic plane by Z and the argument of perihelion by uz (not to be confused with the inclination i and the argument of perihelion u relative to the Solar System plane; the two planes are inclined at 120° relative to one other). The disk tide preserves a and the z-component of the angular momentum Hz = VI —e2 cos I of the comet, while its e and Z change with the precession of uz. This evolution is periodic; e has a maximum and Z a minimum when u = 90°, 270°, while e has

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