Asteroid-type orbit evolution near the 5:2 resonance

In this case of the 5:2 commensurability with the motion of Jupiter, an asteroid can reach the orbits of Mars, Earth, and Venus when eccentricity e is greater than 0.41, 0.65, and 0.74, respectively. For individual fictitious asteroids, Ipatov and Yoshikawa obtained a growth in e from 0.15 to 074-0.76. Rates of changes in orbital orientations are different for Mars, Earth, Venus, and the asteroid. Therefore, for corresponding values of e, the asteroid could encounter these planets and leave the gap at those encounters. In order to investigate this hypothesis of the 5:2 Kirkwood gap formation, Ipatov studied the regions of initial data for which the eccentricities of asteroids located near the 5:2 commensurability exceeded 0.41 during evolution. The orbit evolution for 500 fictitious asteroids was investigated by numerical integration of the complete (unaveraged) equations of motion for the three-body problem (Sun-Jupiter-asteroid). The equations of motion were integrated in the time intervals T is greater than or equal to 5(10)(exp 3)t(sub J) (t(sub J) is the heliocentric orbital period of Jupiter) in the planar model, T is greater than or equal to 10(exp 4)t(sub J) at initial inclination 5 deg is less than or equal to i(sub 0) is less than or equal to 20 deg and T = 10(exp 5)t(sub J) at i(sub 0) = 40 deg. The larger interval T was taken at i(sub 0) = 40 deg because in this case for the majority of runs maximum values of e and i were reached in the time delta(t) is greater than 2(10)(exp 4)t(sub J)

Migration of Jupiter-family comets and resonant asteroids to near-Earth space

We estimated the rate of comet and asteroid collisions with the terrestrial planets by calculating the orbits of 13000 Jupiter-crossing objects (JCOs) and 1300 resonant asteroids and computing the probabilities of collisions based on random-phase approximations and the orbital elements sampled with a 500 yr step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results for orbital evolution, but sometimes give different collision probabilities with the Sun. A small fraction of former JCOs reached orbits with aphelia inside Jupiter's orbit, and some reached Apollo orbits with semi-major axes less than 2 AU, Aten orbits, and inner-Earth orbits (with aphelia less than 0.983 AU) and remained there for millions of years. Though less than 0.1% of the total, these objects were responsible for most of the collision probability of former JCOs with Earth and Venus. Some Jupiter-family comets can reach inclinations i>90 deg. We conclude that a significant fraction of near-Earth objects could be extinct comets that came from the trans-Neptunian region.Comment: Proc. of the international conference "New trends in astrodynamics and applications" (20-22 January 2003, University of Maryland, College Park

Stable Orbits in the Feeding Zone of the Planet Proxima Centauri c

Estimates of the size of the feeding zone of the planet Proxima Centauri c have been made at initial orbital eccentricities of planetesimals equal to 0.02 or 0.15. The research is based on the results of modeling of the evolution of planetesimals' orbits under the influence of the star and planets Proxima Centauri c and b. The considered time interval reached a billion years. It was found that after the accumulation of the planet Proxima Centauri c some planetesimals may have continues to move in stable elliptical orbits within its feeding zone, largely cleared of planetesimals. Usually such planetesimals can move in some resonances with the planet (Proxima Centauri c), for example, in the resonance 1:1 (as Jupiter Trojans), 5:4 and 3:4 and usually have small eccentricities. Some planetesimals that moved for a long time (1-2 million years) along chaotic orbits fell into the resonances 5:2 and 3:10 with the planet Proxima Centauri c and moved in them at least tens of millions of years.Comment: 13 pages, 11 figure