Probabilities of Collisions of Planetesimals from Different Regions of the Feeding Zone of the Terrestrial Planets with the Forming Planets and the Moon

Abstract

Migration of planetesimals from the feeding zone of the terrestrial planets, which was divided into seven regions depending on the distance to the Sun, was simulated. The influence of gravity of all planets was taken into account. In some cases, the embryos of the terrestrial planets rather than the planets themselves were considered; their masses were assumed to be 0.1 or 0.3 of the current masses of the planets. The arrays of orbital elements of migrated planetesimals were used to calculate the probabilities of their collisions with the planets, the Moon, or their embryos. As distinct from the earlier modeling of the evolution of disks of the bodies coagulating in collisions, this approach makes it possible to calculate more accurately the probabilities of collisions of planetesimals with planetary embryos of different masses for some evolution stages. When studying the composition of planetary embryos formed from planetesimals, which initially were at different distances from the Sun, we considered the narrower zones, from which planetesimals came, as compared to those examined earlier, and analyzed the temporal changes in the composition of planetary embryos rather than only the final composition of planets. Based on our calculations, we drew conclusions on the process of accumulation of the terrestrial planets. The embryos of the terrestrial planets, the masses of which did not exceed a tenth of the current planetary masses, accumulated planetesimals mainly from the vicinity of their orbits. When planetesimals fell onto the embryos of the terrestrial planets from the feeding zone of Jupiter and Saturn, these embryos had not yet acquired the current masses of the planets, and the material of this zone (including water and volatiles) could be accumulated in the inner layers of the terrestrial planets and the Moon. For planetesimals which initially were at a distance of 0.7-0.9 AU from the Sun, the probabilities of their infall onto the embryos of the Earth and Venus, the mass of which is 0.3 of the present masses of the planets, differed less than twofold for these embryos. The total mass of planetesimals, which initially were in each part of the region between 0.7 and 1.5 AU from the Sun and collided with the almost-formed Earth and Venus, apparently differed by less than two times for these planets. The inner layers of each of the terrestrial planets were mainly formed from the material located in the vicinity of the orbit of a certain planet. The outer layers of the Earth and Venus could accumulate the same material for these two planets from different parts of the feeding zone of the terrestrial planets. The Earth and Venus could acquire more than half of their masses in 5 Myr. The material ejection that occurred in impacts of bodies with the planets, which was not taken into account in the model, may enlarge the accumulation time for the planets. A relatively rapid growth of the bulk of the Martian mass can be explained by the formation of Mars' embryo (the mass of which is several times less than that of...

Number of Near-Earth Objects and Formation of Lunar Craters over the Last Billion Years

“…Gladman et al (2000) obtained that the median lifetime of NEOs is around 100 Ma. In the paper by Ipatov (2019b), for the bodies with semimajor axes of initial orbits not exceeding 1.5 AU and initial eccentricities of 0.05 and 0.3, the median dynamical lifetime did not exceed 20 Ma. Consequently, the destruction of the asteroid, which induced the present increase in the number of NEOs (in relation to the mean value for the recent billion years), could occur relatively recently rather than 160 Ma ago, as Bottke et al (2006) believed.…”

“…The algorithms for calculating the probabilities of collisions of bodies with planets were used by Ipatov (2000Ipatov ( , 2019b to study the process of accumulation of planets. These algorithms are oriented to considering the collision probabilities of numerous planetesimals over long time periods.…”

“…The model results for the evolution of disks of the gravitating bodies, which are coagulated in collisions, showed that, in the final stages of the Earth's accumulation, the mean eccentricities of orbits of planetesimals could exceed 0.4 (Ipatov, 1993), i.e., they might be comparable to the orbital eccentricities of present ECOs. From the velocities of collisions of planetesimals with the almost completely formed Earth, Ipatov (2019b) concluded that the orbital eccentricities of most planetesimals that impacted the Earth exceeded 0.3. Because of this, it can hardly be supposed that the values of TE for planetesimals, which fell onto the almost completely formed Earth, were substantially smaller than those for presently existing ECOs.…”

Formation of the Earth and Moon: Influence of Small Bodies

“…Data on a span of 20 million years are presented for a larger statistics. Ipatov (2019) arrived at the conclusion that the Earth and Moon have acquired more than half of their masses over a time period of no longer than five million years. Using a formula analogous to (2), we have calculated the vrelE01 values (Table 2) of the relative entry velocities of planetesimals into the action sphere of the Earth's embryo.…”

“…In the calculation variants discussed herein, the ratio rEM of the number of bodies that have fallen onto the Earth to the number of bodies fallen onto the Moon was smaller than the mass ratio of these celestial objects. Calculations of the migration of planetesimals in the feeding zone of the terrestrial planets (Ipatov, 2019) may lead to the conclusion that the ratio rEM of the number of planetesimals colliding with the Earth to that colliding with the Moon mostly varied from 20 to 40. The reason for the scatter of this ratio is that the considered planetesimals have different initial values of the semi-major axes and eccentricities of the orbits.…”