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Migration of matter from the Edgeworth-Kuiper, and main asteroid belts to the Earth
A considerable proportion of near-Earth objects could come from the trans-Neptunian belt. Some of them have aphelia deep inside Jupiter's orbit for > 1 Myr.
The main asteroid belt (MAB), the Edgeworth-Kuiper belt (EKB), and comets, represent the main sources of dust in the Solar System. Most of the Jupiter-family comets come from the EKB, and comets can be disrupted due to close encounters with planets or the Sun, collisions with small bodies, or by internal forces. We support [1,2] Eneev's idea  that the largest objects in the EKB and MAB could be formed directly from the compression of rarefied dust condensations in the protoplanetary cloud rather than by the accretion of small (for example, 1 km) planetesimals. The total mass of planetesimals that entered the EKB from the feeding zone of the giant planets during their accumulation, could exceed tens of Earth's masses Af® [4,5]. These planetesimals increased eccentricities of 'local' trans-Neptunian objects (TNOs) and swept most of these TNOs. A small portion of such planetesimals could be left beyond Neptune's orbit in highly eccentric orbits. The results of previous investigations of migration and collisional evolution of minor bodies were summarized in [6,2], Below we present mainly our recent results.
Asteroids leave the MAB via regions corresponding to resonances with Jupiter, Saturn, and Mars. They enter these regions mainly due to collisions, although gravitational influence of the largest asteroids plays a smaller role. The number of resonances delivering bodies to the Earth is not small (more than 15) , So even small changes in semimajor axis a, will allow some asteroids to enter the resonances. Thus the role of mutual gravitational influence of asteroids in their motion to the Earth may not be very small. Small bodies can also enter the resonant regions due to Yarkovsky orbital drift. For dust particles we also need to take into account the Poynting-Robertson effect, radiation pressure, and solar wind drag.
Objects leave the EKB mainly due to the gravitational influence of the planets . However, during the last 4 Gyr, several percent of the TNO population could change a by
•This work was supported by INTAS (00-240), RFBR (01-02-17540), and NASA (NAG5-10776).
more than 1 AU due to gravitational interactions with other TNOs . For most of the other TNOs, variations in a were less than 0.1 AU. The role of mutual gravitational influence of TNOs in the evolution of their orbits may be greater than that due to collisions. As even small variations in the orbital elements of TNOs can can lead to large variations in orbital elements due to the resulting gravitational influence of planets, TNOs could leave the EKB (and comets leave the Oort cloud) without collisions. Therefore, some cometary objects migrating into the Solar System could be large. The largest objects (with ¿>10 km) that have collided with the Earth during last 4 Gyr, could be of mainly cometary origin.
We investigated the evolution for intervals Ts>5 Myr, of 2500 Jupiter-crossing objects (JCOs) under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits, near the orbits of 30 real Jupiter-family comets with period <10 yr. In the second series we took 500 orbits, close to the orbit of Comet lOP/Tempel 2 (aw3.1 AU, ew0.53, ¿«12°). We calculated the probabilities of collision of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr, and then summarized the results for all time intervals and all bodies, obtaining the total probability P£ of collisions with a planet and the total time interval Ty, during which the perihelion distance q was less than the semimajor axis of the planet. The values of Pr=106, P=106, Pz/N and T=Tz/N are presented in the Table 1 together with the ratio r of the total time interval when orbits were of Apollo type (at a>l AU, q—a( 1 - e)<1.017 AU, e<0.999) to that of Amor type (1.017<g<1.33 AU); r2 is the same as r but for Apollo objects with eccentricity e<0.9. For observed near-Earth objects (NEOs) r is close to 1.
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