arXiv subjects

S. I. Ipatov

Publications and source records attributed to S. I. Ipatov.

At least 19 recordsLinked to original sources

arXiv2026

Formation and evolution of planetary systems

Various problems of the formation and evolution of planetary systems are studied. Most of the studies are devoted to the Solar System. The collapse of the presolar cloud and the accumulation of planets are studied. The author considers the formation of the Earth-Moon system, binary trans-Neptunian objects, and the axial rotations of planets. He discusses the formation of asteroid and trans-Neptunian belts, including the evolution of resonant asteroid orbits and the formation of the Kirkwood gaps in the asteroid belt. The book discusses the migration of bodies during the formation of the Solar System and at present, including a discussion of the delivery of icy bodies from beyond the ice line to the terrestrial planets and the formation of craters on the Moon. The Deep Impact mission is discussed; during this mission the impact module of the spacecraft collided with the comet Tempel 1. The book studies the migration of dust in the Solar System and the formation of the zodiacal belt, as well as the migration of bodies and dust particles ejected from the terrestrial planets and the Moon. The author considers the migration of bodies in some exoplanetary systems (Proxima Centauri, Trappist 1, and Gliese 581), the spectra of Earth-like exoplanets with different rotation periods, as well as the efficiency of exoplanet searches using microlensing observations with various telescopes. English text is only in the list of publications and in the contents. An English reader can look the contents to find an interesting section. In this section he can find the numbers for relative publications. Using these numbers and the list of publications, he can find the websites where he can upload free files with these publications, and then he can read relevant papers in English and can get more detailed information than in this book.

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arXiv2025

Spectra of Earth-like exoplanets with different rotation periods

We investigate the spectra of Earth-like planets but with different axial rotation periods. Using the general circulation model of the atmosphere and considering the atmospheric circulation lasting for two years, we calculated the radiation spectra of the Earth and the exo-Earth rotating with periods of 1 and 100 days, respectively. The radiation spectra of the atmospheres were calculated with the SBDART code. We analyzed the spectrum of upward radiation at altitudes of 1 and 11 km in wavelength ranges of 1 to 18 and 0.3 to 1 micron. The following common features were obtained for the Earth and the exo-Earth: (1) the planets exhibit a wide absorption band of CO2 around 14 micron; (2) the radiation spectra at different locations near the equator show no significant differences; and (3) if the spectrum is integrated over the entire disk of the Earth/exo-Earth, the difference in the spectral signal obtained in observations from different directions becomes substantially lower than the difference between the results of observations of individual regions of the planets. The differences in the spectra of exoplanets, which differ from the Earth only in axial rotation period, are comparable to the differences associated with changes in the angle of viewing the planet. Consequently, if the observation angle is not known, the analysis of the spectrum of the planet cannot be used to determine its axial rotation period. The maximal differences in the spectra of Earth-like exoplanets were obtained for wavelengths of about 5-10 and 13-16 micron. By analyzing the spectrum at wavelengths around 9.4-10 micron, we can determine whether the atmosphere of the exoplanet contains ozone or not. Since ozone is essential for life, the 9.4-10 micron band may be important for future observations of Earth-like exoplanets.

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arXiv2025

Models of the night-sky brightness and the efficiency of searching for exoplanets with the microlensing method

We analyze photometric observations of stars, which experienced microlensing events at the considered time, in order to compare the efficiency of detecting exoplanets in observations performed at thirteen different telescopes and with several approaches to the selection of observable events. In constructing an algorithm of the optimal selection of targets for these observations and in comparing the detection efficiencies for several telescopes, we considered models of the night-sky brightness that satisfy the data of infrared observations carried out in 2011 with the Optical Gravitational Lensing Experiment (OGLE) telescope and the RoboNet telescopes (FTS, FTN, and LT) used to search for planets with the microlensing method. The considered models of the night-sky brightness can be used for various observations (not only microlensing events). The time intervals, during which microlensing events can be observed, were determined with accounting for the positions of the Sun and the Moon and the other constraints on the telescope pointing. Our algorithm allows us to determine the already known microlensing events that are accessible for observation with a particular telescope and to select targets, for which the probability of detecting an exoplanet is maximal. The events, which would maximize the probability of detecting exoplanets, were selected for observations. The probability of detecting an exoplanet is usually proportional to the mirror diameter of a telescope. Telescopes with a wider field of view, such as the OGLE, are more effective in finding new microlensing events. To observe different microlensing events, it is usually better to use different nearby telescopes. However, all such telescopes are often better to use for observing the same event in those relatively short time intervals that correspond to the peak brightness of the event.

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arXiv2024

Exchange of meteorites between the terrestrial planets and the Moon

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.

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arXiv2024

Variations in orbital elements of planets

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.

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arXiv2024

Orbital evolution of the P/1996 R2 and P/1996 N2 objects

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.

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arXiv2024

Evolution of orbits of trans-Neptunian bodies at the 2:3 resonance with Neptune

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 ΔΩ=Ω-Ω_N in the ascending-node longitudes of the body and Neptune, and in the perihelion argument ω. When ΔΩ decreases and ω increases during evolution, then most of the bodies leave the resonance in 20 Myr. In the case of an increase in ΔΩ and a decrease in ω, the bodies stay in the resonance for a much longer time. Regions of eccentricities and inclinations, for which some bodies were in the η_18 secular resonance (ΔΩ is almost constant) and in the Kozai resonance (ω 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.

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arXiv2024

Migration of Bodies to the Earth from Different Distances from the Sun

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.

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arXiv2024

Migration of bodies in the Proxima Centauri and Trappist 1 planetary systems

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.

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arXiv2024

Migration of bodies ejected from the Earth and the Moon

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<vej<16.4 km/s, respectively.

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arXiv2024

Migration of celestial bodies in the Solar system and in several exoplanetary systems

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.

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arXiv2024

Probabilities of collisions of bodies ejected from forming Earth with the terrestrial planets

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.

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arXiv2024

Growth of the Moon due to bodies ejected from the Earth

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.

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arXiv2024

Motion of Planetesimals in the Hill Sphere of the Star Proxima Centauri

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. Most of the planetesimals that first reached 500 AU from Proxima Centauri first reached 1200 AU from the star in less than 1 million years. In the considered model, the disk of planetesimals in the outer part of the star's Hill sphere was rather flat. The results may be of interest for understanding the motion of bodies in other exoplanetary systems, especially those with a single dominant planet. 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.

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arXiv2023

Delivery of icy planetesimals to inner planets in the Proxima Centauri planetary system

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.

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arXiv2023

Stable Orbits in the Feeding Zone of the Planet Proxima Centauri c

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.

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arXiv2023

Migration processes in the Solar System and their role in the evolution of the Earth and planets

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.

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arXiv2021

Formation of the Earth and Moon: Influence of Small Bodies

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.

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