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The evolution of the orbits of bodies ejected from the Earth, Moon, Mercury and Mars was studied. At ejection velocities about 12-14 km/s, the fraction of bodies ejected from the Earth that fall back onto the Earth was about 0.15-0.25. The total number of bodies ejected from the Earth and delivered to the Earth and Venus probably did not differ much. The probability of collisions of bodies ejected from the Earth with the Moon moving in its present orbit was of the order of 0.01. Probabilities of collisions of bodies ejected from the Earth with Mercury were about 0.02-0.08 at ejection velocities greater than 11.3 km/s. The probabilities of collisions of bodies ejected from the Earth with Mars did not exceed 0.025. For the ejection of bodies from the present orbit of the Moon, probabilities of collisions of ejected bodies with planets were similar to those ejected from the Earth if we consider smaller ejection velocities from the Moon than from the Earth. The probability of a collision of a body ejected from Mars with Mars usually did not exceed 0.04 at an ejection velocity greater than 5.3 km/s. The fraction of bodies ejected from Mars and collided with Mercury was typically less than 0.08. Probabilities of collisions of bodies ejected from Mars with the Earth and Venus were about 0.1-0.2 (each) at an ejection velocity between 5.05 and 10 km/s. Most of bodies ejected from Mercury fall back onto Mercury. Probabilities of collisions of bodies ejected from Mercury with the Earth typically did not exceed 0.02 and 0.1 at an ejection velocity less than 8 km/s and 15 km/s, respectively. The fraction of bodies ejected from Mercury and collided with Venus was greater than that with the Earth typically by an order of magnitude. Probabilities of collisions of bodies with Venus were about 0.1-0.3 at a velocity of ejection from Mercury between 4.3 and 10 km/s., Comment: 6 pages. arXiv admin note: substantial text overlap with arXiv:2411.04218

The results of the numerical investigations of the evolution of orbits of trans-Neptunian bodies at the 2 : 3 resonance with Neptune are presented. The gravitational influence of the four giant planets was taken into account. For identical initial values of the semimajor axes, eccentricities, and inclinations, but for different initial orbital orientations and initial positions in orbits, we obtained different types of variations in the difference {\Delta}{\Omega}={\Omega}-{\Omega}_N in the ascending-node longitudes of the body and Neptune, and in the perihelion argument {\omega}. When {\Delta}{\Omega} decreases and {\omega} increases during evolution, then most of the bodies leave the resonance in 20 Myr. In the case of an increase in {\Delta}{\Omega} and a decrease in {\omega}, the bodies stay in the resonance for a much longer time. Regions of eccentricities and inclinations, for which some bodies were in the {\eta}_18 secular resonance ({\Delta}{\Omega} is almost constant) and in the Kozai resonance ({\omega} is almost constant), were obtained to be larger than those predicted for small variations in the critical angle. Some bodies can at the same time be in both these resonances., Comment: 14 pages, 2 fugures

A numerical integration of the equations of motion of the Sun-planets-an object system is used to study the evolution of orbits close to the orbit of the P/1996 R2 object, which is a Jupiter-crossing object, and to the asteroidal orbit of the P/1996 N2 object, which, at the moment of its detection, had a tail similar to a cometary one. Small variations in the initial data considerably affect the evolution of orbits close to that of the P/1996 R2 object. The time elapsed up to the ejection of the object into a hyperbolic orbit varied from 3*10^4 to 2.7*10^7 yr. Some objects were in resonances with Jupiter and Saturn for a long time. For about 20 percent of the runs, objects reached the Earth's orbit during evolution. Orbital elements of the P/1996 N2 object changed quasi-periodically over the considered time span of 200 Myr. Variations in the semimajor axis, eccentricity, and inclination were equal to 0.04 AU, 0.11 deg, and 3.5 deg, respectively., Comment: 14 pages, 2 figures

Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets were found., Comment: 7 pages, 1 fugure

Migration of bodies under the gravitational influence of almost formed planets was studied, and probabilities of their collisions with the Earth and other terrestrial planets were calculated. Based on the probabilities, several conclusions on the accumulation of the terrestrial planets have been made. The outer layers of the Earth and Venus could accumulate similar planetesimals from different regions of the feeding zone of the terrestrial planets. The probabilities of collisions of bodies during their dynamical lifetimes with the Earth could be up to 0.001-0.01 for some initial semi-major axes between 3.2 and 3.6 AU, whereas such probabilities did not exceed 10^-5 at initial semi-major axes between 12 and 40 AU. The total mass of water delivered to the Earth from beyond Jupiter's orbit could exceed the mass of the Earth's oceans. The zone of the outer asteroid belt could be one of the sources of the late-heavy bombardment. The bodies that came from the zone of Jupiter and Saturn typically collided with the Earth and the Moon with velocities from 23 to 26 km/s and from 20 to 23 km/s, respectively., Comment: Proc. IAU Symp. No. 374 "Astronomical Hazards for Life on Earth" (Busan, Rep. of Korea, August 9-11, 2022), ed. by G. Tancredi, Cambridge University Press, Manuscript ID IAU-22-0331, 6 p., in press

This study analyzes the motion of bodies ejected from the Earth or the Moon. We studied the ejection of bodies from several points on the Earth's surface, as well as from the most far point of the Moon from the Sun. Different velocities and angles of ejection of bodies were considered. The dynamical lifetimes of bodies reached a few hundred million years. Over the entire considered time interval, the values of the probability of a collision of a body ejected from the Earth with the Earth were approximately 0.3, 0.2, and 0.15-0.2 at an ejection velocity vej equaled to 11.5, 12, and 14 km/s, respectively. At vej<11.3 km/s, most of the ejected bodies fell back onto the Earth. The total number of bodies delivered to the Earth and Venus probably did not differ much. The probabilities of collisions of bodies with Mercury and Mars usually did not exceed 0.1 and 0.02, respectively. At vej>11.5 km/s, the probability of a collision of a body ejected from the Earth with the Moon was about 15-35 times less than that with the Earth, and it was about 0.01. The probability of a collision with the Earth for a body ejected from the Moon moving in its present orbit was about 0.3-0.32, 0.2-0.22, and 0.1-0.14 at vej=2.5 km/s, vej=5 km/s, and at 12

The motion of planetesimals was studied in the Proxima Centauri and TRAPPIST 1 exoplanetary systems. The size of the feeding zone of planet Proxima Centauri c is discussed. It was noted that after hundreds of Myrs, some planetesimals could still move in elliptical resonant orbits inside the feeding zone of this planet that had been mainly cleared from planetesimals. The probability of a collision of a planetesimal initially located in the feeding zone of planet c with inner planet b was obtained to be about 0.0002 and 0.001 at initial eccentricity of orbits of planetesimals equal to 0.02 or 0.15, respectively. A lot of icy material and volatiles could be delivered from the icy zone near the orbit of planet c to inner planets b and d. The inclinations of orbits of 80% of the planetesimals that moved between 500 or 1200 AU from the star did not exceed 10o. It was obtained that several planets in the TRAPPIST-1 system accumulated planetesimals initially located at the same distance. Outer layers of neighbouring TRAPPIST-1 planets can include similar material., Comment: Proc. IAU Symposium 393 "Planetary Science and Exoplanets in the Era of the James Webb Space Telescope" (August 13-15, 2024, Cape Town, South Africa). 5 pages, in press

A review of the results on the migration of celestial bodies in the Solar System and in some exoplanetary systems is presented. Some problems of planet accumulation and migration of planetesimals, small bodies and dust in the forming and present Solar System are considered. It has been noted that the outer layers of the Earth and Venus could have accumulated similar planetesimals from different areas of the feeding zone of the terrestrial planets.The formation of the embryos of the Earth and the Moon from a common rarefied condensation with subsequent growth of the main mass of the embryo of the Moon near the Earth is also discussed. The influence of changes in the semimajor axis of Jupiter's orbit on the formation of the asteroid belt is discussed, as well as the influence of planetesimals from the feeding zone of the giant planets on the formation of bodies beyond the orbit of Neptune. The migration of bodies to the terrestrial planets from different distances from the Sun is considered. It is noted that bodies from the feeding zone of the giant planets and from the outer asteroid belt could deliver to the Earth a quantity of water comparable to the mass of water in the Earth's oceans. The migration of bodies ejected from the Earth is considered. The probabilities of collisions of dust particles with the Earth are usually an order of magnitude greater than the probabilities of collisions of their parent bodies with the Earth. The migration of planetesimals is considered in exoplanetary systems Proxima Centauri and TRAPPIST-1. The amount of water delivered to the inner planet Proxima Centauri b, may have been more than the amount delivered to the Earth. The outer layers of neighboring planets in the TRAPPIST-1 system may contain similar material if there were many planetesimals near their orbits during the late stages of planetary accumulation., Comment: 14 pages

The motion of bodies ejected from the Earth was studied, and the probabilities of collisions of such bodies with the present terrestrial planets were calculated. The dependences of these probabilities on velocities, angles and points of ejection of bodies were studied. These dependences can be used in the models with different distributions of ejected material. On average, about a half and less than 10\% of initial ejected bodies remained moving in elliptical orbits in the Solar System after 10 and 100 Myr, respectively. A few ejected bodies collided with planets after 250 Myr. As dynamical lifetimes of bodies ejected from the Earth can reach hundreds of million years, a few percent of bodies ejected at the Chicxulub and Popigai events about 36-65 Myr ago can still move in the zone of the terrestrial planets and have small chances to collide with planets, including the Earth. The fraction of ejected bodies that collided with the Earth was greater for smaller ejection velocity. The fractions of bodies delivered to the Earth and Venus probably did not differ much for these planets and were about 0.2-0.3 each. Such obtained results testify in favour of that the upper layers of the Earth and Venus can contain similar material. The fractions of bodies ejected from the Earth that collided with Mercury and Mars did not exceed 0.08 and 0.025, respectively. The fractions of bodies collided with Jupiter were of the order of 0.001. In most calculations the fraction of bodies collided with the Sun was between 0.2 and 0.5. Depending on parameters of ejection, the fraction of bodies ejected into hyperbolic orbits could vary from 0 to 1. Small fractions of material ejected from the Earth can be found on other terrestrial planets and Jupiter, as the ejected bodies could collide with these planets. Bodies ejected from the Earth could deliver organic material to other celestial objects, e.g. to Mars., Comment: 24 pages, 4 figures

The evolution of the orbits of bodies ejected from the Earth has been studied at the stage of its accumulation and early evolution after impacts of large planetesimals. In the considered variants of calculations of the motion of bodies ejected from the Earth, most of the bodies left the Hill sphere of the Earth and moved in heliocentric orbits. Their dynamical lifetime reached several hundred million years. At higher ejection velocities vej the probabilities of collisions of bodies with the Earth and Moon were generally lower. Over the entire considered time interval at the ejection velocity vej, equal to 11.5, 12 and 14 km/s, the values of the probability of a collision of a body with the Earth were approximately 0.3, 0.2 and 0.15-0.2, respectively. At ejection velocities vej<11.25 km/s, i.e., slightly exceeding a parabolic velocity, most of the ejected bodies fell back to the Earth. The probability of a collision of a body ejected from the Earth with the Moon moving in its present orbit was approximately 15-35 times less than that with the Earth at vej>11.5 km/s. The probability of a collision of such bodies with the Moon was mainly about 0.004-0.008 at ejection velocities of at least 14 km/s and about 0.006-0.01 at vej=12 km/s. It was larger at lower ejection velocities and was in the range of 0.01-0.02 at vej=11.3 km/s. The Moon may contain material ejected from the Earth during the accumulation of the Earth and during the late heavy bombardment. At the same time, as obtained in our calculations, the bodies ejected from the Earth and falling on the Moon embryo would not be enough for the Moon to grow to its present mass from a small embryo moving along the present orbit of the Moon. This result argues in favor of the formation of a lunar embryo and its further growth to most of the present mass of the Moon near the Earth., Comment: 18 pages, 3 figures, 3 tables

Understanding the structural and magnetic properties in layered hybrid organic-inorganic metal halide perovskites (HOIPs) is key for their design and integration in spin-electronic devices. Here, we have conducted a systematic study on ten compounds to understand the effect of the transition metal (Cu$^{2+}$, Mn$^{2+}$, Co$^{2+}$), organic spacer (alkyl- and aryl-ammonium) and perovskite phase (Ruddlesden-Popper and Dion-Jacobson) on the properties of these materials. Temperature-dependent Raman measurements show that the crystals' structural phase transitions are triggered by the motional freedom of the organic cations as well as by the flexibility of the inorganic metal-halide lattice. In the case of Cu$^{2+}$ HOIPs, an increase of the in-plane anisotropy and a reduction of the octahedra interlayer distance is found to change the behavior of the HOIP from that of a 2D ferromagnet to that of a quasi-3D antiferromagnet. Mn$^{2+}$ HOIPs show inherent antiferromagnetic octahedra intralayer interactions and a phenomenologically rich magnetism, presenting spin-canting, spin-flop transitions and metamagnetism controlled by the crystal anisotropy. Co$^{2+}$ crystals with non-linked tetrahedra show a dominant paramagnetic behavior irrespective of the organic spacer and the perovskite phase. This work demonstrates that the chemical flexibility of HOIPs can be exploited to develop novel layered magnetic materials with tailored magnetic properties., Comment: 5 figures

We discuss problems of planetesimal migration in the emerging Solar System and exoplanetary systems. Protoplanetary disk evolution models and the formation of planets are considered. The formation of the Moon and of the asteroid and trans-Neptunian belts is studied. We show that Earth and Venus could acquire more than half of their mass in 5 million years, and their outer layers could accumulate the same material from different parts of the feeding zone of these planets. The migration of small bodies toward the terrestrial planets from various regions of the Solar System is simulated numerically. Based on these computations, we conclude that the mass of water delivered to the Earth by planetesimals, comets, and carbonaceous chondrite asteroids from beyond the ice line could be comparable to the mass of Earth's oceans. The processes of dust migration in the Solar System and sources of the zodiacal cloud are considered., Comment: 30 pages, 9 figures

The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7mE, mE is the mass of the Earth) to inner planets b and d were made. They included the studies of the total mass of planetesimals in the feeding zone of planet c and the probabilities of collisions of such planetesimals with inner planets. This total mass could be about 10-15mE. It was estimated based on studies of the ratio of the mass of planetesimals ejected into hyperbolic orbits to the mass of planetesimals collided with forming planet c. At integration of the motion of planetesimals, the gravitational influence of planets c and b and the star was taken into account. In most series of calculations, planetesimals collided with planets were excluded from integrations. Based on estimates of the mass of planetesimals ejected into hyperbolic orbits, it was concluded that during the growth of the mass of planet c the semi-major axis of its orbit could decrease by at least a factor of 1.5. Depending on possible gravitational scattering due to mutual encounters of planetesimals, the total mass of material delivered by planetesimals from the feeding zone of planet c to planet b was estimated to be between 0.002mE and 0.015mE. Probably, the amount of water delivered to Proxima Centauri b exceeded the mass of water in Earth's oceans. The amount of material delivered to planet d could be a little less than that delivered to planet b., Comment: 23 pages, 7 figures, 10 tables

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 figures

The paper discusses a model of the bombardment of the Earth and the Moon by small bodies when these planets were formed. It is shown that the total ice mass delivered with the bodies to the Earth from the feeding zone of the giant planets and the outer asteroid belt could have been comparable to the total mass of the Earth's oceans. Objects that initially crossed Jupiter's orbit could become Earth-crossers mainly within the first one million years. Most collisions of bodies originally located at a distance of 4 to 5 AU (astronomical units) from the Sun with the Earth occurred during the first ten million years. Some bodies from the Uranus and Neptune zones could fall onto the Earth in more than 20 million years. From their initial distances from the Sun of about 3 to 3.5 AU, some bodies could fall onto the Earth and Moon in a few billion years for the model that takes into account only the gravitational influence of the planets. The ratio of the number of bodies that collided with the Earth to the number of bodies that collided with the Moon varied mainly from 20 to 40 for planetesimals from the feeding zone of the terrestrial planets. For bodies originally located at a distance of more than 3 AU from the Sun, this ratio was mainly in the range between 16.4 and 17.4. The characteristic velocities of collisions of planetesimals from the feeding zones of the terrestrial planets with the Moon varied from 8 to 16 km/s, depending on the initial values of the semi-major axes and eccentricities of orbits of the planetesimals. The collision velocities of bodies that came from the feeding zones of Jupiter and Saturn with the Moon were mainly from 20 to 23 km/s., Comment: 8 pages

We present a study on the relationship between the ratio of the depth of a crater to its diameter and the diameter for lunar craters both on the maria and on the highlands. We consider craters younger than 1.1 billion years in age, i.e. of Copernican period. The aim of this work is to improve our understanding of such relationships based on our new estimates of the craters's depth and diameter. Previous studies considered similar relationships for much older craters (up to 3.2 billion years). We calculated the depths of craters with diameters from 10 to 100 km based on the altitude profiles derived from data obtained by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter (LRO). The ratio h/D of the depth h of a crater to its diameter D can diverge by up to a factor of two for craters with almost the same diameters. The linear and power approximations (regressions) of the dependence of h/D on D were made for simple and complex Copernican craters selected from the data from Mazrouei et al. (2019) and Losiak et al. (2015). For the separation of highland craters into two groups based only on their dependences of h/D on D, at D<18 km these are mostly simple craters, although some complex craters can have diameters D>16 km. Depths of mare craters with D<14 km are greater than 0.15D. Following Pike's (1981) classification, we group mare craters of D<15 km as simple craters. Mare craters with 1518 km are in a better agreement with the approximation curve of h/D vs. D for complex craters than for simple craters. At the same diameter, mare craters are deeper than highland craters at a diameter smaller than 30-40 km. For greater diameters, highland craters are deeper., Comment: 23 pages, 6 figures

We compare the number of lunar craters larger than 15 km across and younger than 1.1 Ga to the estimates of the number of craters that could have been formed for 1.1 Ga if the number of near-Earth objects and their orbital elements during that time were close to the corresponding current values. The comparison was performed for craters over the entire lunar surface and in the region of the Oceanus Procellarum and maria on the near side of the Moon. In these estimates, we used the values of collision probabilities of near-Earth objects with the Moon and the dependences of the crater diameters on the impactor sizes. According to the estimates made by different authors, the number density of known Copernican craters with diameters D>15 km in mare regions is at least double the corresponding number for the remaining lunar surface. Our estimates do not contradict the growth in the number of near-Earth objects after probable catastrophic fragmentations of large main-belt asteroids, which may have occurred over the recent 300 Ma; however, they do not prove this increase. Particularly, they do not conflict with the inference made by Mazrouei et al. (2019) that 290 Ma ago the frequency of collisions of near-Earth asteroids with the Moon increased by 2.6 times. For a probability of a collision of an Earth-crossing object (ECO) with the Earth in a year equaled to 10^-8, our estimates of the number of craters agree with the model, according to which the number densities of the 15-km Copernican craters for the whole lunar surface would have been the same as that for mare regions if the data by Losiak et al. (2015) for D<30 km were as complete as those for D>30 km. With this collision probability of ECOs with the Earth and for this model, the cratering rate may have been constant over the recent 1.1 Ga., Comment: 21 pages, 1 figure

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. 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. 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. 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 Mars) due to contraction of a rarefied condensation., Comment: 30 pages

From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter's orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth's embryo, when its mass was smaller than the current mass of the Earth. While the Earth's embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter's orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two-three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter's orbit could be less than that for the Earth by a factor not more than 20., Comment: 9 pages

Embryos of the Moon and the Earth may have formed as a result of contraction of a common parental rarefied condensation. The required angular momentum of this condensation could largely be acquired in a collision of two rarefied condensations producing the parental condensation. With the subsequent growth of embryos of the Moon and the Earth taken into account, the total mass of as-formed embryos needed to reach the current angular momentum of the Earth-Moon system could be below 0.01 of the Earth mass. For the low lunar iron abundance to be reproduced with the growth of originally iron-depleted embryos of the Moon and the Earth just by the accretion of planetesimals, the mass of the lunar embryo should have increased by a factor of 1.3 at the most. The maximum increase in the mass of the Earth embryo due to the accumulation of planetesimals in a gas-free medium is then threefold, and the current terrestrial iron abundance is not attained. If the embryos are assumed to have grown just by accumulating solid planetesimals (without the ejection of matter from the embryos), it is hard to reproduce the current lunar and terrestrial iron abundances at any initial abundance in the embryos. For the current lunar iron abundance to be reproduced, the amount of matter ejected from the Earth embryo and infalling onto the Moon embryo should have been an order of magnitude larger than the sum of the overall mass of planetesimals infalling directly on the Moon embryo and the initial mass of the Moon embryo, which had formed from the parental condensation, if the original embryo had the same iron abundance as the planetesimals. The greater part of matter incorporated into the Moon embryo could be ejected from the Earth in its multiple collisions with planetesimals (and smaller bodies)., Comment: 16 pages