The process of the transition of a comet nucleus from an initial heliocentric parabolic orbit into a heliocentric elliptical (parabolic with different parameters or hyperbolic) trajectory is investigated in terms of a pairwise three dimensional two-body problem: the Sun – comet nucleus and terrestrial planet — comet nucleus. Analytical formulas are reported for the orbital parameters of a nucleus after its passing through the sphere of influence of a terrestrial planet. It should be noted that the new minimal values of the orbital periods of the nuclei Ρ_min are within the limits 10-10⁴ years (Ρ_min for "families" of comets of Mercury, Venus, Earth, and Mars is equal to 10130, 34, 19, 632 tropical years, respectively). The angles between directions "the Earth - the Sun" and "the Earth - the planet (Mercury, Venus)", corresponding to the epochs of collisions of the comet nuclei with the Earth (or epochs of appearance of new meteor streams associated with existing or disintegrated comet nuclei) are determined. The bottleneck of revealing of such meteoroid complexes is concerned with the small value of the corresponding impact parameter. The value is on the order of magnitude of 10 % of the radius of the terrestrial type planet (whereas for the giant planets it is equal to 10 radii).