Collisions With The Earth

The number of TNOs migrating to the inner regions of the Solar System can be evaluated on the basis of simple formulae and the results of numerical integration. Let Nj=PjnPnNjno be the number of former TNOs with d>D reaching Jupiter's orbit for the given time span Tss, where Ntno is the number of TNOs with d>D\ P/v is the fraction of TNOs leaving the EKB and migrating to Neptune's orbit during Tss'-, and pj/v is the fraction of Neptune-crossing objects which reach Jupiter's orbit for their lifetimes. Then the current number of Jupiter-crossers that originated in the zone with 30<a<50 AU equals Njn — NjAtj/Tss, where Atj is the average time during which the object crosses Jupiter's orbit. According to [8], the fraction P/v of TNOs that left this zone during 7ss=4 Gyr under the influence of the giant planets is 0.1-0.2 and pjn= 0.34. As mutual gravitational influence of TNOs also takes place [2], we take P/v = 0.2. Hence, at A£j=0.13 Myr and Ntno=1010 (¿>1 km), we have NJn=2 • 104. The number of former

TNOs now moving in Earth-crossing orbits equals Ne=Nj„T/Atj. The characteristic time Tcn between collisions of former TNOs with the Earth is T/(NjnP). For T=0.014 Myr and A£j=0.13 Myr, we have NE-2150 and T,cW~0.1 Myr. NE is larger than the estimated number Ne£ of Earth-crossers with ¿>1 km (750), and Tc=-T/P is larger than the characteristic time Tcoftil00 Myr ellapsed before a collision with the Earth is obtained for the fixed orbits of the observed NEOs. Such differences can be due to the fact that it is difficult to observe NEOs with high e and % and Nse doesn't include such NEOs. It may also be probable that the number of 1 km TNOs is smaller than lO10. As comets can obtain NEO and asteroidal orbits, a considerable portion of dust produced by NEOs and even some dust produced in the MAB, can be of cometary origin.

The total mass of water delivered to the Earth during the formation of the giant planets is Mw=MjPjEh, where Mj is the total mass of planetesimals from the feeding zones of these planets that became Jupiter-crossers during their evolution, Pje is a probability P of a collision of a former JCO with the Earth during its lifetime, and k{ is the proportion of water ice in the planetesimals. For Mj=100Mffi, ^¿=0.5, and Pje—6.65 • 10~6, we have Mw—3.3 • 10This value is greater by a factor of 1.5 than the mass of the Earth's oceans. The mass of water delivered to Venus can be of the same order of magnitude, and that delivered to Mars will be less by a factor of 3. Some TNOs with a>50 AU can also migrate to the orbits of Jupiter and Earth. Collisions of comets with small bodies and non-gravitational forces can decrease Q. Asher et al. [10] showed that the rate at which objects may be decoupled from Jupiter and attain NEO orbits is increased by a factor of four or five, if non-gravitational forces are included as impulsive effects. So the values of Pr and T can be larger than those in Table 1. Rickman et al. [11] also concluded that comets play an important role among all km-sized impactors. As it is easier to disrupt icy bodies than stone or metal bodies, the proportion of TNOs among NEOs for bodies with ci<100 m may be greater than that for 1 km bodies. Perhaps in the future, when people make settlements on the Moon and other terrestrial planets, small icy comets could be moved by rockets into orbits around these celestial bodies in order to be sources of water.

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