On the Problem of Searching for Undiscovered Cometary Families Colliding with Terrestrial Type Planets

N. I. Perov, D. V. Kolesnikov

Protecting the Earth against Collisions with Asteroids and Comet Nuclei, In: A. M. Finkelstein, W. F. Huebner, V. A. Shor (Eds) Proceedings of the International Conference “Asteroid-Comet Hazard-2009”, StP: Nauka, 146–151 (2010)

Ключевые слова: Very Long Baseline Interferometry (VLBI), Near Earth Objects (NEOs), cometary families, terrestrial type planets, collidings, transition of a comet nucleus, initial heliocentric parabolic orbit, heliocentric elliptical trajectory, a pairwise three dimensional two-body problem, the Sun - comet nucleus, terrestrial planet - comet nucleus, orbital parameters of a nucleus, sphere of influence of a terrestrial planet, orbital periods of the nuclei, "families" of comets, Mercury, Venus, Earth, Mars, tropical years, angles between directions, "the Earth - the Sun" direction, "the Earth - the planet" direction, epochs of collisions of the comet nuclei with the Earth, epochs of appearance of new meteor streams, existing or disintegrated comet nuclei, meteoroid complexes, impact parameters, the magnitude, the radius of the terrestrial type planet, giant planets

Аннотация

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 are within the limits 10-10 years ( 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)