Sergei Ipatov - Academia.edu (original) (raw)

Papers by Sergei Ipatov

Astrophysical Journal, v. 708, 1268-1280, 2010

The discovery of decay products of a short-lived radioisotope (SLRI) in the Allende meteorite led... more The discovery of decay products of a short-lived radioisotope (SLRI) in the Allende meteorite led to the hypothesis that a supernova shock wave transported freshly synthesized SLRI to the presolar dense cloud core, triggered its self-gravitational collapse, and injected the SLRI into the core. Previous multidimensional numerical calculations of the shock–cloud collision process showed that this hypothesis is plausible when the shock wave and dense cloud core are assumed to remain isothermal at ∼10 K, but not when compressional heating to ∼1000 K is assumed. Our two-dimensional models with the FLASH2.5 adaptive mesh refinement hydrodynamics code have shown that a 20 km s^−1 shock front can simultaneously trigger collapse of a 1M core and inject shock wave material, provided that cooling by molecular species such as H2O, CO, and H_2 is included. Here, we present the results for similar calculations with shock speeds ranging from 1 km s^−1 to 100 km s^−1. We find that shock speeds in the range from 5 km s^−1 to 70 km s^−1 are able to trigger the collapse of a 2.2M_Sun cloud while simultaneously injecting shock
wave material: lower speed shocks do not achieve injection, while higher speed shocks do not trigger sustained collapse. The calculations continue to support the shock-wave trigger hypothesis for the formation of the solar system, though the injection efficiencies in the present models are lower than desired.

Kinematics and Physics of Celestial Bodies, v. 4, N 4, pp. 49-57, 1988

The time dependence of the orbital elements of some fictitious asteroids in the case of 1:3, 2:5,... more The time dependence of the orbital elements of some fictitious asteroids in the case of 1:3, 2:5, and 1:2 commensurabilities with Jovian motion are studied via numerical integration of the equations of motion of the planar three-body problem. The time interval studied amounted to 35,000 revolutions of Jupiter around the sun. The orbits of many of the fictitious asteroids from the 1:2 and 2:5 gaps acquired such eccentricities during evolution that their perihelia lie inside the Martian orbit. Asteroid encounters with Mars may be one of the reasons for the formation of these gaps.

Kinematics and Physics of Celestial Bodies, v. 4, pp. 76-82, 1988

The variations of the orbital elements of three gravitationally interacting bodies moving around ... more The variations of the orbital elements of three gravitationally interacting bodies moving around the Sun in the same plane are investigated by numerical solution of the equations of motion of the four-body problem. The mases of the bodies are about equal to that of Pluto, and their initial orbits are circular. In the variant considered, the eccentricity of the orbit of one of the bodies increases to 0.05 after about 2.5*10^5 revolutions of the bodies around the Sun, and its perihelion distance decreased by 10%. The subsequent evolution of the orbit can be investigated by the method of spheres of action. It is found with the aid of this method that the perihelion distance of one of the bodies may increase by half during approximately 10^7 revolutions of the body around the Sun. The results of these studies indicate that certain bodies of the trans-Neptunian belt (which T.M. Eneev believes included Pluto) may have migrated to the orbit of Neptune.

Solar System Research, 1995, v. 29, p. 9-20, 1995

The evolution of two, three, and one hundred gravitating objects, i.e., material points moving ar... more The evolution of two, three, and one hundred gravitating objects, i.e., material points moving around the Sun in crossing orbits, is investigated numerically, mainly by the action spheres method. It is demonstrated that in the case of three identical objects, maximum eccentricities can exceed those for two like objects by a factor of several tens. Eccentricities of heliocentric orbits of objects moving in a sphere of action are examined to reveal the dependence of their mean variations on the starting data, i.e., masses, eccentricities, and semimajor axes. The results of these examinations and analytical evaluations provide a basis for treating cases, where, in the course of the evolution of a disk comprising many small objects and that comprising a lesser number of bigger objects, the increments of average eccentricities are the same. The obtained results suggest that, due to their gravitational interaction, the possibility of migration of several bodies to Neptune's from the belt beyond the Neptune exists.

Solar System Research, 2024

A review of the results on the migration of celestial bodies in the Solar System and in some exop... more 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. In addition to the theory of coaccretion and the mega-impact and multi-impact models, 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. Along with the Nice model and the “grand tack” model, a model is considered in which the embryos of Uranus and Neptune increased the semimajor axes of their orbits from values of no more than 10 AU to present values only due to gravitational interactions with planetesimals (without the motions of Jupiter and Saturn entering into resonance). 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. It is noted that about 20% of the ejected bodies that left the Earth’s sphere of influence eventually fell back to the Earth. 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.

Icarus, v. 425, id. 116341 (24 p.) , 2025

During formation of the Earth and at the stage of the Late Heavy Bombardment, some bodies collide... more During formation of the Earth and at the stage of the Late Heavy Bombardment, some bodies collided with the Earth. Such collisions caused ejection of material from the Earth. 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.

Solar System Research, Nov 30, 2023

The motion of planetesimals initially located in the feeding zone of the planet Proxima Centauri ... more The motion of planetesimals initially located in the feeding zone of the planet Proxima Centauri c, at distances of 500 AU from the star to the star's Hill sphere radius of 1200 AU was considered. In the analyzed non-gaseous model, the primary ejection of planetesimals from most of the feeding zone of an almost formed planet c to distances greater than 500 AU from the star occurred during the first 10 million years. Only for planetesimals originally located at the edges of the planet's feeding zone, the fraction of planetesimals that first reached 500 AU over the time greater than 10 million years was more than half. Some planetesimals could reach the outer part of the star's Hill sphere over hundreds of millions of years. Approximately 90% of the planetesimals that first reached 500 AU from Proxima Centauri first reached 1200 AU from the star in less than 1 million years, given the current mass of the planet c. No more than 2% of planetesimals with aphelion orbital distances between 500 and 1200 AU followed such orbits for more than 10 million years (but less than a few tens of millions of years). With a planet mass equal to half the mass of the planet c, approximately 70-80% of planetesimals increased their maximum distances from the star from 500 to 1200 AU in less than 1 million years. For planetesimals that first reached 500 AU from the star under the current mass of the planet c, the fraction of planetesimals with orbital eccentricities greater than 1 was 0.05 and 0.1 for the initial eccentricities of their orbits e o = 0.02 and e o = 0.15, respectively. Among the planetesimals that first reached 1200 AU from the star, this fraction was approximately 0.3 for both e o values. The minimum eccentricity values for planetesimals that have reached 500 and 1200 AU from the star were 0.992 and 0.995, respectively. In the considered model, the disk of planetesimals in the outer part of the star's Hill sphere was rather flat. Inclinations i of the orbits for more than 80% of the planetesimals that first reached 500 or 1200 AU from the star did not exceed 10°. With the current mass of the planet c, the percentage of such planetesimals with i > 20°d id not exceed 1% in all calculation variants. The results may be of interest for understanding the motion of bodies in other exoplanetary systems, especially those with a single dominant planet. They can be used to provide the initial data for models of the evolution of the disk of bodies in the outer part of Proxima Centauri's Hill sphere, which take into account gravitational interactions and collisions between bodies, as well as the influence of other stars. The strongly inclined orbits of bodies in the outer part of Proxima Centauri's Hill sphere can primarily result from bodies that entered the Hill sphere from outside. The radius of Proxima Centauri's Hill sphere is an order of magnitude smaller than the radius of the outer boundary of the Hills cloud in the Solar System and two orders of magnitude smaller than the radius of the Sun's Hill sphere. Therefore, it is difficult to expect the existence of a similarly massive cloud around this star as the Oort cloud around the Sun.

Solar System Research, v. 58, pp. 94-111, 2024

The evolution of the orbits of bodies ejected from the Earth has been studied at the stage of its... more 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 v ej the probabilities of collisions of bodies with the Earth and Moon were generally lower. Over the entire considered time interval at the ejection velocity v ej , 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 v ej ≤ 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 v ej ≥ 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 v ej = 12 km/s. It was larger at lower ejection velocities and was in the range of 0.01-0.02 at v ej = 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. It seems more likely to us that the initial embryo of the Moon with a mass of no more than 0.1 of the mass of the Moon was formed simultaneously with the embryo of the Earth from a common rarefied condensation. For more efficient growth of the Moon embryo, it is desirable that during some collisions of impactor bodies with the Earth, the ejected bodies do not simply fly out of the crater, but some of the matter goes into orbits around the Earth, as in the multi-impact model. The average velocity of collisions of ejected bodies with the Earth is greater at a greater ejection velocity. The values of these collision velocities were about 13, 14-15, 14-16, 14-20, 14-25 km/s with ejection velocities equal to 11.3, 11.5, 12, 14 and 16.4 km/s, respectively. The velocities of collisions of bodies with the Moon were also higher at high ejection velocities and were mainly in the range of 7-8, 10-12, 10-16 and 11-20 km/s at v ej , equal to 11.3, 12, 14 and 16.4 km/s, respectively.

System Research, 2023, v. 57, N 6. P. 612-628. , 2023

Meteoritics and Planetary Science, 2023

The model and initial data used for calculations: The model of migration of planetsimals initiall... more The model and initial data used for calculations: The model of migration of planetsimals initially located in the feeding zone of the exoplanet c with a semi-major axis ac=1.489 AU in the Proxima Centauri system was studied. The aim of these studies is to compare the delivery of icy planetesimals to potentially habitable planets in the Proxima Centauri system and in our Solar System. Integration of the motion of planetesimals and exoplanets was calculated with the use of the symplectic code from [1] for a star with a mass equal to 0.122 of the solar mass and two exoplanets. It was considered that the exoplanet b is located in a habitable zone. In the main series M of calculations, based on recent observational data, the following initial semi-major axes, eccentricities, inclinations and masses of two exoplanets were considered: ab=0.04857 AU, eb=0.11, mb=1.17mE, ac=1.489 AU, ec=0.04, mc=7mE, ib=ic=0, where mE is the mass of the Earth. In the series F of calculations, based on older observations, it was considered that ab=0.0485 AU, ac=1.489 AU, mb=1.27mE, mc=12mE, eb=ib=0, ic=ec/2=0.05 rad or ic=ec=0. In each calculation variant, initial semimajor axes of orbits of 250 exocomets were in the range from amin to amin+0.1 AU, with amin from 1.2 to 1.7 AU with a step of 0.1 AU. Initial eccentricities eo of orbits of planetesimals equaled to 0.02 or 0.15 for the M series, and equaled to 0 or 0.15 for the F series of calculations. Initial inclinations of orbits of the planetesimals equaled to eo/2 rad. Considered time interval exceeded 50 Myr. Based on the obtained arrays of orbital elements of migrated planetesimals and exoplanets stored with a step of 100 yr, I calculated the probabilities of collisions of planetesimals with the exoplanets. The probabilities of collisions were calculated also with the unconfirmed exoplanet d (ad=0.02895 AU, md=0.29mE, ed=id=0). The calculations were made similar to those in [2-4]. Probabilities of collisions of planetesimals with the exoplanet c: For the M series of calculations, the values of the probability pс of a collision of one planetesimal, initially located near the exoplanet c, with this exoplanet were about 0.1-0.3, exclusive for amin=1.4 AU and eo=0.02 when pс was about 0.6. For the F series of calculations at iс=eс=0 and eo=0.15, pс was about 0.06-0.1. For ic=ec/2=0.05 and eo=0.15, pс was about 0.02-0.04. For both series of calculations, most of planetesimals were usually ejected into hyperbolic orbits in 10 Myr. Usually there was a small growth of pc after 20 Myr. In some calculations a few planetesimals could still move in elliptical orbits after 100 Myr. The number of planetesimals ejected into hyperbolic orbits was greater by a factor of several than the number of planetesimals collided with exoplanets. Therefore, a cometary cloud similar to the Oort cloud can exist in the Proxima Centauri system. Probabilities of collisions of planetesimals with the exoplanets b and d: For the M series of calculations, the probability pb of a collision of one planetesimal, initially located near the orbit of the exoplanet c, with the exoplanet b was non-zero in 5 among 18 variants at eo=0.02 and in 3 among 6 variants at eo=0.15. At eo=0.02 for the five variants, pb equaled to 0.004, 0.004, 1.28×10-5 , 0.00032 и 9.88×10-5. At eo=0.02 the mean value of pb for one of 4500 exocomets equaled to 4.7×10-4 , but among them there were two planetesimals with pb≈1. At eo=0.15 for three variants, pb equaled to 0.008, 0.004 and 3.6×10-6. The mean value of pb for one of 1500 exocomets equaled to 2.0×10-3 , but among them there were three planetesimals with pb≈1. The mean value of the probability pd of a collision of a planetesimal with the exoplanet d equaled to 2.7×10-4 and 2.0×10-3 at eo=0.02 and eo=0.15, respectively. For the M series, the mean values of pb and pd averaged over 6000 planetesimals equaled to 8.5×10-4 and 7.0×10-4. For all three considered variants of the series F at ec=0.1 and eo=0.15, the values of pb were in the range 0.008-0.019. For other calculations of the F series, pb=0. Only one of several hundreds of planetesimals reached the orbits of the exoplanet b and d, but the probabilities pb and pd of a collision of one planetesimal with these exoplanets (averaged over thousands planetesimals) are greater than the probability of a collision with the Earth of a planetesimal from the zone of the giant planets in the Solar System. The latter probability for most calculations with 250 planetesimals was less than 10-5 per one planetesimal [5]. Therefore, a lot of icy material could be delivered to the exoplanets b and d. Acknowledgments: For studies of formation of exoplanets and of the ejection of exocomets into hyperbolic orbits, the author acknowledges the support of Ministry of Science and Higher Education of the Russian Federation under the grant 075-15-2020-780 (N13.1902.21.0039). Migration of icy planetesimals to exoplanets located in the habitable zone was carried out…

Probabilities of collisions of migrating small bodies and dust particles produced by these bodies... more Probabilities of collisions of migrating small bodies and dust particles produced by these bodies with planets were studied. Various Jupiter-family comets, Halley-type comets, longperiod comets, trans-Neptunian objects, and asteroids were considered. The total probability of collisions of any considered body or particle with all planets did not exceed 0.2. The amount of water delivered from outside of Jupiter's orbit to the Earth during the formation of the giant planets could exceed the amount of water in Earth's oceans. The ratio of the mass of water delivered to a planet by Jupiter-family comets or Halley-type comets to the mass of the planet can be greater for Mars, Venus, and Mercury, than that for Earth.

Solar System Research, 2023

Estimates of the size of the feeding zone of the planet Proxima Centauri c have been made at init... more 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 continued 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 resonances 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 for at least tens of millions of years.

Solar System Research, 2023

Meteoritics and Planetary Science, 2023

The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (w... more The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7m E , m E 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 10-15m E. 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 0.002m E and 0.015m E. 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.

Advances in Geochemistry, Analytical Chemistry, and Planetary Sciences: 75th Anniversary of the Vernadsky Institute of the Russian Academy of Sciences. Ed. by V.P. Kolotov and N.S. Bezaeva. Springer. Cham. Springer eBooks, 2023

This paper is based on the studies made by leading researchers of the Laboratory of thermodynamic... more This paper is based on the studies made by leading researchers of the Laboratory of thermodynamics and mathematical modeling of natural processes at the Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences in the field of cosmogony, geochemistry and cosmochemistry. The main research method is mathematical modeling using the restrictions obtained from experimental studies of bodies of the Solar System and exoplanetary systems. Verification of models is also carried out by comparing the obtained results and available experimental data. The article consists of four sections reflecting the main directions of the laboratory’s work. The section “Studies in the field of stellar-planetary cosmogony is written by scientists under the leadership of Academician M. Ya. Marov. The section includes studies of the formation and evolution of dust clusters, primary bodies, the terrestrial planets, and some exoplanets, the delivery of water to the terrestrial planets, and the problem of the asteroid-comet hazard. The sections containing the results of the study of the internal structure of the satellites—the Moon and Titan, were carried out under the guidance of the Corresponding Member of RAS O. L. Kuskov. The section “Estimation of the composition and mass of the ice component in primary ice-rock bodies of the protoplanetary disk” contains some results obtained by D.Sc. V. A. Dorofeeva in the study of the behavior and conditions of accumulation of volatile components in the early Solar System.

ASTRONOMY AT THE EPOCH OF MULTIMESSENGER STUDIES. Proceedings of the VAK-2021 conference, Aug 23–28, 2021, Feb 22, 2022

Bulletin of the American Astronomical Society, Mar 1, 2021

For the Proxima Centauri planetary system, most of planetesimals from the vicinity of the exoplan... more For the Proxima Centauri planetary system, most of planetesimals from the vicinity of the exoplanet “c” with a semi-major axis ac of about 1.5 AU were ejected into hyperbolic orbits in 10 Myr. Some planetesimals could collide with this exoplanet after 20 Myr. Only one of several hundreds of planetesimals from the vicinity of this exoplanet reached the orbit of the exoplanet “b” with a semi-major axis ab=0.0485 AU or the orbit of the exoplanet “d” with a semi-major axis ad=0.029 AU, but the probability of a collision of such planetesimal (that reached the orbits) with the exoplanets b and d can reach 1, and the collision probability averaged over all planetesimals from the vicinity of the exoplanet “c” was ~10-3. If averaged over all considered planetesimals from the vicinity of exoplanet “c”, the probability of a collision of a planetesimal with the exoplanet “b” or “d” is greater than the probability of a collision with the Earth of a planetesimal from the zone of the giant planets in the Solar System (which is less than 10-5 per one planetesimal). A lot of icy material could be delivered to the exoplanets “b” and “d”.

ASTRONOMY AT THE EPOCH OF MULTIMESSENGER STUDIES. Proceedings of the VAK-2021 conference, Aug 23–28, 2021, 2022

The amounts of material from diﬀerent parts of the zone from 0.7 to 1.5 AU from the Sun, which en... more The amounts of material from diﬀerent parts of the zone from 0.7 to 1.5 AU from the Sun, which entered into almostformed the Earth and Venus, diﬀered for these planets by no more than 3 times. For the TRAPPIST exoplanetary system,the ratio of the fraction of planetesimals collided with the planet, around which orbit initial orbits of planetesimals werelocated, to the fraction of planetesimals collided with the neighbouring planet was typically less than 4. Embryos of theEarth and the Moon with a total mass equaled to about 0.01-0.1 Earth mass could be formed as a result of compressionof a rareﬁed condensation. The fraction of material ejected from the Earth’s embryo and acquired by the Moon’s embryocould exceed by an order of magnitude the sum of the total mass of the planetesimals acquired by the Moon’s embryo andof the initial mass of the Moon’s embryo.

Science, 2005

Deep Impact collided with comet Tempel 1, excavating a crater controlled by gravity. The comet&#3... more Deep Impact collided with comet Tempel 1, excavating a crater controlled by gravity. The comet's outer layer is composed of 1- to 100-micrometer fine particles with negligible strength (<65 pascals). Local gravitational field and average nucleus density (600 kilograms per cubic meter) are estimated from ejecta fallback. Initial ejecta were hot (>1000 kelvins). A large increase in organic material occurred during and after the event, with smaller changes in carbon dioxide relative to water. On approach, the spacecraft observed frequent natural outbursts, a mean radius of 3.0 Â± 0.1 kilometers, smooth and rough terrain, scarps, and impact craters. A thermal map indicates a surface in equilibrium with sunlight.

Uspekhi Fizicheskih Nauk = Physics – Uspekhi, 2023

We discuss problems of planetesimal migration in the emerging Solar System and exoplanetary syste... more 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.

Astrophysical Journal, v. 708, 1268-1280, 2010

Kinematics and Physics of Celestial Bodies, v. 4, N 4, pp. 49-57, 1988

Kinematics and Physics of Celestial Bodies, v. 4, pp. 76-82, 1988

Solar System Research, 1995, v. 29, p. 9-20, 1995

Solar System Research, 2024

Icarus, v. 425, id. 116341 (24 p.) , 2025

Solar System Research, Nov 30, 2023

Solar System Research, v. 58, pp. 94-111, 2024

System Research, 2023, v. 57, N 6. P. 612-628. , 2023

Meteoritics and Planetary Science, 2023

Solar System Research, 2023

Meteoritics and Planetary Science, 2023

ASTRONOMY AT THE EPOCH OF MULTIMESSENGER STUDIES. Proceedings of the VAK-2021 conference, Aug 23–28, 2021, Feb 22, 2022

Bulletin of the American Astronomical Society, Mar 1, 2021

ASTRONOMY AT THE EPOCH OF MULTIMESSENGER STUDIES. Proceedings of the VAK-2021 conference, Aug 23–28, 2021, 2022

Science, 2005

Uspekhi Fizicheskih Nauk = Physics – Uspekhi, 2023

Modern astronomy: from the Early Universe to exoplanets and black holes. 2024. P. 904-909, 2024

The evolution of the orbits of bodies ejected from the Earth, Moon, Mercury and Mars was studied.... more The evolution of the orbits of bodies ejected from the Earth, Moon, Mercury and Mars was studied. The probabilities of collisions of ejected bodies with planets depended on ejection velocities, ejection angles and points of ejection. At a velocity of ejection close to the parabolic velocity, most of bodies fell onto the planet from which they had been ejected. Below results are presented not for such small ejection velocities. 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.

Modern astronomy: from the Early Universe to exoplanets and black holes. 2024. P. 845-851., 2024

The motion of the planetesimals and dust particles from the vicinity of the orbit of planet c in ... more The motion of the planetesimals and dust particles from the vicinity of the orbit of planet c in the Proxima Centauri exoplanetary system was studied. The computer simulations of planetesimal motion showed that during the growth of the mass of planet c by a factor of 2, the semimajor axis of its orbit could decrease by at least a factor of 1.5. After hundreds of millions of years, some planetesimals could still move in elliptical resonant orbits inside the feeding zone of planet c that had been mainly cleared from planetesimals. The amount of water delivered to the inner planet Proxima Centauri b probably exceeded the mass of water in Earth’s oceans. It is difficult to expect the existence of such a massive analogue of the Oort cloud around Proxima Centauri as around the Sun. The probability of the collisions of the dust particles with a diameter of about 100 microns migrated from the feeding zone of planet c with planet b could exceed 0.1, and it could be much greater than for the planetesimals from the same zone. More particles with diameters of the order of 10 and 100 microns can be delivered from the feeding zone of planet c to planet b than to planet c.

Modern astronomy: from the Early Universe to exoplanets and black holes. 2024. P. 852-855, 2024

The calculations of the motion of planetesimals at the late stages of accumulation of planets in ... more The calculations of the motion of planetesimals at the late stages of accumulation of planets in the TRAPPIST-1 system were made. In each calculation variant, initial orbits of planetesimals were near one of the planets. The number of collisions of planetesimals with the planets were calculated. The calculations have shown that the outer layers of neighboring exoplanets in the TRAPPIST-1 system can include similar material if there were a lot of planetesimals near their orbits at the late stages of the accumulation of the exoplanets.

Abstracts of 55th Lunar and Planetary Science Conference . #1054, 2024

I studied the motion of planetesimals in the Proxima Centauri, TRAPPIST-1 and Gliese 581 planetar... more I studied the motion of planetesimals in the Proxima Centauri, TRAPPIST-1 and Gliese 581 planetary systems. Such studies were compared in with the studies of the motion of bodies in our Solar System.

Abstracts of 55th Lunar and Planetary Science Conference . #1231, 2024

The probabilities of collisions of the bodies ejected from the Earth with the terrestrial planets... more The probabilities of collisions of the bodies ejected from the Earth with the terrestrial planets were calculated. The total number of bodies delivered to the Earth and Venus probably did not differ much.

Meteoritics and Planetary Science. 2024. V.59. P. A204. Supplement 1., 2024

In each calculation variant, the motion of 250 bodies ejected from the Earth was studied for the ... more In each calculation variant, the motion of 250 bodies ejected from the Earth was studied for the fixed values of an ejection angle iej, a velocity vej of ejection, and a time step ts of integration. In different variants, the values of iej equaled to 15o, 30o, 45o, 60o, 89o or 90o, and vej equaled mainly to 11.22, 11.5, 12, 12.7, 14, 16.4, or 20 km/s. In most calculations, bodies started directly from the Earth. In each variant, bodies started from one of six considered opposite points. The motion of bodies was studied during the dynamical lifetime Tend of all bodies, which equaled to a few hundreds of Myr. Similar calculations were made for migration of bodies ejected from Mars, Mercury and Moon, but for smaller minimum values of vej close to the parabolic velocity.

The Fifteenth Moscow Solar System Symposium. 15MS3-SB-06. P. 236-238 (15M-S3). , 2024

The probabilities of collisions of bodies ejected from Mars with planets depended on ejection vel... more The probabilities of collisions of bodies ejected from Mars with planets depended on ejection velocities, ejection angles and points of ejection. The probability pma of a collision of a body ejected from Mars with Mars was considerable only at an ejection velocity vej close to the parabolic velocity. This probability usually did not exceed 0.04 at vej≥5.3 km/s. The fraction pme of bodies collided with Mercury was typically less than 0.08. Probabilities pe and pv of collisions of bodies ejected from Mars with the Earth and Venus were about 0.1-0.2 (each) at 5.05≤vej≤10 km/s, with pv typically a little greater than pe at vej≥5.2 km/s. The probability of ejection of a body into a hyperbolic orbit was less than 0.1 at vej≤5.3 km/s, but it could exceed 1 at vej=20 km/s. For different ejection velocities, angles and points, the probability of a collision of a body with the Sun could be between 0 and 0.9.

The Fifteenth Moscow Solar System Symposium (15M-S3). 15MS3-EP-01. p. 320-322, 2024

Outer layers of neighbouring exoplanets in the TRAPPIST-1 and Glisse 581 systems can include simi... more Outer layers of neighbouring exoplanets in the TRAPPIST-1 and Glisse 581 systems can include similar material, if there were a lot of planetesimals near their orbits at the late stages of the accumulation of the exoplanets. Most of collisions of planetesimals with planets in these exoplanetary systems took place in less than 10 Kyr, but some bodies can still move in elliptical orbits after millions or tens of million years.

12th Moscow International Solar System Symposium, 11-15 October 2021, IKI, Moscow, Russia, https://ms2021.cosmos.ru/docs/2021/12ms3\_book\_5.pdf, 12MS3-EP-11, p. 199-201. 3 pages., 2021

12th Moscow International Solar System Symposium, 11-15 October 2021, IKI, Moscow, Russia, https://ms2021.cosmos.ru/docs/2021/12ms3\_book\_5.pdf, 12MS3-SB-11, p. 293-295, 3 стр. , 2021

12th Moscow International Solar System Symposium, 11-15 October 2021, IKI, Moscow, Russia, https://ms2021.cosmos.ru/docs/2021/12ms3\_book\_5.pdf, 12MS3-EP-11, p. 199-201. , 2021

Meteoritics and Planetary Science. 2021. V. 56. Issue S1, #6040, p. 113. LPI Contribution No. 2609, id.6040., 2021

Introduction: Delivery of material to the Earth from different distances from the Sun was studied... more Introduction: Delivery of material to the Earth from different distances from the Sun was studied by different scietists. In [1] I presented the probabilities of collisions with the Earth for bodies migrated from distances from the Sun from 5 to 40 AU. Migration of bodies-planetesimals with initial semi-major axes between 3 and 5 AU is considered below. Initial data: The motion of bodies under the gravitational influence of 7 planets (from Venus to Neptune) was studied with the use of the symplectic code from [2]. In each variant of the calculations, the initial values of semimajor axes of orbits of 250 bodies-planetesimals varied from a min to a min +0.1 AU, their initial eccentricities equaled to e o =0.02 or to e o =0.15, and the initial inclinations equaled to e o /2 rad. The number of planetesimals with a semimajor axis a was proportional to a 1/2. The values of a min varied from 3 to 4.9 AU with a step of 0.1 AU. Based on the obtained arrays of orbital elements of migrated bodies, I calculated the probability p E of a collision of a bodyplanetesimal with the Earth during time interval T (up to 5 Gyr in some variants). The calculations of p E were made similar to the calculations presented in [3-5]. In each calculation variant the value of p E is the ratio of the sum of the probabilities of collisions of 250 bodies with the Earth to 250. Results of calculations: The value of p E could vary by a factor more than a hundred for different calculation variants with 250 bodies and the same values of a min and e o. Such difference was earlier found for calculations of migration of Jupiter-crossing objects [3-4]. One among hundreds or thousands of such objects moved in an Earthcrossing orbit during millions or even tens of millions of years, though the mean time of motion of a former Jupitercrossing object in an Earth-crossing orbit was about 30 Kyr. At 3.0≤a min ≤3.6 AU or a min =4.2 AU and e o =0.02, and also at 3.0≤a min ≤3.1 AU and e o =0.15, more than a half of bodies still moved in an elliptical orbit after T=100 Myr. At a min =4.2 AU bodies were close to the Hilda family asteroids. At a min ≥4.2 AU and e o =0.02, the values of p E mainly were in the range from 10-6 and 10-5 , as for many calculations with a min ≥5 AU considered in [1]. At some other values of a min and e o , the values of p E could be much greater-up to the values of the order of 10-3 at T=100 Myr and of 0.01 at T=1000 Myr. Though p E =0 at a min =3 AU and e o =0.02. It is not clear how much material was at distances from 3 to 4 AU from the Sun, compared to that in the zone of the giant planets. If we suppose that the density of a protoplanetary disk is proportional to R-0.5 , then the ratio of the mass of material with a distance R from the Sun between 4 and 15 AU is greater by a factor of ≈30 than that with R between 3 and 4 AU. For such a model, the amount of material delivered to the Earth from the zone of the outer asteroid belt could be comparable with the amount of material delivered from the zone of Jupiter and Saturn. Initially Jupiter-crossing bodies that have come to the Earth's orbit did it mostly within the first million years. Most of collisions with the Earth of bodies, originally located at a distance from 4 to 5 AU from the Sun, occurred during the first 10 million years. At 3≤a min ≤3.5 AU and e o ≤0.15, some bodies could fall onto the Earth in a few billion years. For example, for a min =3.3 AU and e o =0.02, p E =4×10-5 at 0.5≤t≤0.8 Myr and p E =6×10-6 at 2≤t≤2.5 Myr. For a min =3.2 AU and e o =0.15, p E =0.015 at 0.5≤t≤1 Myr, and p E =6×10-4 at 1≤t≤2 Myr. The zone of the outer asteroid belt can be one of the sources of the late heavy bombardment. At a min >3 AU, the ratio of the number of bodies colliding with the Earth to that with the Moon was mainly in the interval from 16.4 to 17.4. This ratio varied mainly from 20 to 40 for planetesimals from the feeding zone of the terrestrial planets [5]. So more planetesimals per mass of a celestial body collided with the Moon than with the Earth. However, at collisions of planetesimals with the Moon the fraction of ejected material was greater than that with the Earth. The characteristic velocities of collisions with the Moon and the Earth of bodies in calculations with a min from 3 to 15 AU were mainly from 20 to 23 km/s and from 23 to 26 km/s, respectively.

Meteoritics and Planetary Science. 2021. V. 56. Issue S1, #6042, p. 114. LPI Contribution No. 2609, id.6042., 2021

European Planetary Science Congress 2021, online, 13–24 Sep 2021, EPSC Abstracts, Vol. 15, EPSC2021-100, 2021

The ratio of the number of bodies colliding with the Earth to that with the Moon varied mainly fr... more The ratio of the number of bodies colliding with the Earth to that with the Moon varied mainly from 20 to 40 for planetesimals from the feeding zone of the terrestrial planets. For bodies arriving from distances from the Sun greater than 3 AU, this ratio was mainly in the interval from 16.4 to 17.4. So more planetesimals per mass of a celestial body collided with the Moon than with the Earth. However, at collisions of planetesimals with the Moon the fraction of ejected material was greater than that for the Earth. The characteristic velocities of collisions with the Moon and the Earth of bodies in calculations with amin from 3 to 15 AU were mainly from 20 to 23 km/s and from 23 to 26 km/s, respectively. The characteristic velocities of collisions of planetesimals from the feeding zone of the terrestrial planets with the Moon varied from 8 to 16 km/s depending on initial semi-major axes and eccentricities of planetesimals.

Bulletin of the American Astronomical Society, 2021, Vol. 53, No. 3 e-id 2021n3i1126. https://baas.aas.org/pub/2021n3i1126/release/2 , 5 страниц, 2021

For the Proxima Centauri planetary system, most of planetesimals from the vicinity of the exoplan... more For the Proxima Centauri planetary system, most of planetesimals from
the vicinity of the exoplanet “c” with a semi-major axis ac of about 1.5 AU were ejected into hyperbolic orbits in 10 Myr. Some planetesimals could collide with this exoplanet after 20 Myr. Only one of several hundreds of planetesimals from the vicinity of this exoplanet reached the orbit of the exoplanet “b” with a semi-major axis ab=0.0485 AU or the orbit of the exoplanet “d” with a semi-major axis ad=0.029 AU, but the probability of a collision of such planetesimal (that reached the orbits) with the exoplanets b and d can reach 1, and the collision probability averaged over all planetesimals from the vicinity of the exoplanet “c” was ~10-3. If averaged over all considered planetesimals from the vicinity of exoplanet “c”, the probability of a collision of a planetesimal with the exoplanet “b” or “d” is greater than the probability of a collision with the Earth of a planetesimal from the zone of the giant planets in the Solar System (which is less than 10-5 per one planetesimal). A lot of icy material could be delivered to the exoplanets “b” and “d”.

Meteoritics and Planetary Science. 2022. Volume 57, Issue S1. P. A209, 2022

The model and initial data used for calculations: In each calculation variant, migration of 250 b... more The model and initial data used for calculations: In each calculation variant, migration of 250 bodies ejected from the Earth was studied for the same values of an ejection angle iej (measured from the surface plane), a velocity vesc of ejection, and a time step ts of integration. The bodies started their motion at the height of 10 km from the point of Earth's surface located most far from the Sun. In different variants, the values of iej equaled to 30 o , 45 o , or 60 o , and vesc equaled to 11.22, 12, 12.7 or 16.4 km/s. The symplectic code from the SWIFT integration package [1] was used for integration of the motion equations with ts equal to 1, 2, 5, or 10 days. The gravitational influence of the Sun and all eight planets was taken into account. Bodies that collided with planets or the Sun or reached 2000 AU from the Sun were excluded from integration. The motion of bodies was studied during dynamical lifetime Tend of all bodies which was about 200-350 Myr. The probabilities of collisions of bodies with the Moon were calculated based on the arrays of orbital elements of migrated bodies (stored with a step of 500 years) similar to [2]. Calculations with different values of an integration time step: Most of calculations were made with a step ts equal to 10 days. The motion of considered bodies is chaotic due to close encounters of bodies with planets. Therefore, the probabilities of collisions of bodies with planets are different for integrations with a different time step and for close initial data. Calculations with smaller values of a time step (equaled to 1, 2, and 5 days), made for vesc=11.22 km/s and iej=30 o or iej=45 o , and at vesc=12.7 km/s and iej=45 o , showed that the probabilities of collisions of considered bodies with the Earth, the Sun, Mercury and Mars and of ejection into hyperbolic orbits obtained at ts=10 d are similar to those obtained at smaller ts. However, the ratio of the probability pV of a collision of a body with Venus at ts=10 d to that at smaller ts was in the range from 1.2 to 1.8 at a time interval T=10 Myr and from 1 to 1.2 at T=100 Myr. Probabilities of collisions of bodies with the Earth: The fraction pE of bodies collided with the Earth during the first million years was about 0.01-0.02 at vesc equal to 11.22 and 12 km/s, and it equaled to 0.004 at vesc=16.4 km/s. For Т=10 Myr, pE was about 0.056-0.12 at vesc equal to 11.22, 12 and 12.7 km/s, and was in the range 0.02-0.05 at vesc=16.4 km/s. For Т=10 Myr, the ratio of the values of pE at iej=45 o to the values at iej=30 o was mainly greater at greater vesc and varied between 1.2 and 2.4. At iej=60 o the value of pE was mainly not smaller than that at iej=45 o. For Т=100 Myr and at T=Tend, the values of pE were typically greater by a factor of 1.5-2 than at Т=10 Myr, and were in the range 0.1-0.2. In total for the considered calculations, about 16% of bodies fall back onto the Earth during Tend. The values of pE at T=Tend usually exceeded the values of pE at T=100 Myr by less than a factor of 1.1. Probabilities of ejection of bodies and of collisions of bodies with other planets and with the Sun: After 100 Myr less than 10% of bodies were left in elliptical orbits. The fraction pej of bodies ejected into hyperbolic orbits during a whole considered time interval Tend did not exceed 0.1, exclusive for vesc=16.4 km/s and iej=30 o (with pej=0.26). At 12≤vesc≤16.4 km/s pej was greater for iej=30 o than for iej=45 o and iej=60 o. The values of pej were mainly greater for greater vesc. The fraction pSun of bodies collided with the Sun was between 0.34 and 0.49. The probability of a collision of a body with Mercury was between 0.036 and 0.08, and the probability of a collision with Mars did not exceed 0.024. The probability pV of a collision of a body with Venus was about 0.2-0.25. Discussion on the growth of the Moon embryo: The ratio of probabilities of collisions of bodies with the Earth and the Moon was mainly about 20-30, and the values of the probability with the Moon were often about 0.006. In my calculations of the ejection of bodies from the Earth, I considered bodies that left the Hill's sphere of the Earth and moved in heliocentric orbits. At some collisions, the mass of the Moon could not increase due to ejection of material. With the present orbit of the Moon, the probability of collisions of the ejected bodies with the Moon was even less for the bodies that did not leave the Hill's sphere of the Earth than for the bodies that moved in heliocentric orbits. Bodies ejected from the Earth could participate in the formation of the outer layers of the Moon. In order to contain the present fraction of iron, the Moon had to accumulated the main fraction of its mass from the mantle of the Earth [3]. Bodies ejected from the Earth and fallen onto the Moon embryo in its present orbit probably were not enough for the growth of the Moon from a small embryo. So formation of a large Moon embryo close to the Earth is preferred. Acknowledgements: The studies of falls of bodies onto planets were carried out under government-financed research project for the Vernadsky Institute. The studies of falls of bodies onto the Moon and its growth were supported by the Russian Science Foundation, project 21-17-00120.

Meteoritics and Planetary Science. 2022. Volume 57, Issue S1. P. A208, 2022

The model and initial data: Mixing of planetesimals in the TRAPPIST-1 exoplanetary system is stud... more The model and initial data: Mixing of planetesimals in the TRAPPIST-1 exoplanetary system is studied at the late gas-free stage of formation of almost formed planets. The previous formation of embryos of planets could include their migration from greater distances and pebble accretion when gas presented in the protoplanetary disk. The TRAPPIST-1 system consists of a star with a mass equal to 0.0898 of the mass of the Sun and 7 planets. The motion of planetesimals under the gravitational influence of the star and seven planets (from b to h) was calculated with the use of the symplectic code from [1]. In different variants, the step ts of integration equaled to 0.1 day or 0.01 day. Planetesimals that collided with planets or the star or reached 50 AU from the star were excluded from integration. In each variant of the calculations, a disk of planetesimals was located near the orbit of one of the planets and is marked by the same letter as the planet. The initial values of semi-major axes of orbits of 250 planetesimals varied from amin to amax, their initial eccentricities were equal to eo=0.02 or eo=0.15, and the initial inclinations equaled to eo/2 rad. The orbital elements and masses of the planets and the values of amin and amax are presented in Table 1. Table 1. Semi-major axes a (in AU), eccentricities e, and masses m (in Earth masses mE) of exoplanets in the TRAPPIST-1 system, and the values of amin and amax for the considered disks near orbits of planets b, c, d, e, f, g, h. T0.02 and T0.15 are the times of evolution of disks at eo equaled to 0.02 or 0.15, respectively. f0.02 and f0.15 are the fractions of planetesimals collided with the 'host' planet during evolution at eo=0.02 and eo=0.15, respectively. The left and right values in the colums are for integrations with the step ts of integration equaled to 0.1 day or 0.01 day, respectively. m/mE a, AU e amin, AU amax, AU T0.02, Kyr T0.15, Kyr f0.02 f0.15 b 1.

Thirteenth Moscow Solar System Symposium(13M-S3) (October 10-14, 2022, Moscow, the Space Research Institute). https://ms2022.cosmos.ru/docs/2022/13-MS3\_BOOK\_final.pdf. ISBN: 978-5-00015-057-3. DOI: 10.21046/13MS3-2022. 2022. 13MS3-EP-PS-02 p. 378-380. , 2022

Outer layers of neighbouring exoplanets in the TRAPPIST-1 system can include similar material, if... more Outer layers of neighbouring exoplanets in the TRAPPIST-1 system can include similar material, if there were a lot of planetesimals near their orbits at the late stages of the accumulation of the exoplanets.

Thirteenth Moscow Solar System Symposium (13M-S3) (October 10-14, 2022, Moscow, the Space Research Institute). ISBN: 978-5-00015-057-3. DOI: 10.21046/13MS3-2022. 2022. 13MS3-EP-08. p. 372-374. , 2022

During the growth of the mass of planet c by a factor of 2, the semi-major axis of its orbit coul... more During the growth of the mass of planet c by a factor of 2, the semi-major axis of its orbit could decrease by at least a factor of 1.5. After hundreds of millions of years, some planetesimals could still move in elliptical orbits inside the feeding zone of planet c that had been mainly cleared from planetesimals. The amount of water delivered to Proxima Centauri b probably exceeded the mass of water in Earth’s oceans.

Editorial URSS Publishing Company, Moscow, 320 P, in Russian, 2000

The book is devoted to the investigations of migration of celestial bodies in the present and for... more The book is devoted to the investigations of migration of celestial bodies in the present and forming Solar System. It may be useful to various readers (both specialists andastronomers--amateurs), which are interesting in the structure, formation, and evolution of the Solar System. The material devoted to the structure of the Solar System and to the foreign and Russian organization of the work on dynamical astronomy is available to any reader. Students and lecturers can use the book as a textbook on dynamical astronomy and planet cosmogony. Specialists in various problems of astronomy, celestial mechanics, and asteroid and comet hazard can use it as a reference book. The scientists, which investigate the problem of the formation of the Solar System or the evolution of orbits of asteroids, trojans, trans--Neptunian objects, near--Earth objects, and other celestial bodies, can find the reviews of papers and original results on these problems.

Дельфис (Delfis). 2024. N 3. P. 39-42 (in Russian), 2024

Several models of the formation of the Moon are discussed.