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- A scientist with more than 40 years of experience in modeling and interpreting various physical processes, including ... moreA scientist with more than 40 years of experience in modeling and interpreting various physical processes, including formation and evolution of the Solar System. Web site: http://siipatov.webnode.ru/edit
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... 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.
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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... 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.
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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... 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…
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Research Interests:
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... 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.
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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... 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.
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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... 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.
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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... 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.
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Research Interests:
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... 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”.
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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... 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.
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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... 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 ± 0.1 kilometers, smooth and rough terrain, scarps, and impact craters. A thermal map indicates a surface in equilibrium with sunlight.
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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... 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&#39;s oceans. The processes of dust migration in the Solar System and sources of the zodiacal cloud are considered.
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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 (G65 pascals). Local gravitational field and average... 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 (G65 pascals). Local gravitational field and average nucleus density (600 kilograms per cubic meter) are estimated from ejecta fallback. Initial ejecta were hot (91000 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 T 0.1 kilometers, smooth and rough terrain, scarps, and impact craters. A thermal map indicates a surface in equilibrium with sunlight.
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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... 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.
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.
Research Interests:
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... 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.
Research Interests:
Computer simulations of migration of planetesimals from beyond the Jupiter’s orbit to the terrestrial planets have been made. Based on obtained arrays of orbital elements of planetesimals and planets during the dynamical lifetimes of... more
Computer simulations of migration of planetesimals from beyond the Jupiter’s orbit to the terrestrial planets have been made. Based on obtained arrays of orbital elements of planetesimals and planets during the dynamical lifetimes of planetesimals, we calculated the probabilities of collisions of planetesimals with planets, the Moon, and their embryos. The results of calculations showed that for the total mass of planetesimals of about 200 Earth masses, the mass of water delivered to the Earth from beyond the orbit of Jupiter could be about the mass of the terrestrial oceans. For the growth of the mass of the Earth embryo up to a half of the present mass of the Earth, the mass of water delivered to the embryo could be up to 30% of all water delivered to the Earth from the zone of Jupiter and Saturn. The water of the terrestrial oceans and its D/H ratio could be the result of mixing of water from several exogenic and endogenic sources with large and low D/H ratios. The ratio of the m...
Research Interests:
Probabilities of Collisions of Planetesimals from Different Regions of the Feeding Zone of the Terrestrial Planets with the Forming Planets and the MoonS. I. IpatovISSN 0038-0946, Solar System Research, 2019, Vol. 53, No. 5, pp. 332–361.... more
Probabilities of Collisions of Planetesimals from Different Regions of the Feeding Zone of the Terrestrial Planets with the Forming Planets and the MoonS. I. IpatovISSN 0038-0946, Solar System Research, 2019, Vol. 53, No. 5, pp. 332–361. © Pleiades Publishing, Inc., 2019.Russian Text © The Author(s), 2019, published in Astronomicheskii Vestnik, 2019, Vol. 53, No. 5, pp. 349–379.<br>
We numerically investigate the migration of dust particles with initial orbits close to those of the numbered asteroids, observed trans-Neptunian objects, and Comet Encke. The fraction of silicate asteroidal particles that collided with... more
We numerically investigate the migration of dust particles with initial orbits close to those of the numbered asteroids, observed trans-Neptunian objects, and Comet Encke. The fraction of silicate asteroidal particles that collided with the Earth during their lifetime varied from 1.1% for 100 micron particles to 0.008% for 1 micron particles. Almost all asteroidal particles with diameter d>4 microns collided with the Sun. The peaks in the migrating asteroidal dust particles' semi-major axis distribution at the n:(n+1) resonances with Earth and Venus and the gaps associated with the 1:1 resonances with these planets are more pronounced for larger particles. The probability of collisions of cometary particles with the Earth is smaller than for asteroidal particles, and this difference is greater for larger particles.
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The dependences of inclinations of orbits of secondaries in the discovered trans-Neptunian binaries on the distance between the primary and the secondary, on the eccentricity of orbits of the secondary around the primary, on the ratio of... more
The dependences of inclinations of orbits of secondaries in the discovered trans-Neptunian binaries on the distance between the primary and the secondary, on the eccentricity of orbits of the secondary around the primary, on the ratio of diameters of the secondary and the primary, and on the elements of heliocentric orbits of these binaries are studied. These dependences are interpreted using the model of formation of a satellite system in a collision of two rarefied condensations composed of dust and/or objects less than 1 m in diameter. It is assumed in this model that a satellite system forms in the process of compression of a condensation produced in such a collision. The model of formation of a satellite system in a collision of two condensations agrees with the results of observations: according to observational data, approximately 40% of trans-Neptunian binaries have a negative angular momentum relative to their centers of mass.
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The simulated Doppler shifts of the solar Mg I Fraunhofer line produced by scattering on the solar light by asteroidal, cometary, and trans-Neptunian dust particles are compared with the shifts obtained by Wisconsin H-Alpha Mapper (WHAM)... more
The simulated Doppler shifts of the solar Mg I Fraunhofer line produced by scattering on the solar light by asteroidal, cometary, and trans-Neptunian dust particles are compared with the shifts obtained by Wisconsin H-Alpha Mapper (WHAM) spectrometer. The simulated spectra are based on the results of integrations of the orbital evolution of particles. The deviation of the derived spectral parameters for various sources of dust used in the model reached maximum at the elongation (measured eastward from the Sun) between 90 deg and 120 deg. For the future zodiacal light Doppler shifts measurements, it is important to pay a particular attention to observing at this elongation range. At the elongations of the fields observed by WHAM, the model-predicted Doppler shifts were close to each other for several scattering functions considered. Therefore the main conclusions of our paper don't depend on a scattering function and mass distribution of particles if they are reasonable. A compar...
Research Interests: Geochemistry, Geophysics, Physics, Eccentricity, Dps, and 15 morePosition, Model development, Solar Radiation Pressure, Numerical Integration, Particle Size, Icarus, Dynamic Model of WSN, Signal to Noise Ratio, Particle Size Distribution, Doppler shift, Kuiper Belt, Fraunhofer lines, dynamic model, Line of sight, and radiation pressure
The angular momentum of the present Earth-Moon system could be acquired at the collision of two identical rarefied condensations with sizes of Hill spheres which total mass was about 0.1 of the mass of the Earth. Solid embryos of the... more
The angular momentum of the present Earth-Moon system could be acquired at the collision of two identical rarefied condensations with sizes of Hill spheres which total mass was about 0.1 of the mass of the Earth. Solid embryos of the Earth and the Moon could be originated as a result of contraction of the condensation formed at the collision. Depending on eccentricities of planetesimals that collided with solid embryos of the Earth and the Moon, the Moon could acquire 0.04-0.3 of its mass at the stage of accumulation of solid bodies while the mass of the growing Earth increased by a factor of ten.
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This paper studies the mean angular momentum associated with the collision of two celestial objects in the earliest stages of planet formation. Of primary concern is the scenario of two rarefied preplanetesimals (RPPs) in circular... more
This paper studies the mean angular momentum associated with the collision of two celestial objects in the earliest stages of planet formation. Of primary concern is the scenario of two rarefied preplanetesimals (RPPs) in circular heliocentric orbits. The theoretical results are used to develop models of binary or multiple system formation from RPPs, and explain the observation that a greater fraction of binaries originated farther from the Sun. At the stage of RPPs, small-body satellites can form in two ways: a merger between RPPs can have two centers of contraction, or the formation of satellites from a disc around the primary or the secondary. Formation of the disc can be caused by that the angular momentum of the RPP formed by the merger is greater than the critical angular momentum for a solid body. One or several satellites of the primary (moving mainly in low-eccentricity orbits) can be formed from this disc at any separation less than the Hill radius. The first scenario can ...
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Time variations in velocities and relative amount of observed particles (mainly icy particles with diameter d<3 μm) ejected from Comet 9P/Tempel 1 are studied based on analysis of the images made by Deep Impact (DI) cameras during the... more
Time variations in velocities and relative amount of observed particles (mainly icy particles with diameter d<3 μm) ejected from Comet 9P/Tempel 1 are studied based on analysis of the images made by Deep Impact (DI) cameras during the first 13 minutes after the collision of the DI impactor with the comet. Analysis of maxima or minima of plots of the time variations in distances of contours of constant brightness from the place of ejection allowed us to estimate the characteristic velocities of particles at several moments in time te of ejection after impact for te ≤ 115 s. Other approaches for estimates of the velocities were also used. All these estimates are in accordance with the same exponential decrease in velocity. The estimates of time variations in the relative amount of ejected particles were based also on results of the analysis of time variations in the size of the bright region of ejected material. At te 10 s, the morphology of the ejecta (e.g. the location and bright...
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We estimated the rate of comet and asteroid collisions with the terrestrial planets by calculating the orbits of 13000 Jupiter-crossing objects (JCOs) and 1300 resonant asteroids and computing the probabilities of collisions based on... more
We estimated the rate of comet and asteroid collisions with the terrestrial planets by calculating the orbits of 13000 Jupiter-crossing objects (JCOs) and 1300 resonant asteroids and computing the probabilities of collisions based on random-phase approximations and the orbital elements sampled with a 500 yr step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results for orbital evolution, but sometimes give different collision probabilities with the Sun. A small fraction of former JCOs reached orbits with aphelia inside Jupiter's orbit, and some reached Apollo orbits with semi-major axes less than 2 AU, Aten orbits, and inner-Earth orbits (with aphelia less than 0.983 AU) and remained there for millions of years. Though less than 0.1% of the total, these objects were responsible for most of the collision probability of former JCOs with Earth and Venus. Some Jupiter-family comets can reach inclinations i>90 deg. We conclude that a significant fraction of nea...
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Solid embryos of the Earth and the Moon, as well as trans-Neptunian binaries, could form as a result of contraction of the rarefied condensation which was parental for a binary. The angular momentum of the condensation needed for... more
Solid embryos of the Earth and the Moon, as well as trans-Neptunian binaries, could form as a result of contraction of the rarefied condensation which was parental for a binary. The angular momentum of the condensation needed for formation of a satellite system could be mainly acquired at the collision of two rarefied condensations at which the parental condensation formed. The minimum value of the mass of the parental condensation for the Earth-Moon system could be about 0.02 of the Earth mass. Besides the main collision, which was followed by formation of the condensation that was a parent for the embryos of the Earth and the Moon, there could be another main collision of the parental condensation with another condensation. The second main collision (or a series of similar collisions) could change the tilt of the Earth. Depending on eccentricities of the planetesimals that collided with the embryos, the Moon could acquire 0.04-0.3 of its mass at the stage of accumulation of solid ...
Research Interests: Physics and Astrobiology
The distance between the pre-impact surface of Comet 9P/Tempel 1 and the upper border of the largest cavity excavated during ejection of material after the collision of the impact module of the Deep Impact spacecraft with the comet is... more
The distance between the pre-impact surface of Comet 9P/Tempel 1 and the upper border of the largest cavity excavated during ejection of material after the collision of the impact module of the Deep Impact spacecraft with the comet is estimated to be about 5-6 metres if the diameter of the DI transient crater was about 150-200 m. The estimated distance was 4 m at the diameter was 100 m. This result suggests that cavities containing dust and gas under pressure located a few metres below surfaces of comets can be frequent.
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Probabilities of collisions of migrating dust particles with the Earth and the Moon were studied for various sizes of particles. Particles launched from different asteroids, comets and planetesimals were considered.
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Trans-Neptunian satellite systems and embryos of the Earth-Moon system could be formed as a result of contraction of rarefied condensations. The angular momenta of rarefied condensations needed for such formation could be acquired at... more
Trans-Neptunian satellite systems and embryos of the Earth-Moon system could be formed as a result of contraction of rarefied condensations. The angular momenta of rarefied condensations needed for such formation could be acquired at collisions of condensations. The angular momentum of the present Earth-Moon system could be acquired at a collision of two rarefied condensations with a total mass not smaller than 0.1ME, where ME is the mass of the Earth. The mass of the condensation that was a parent for the embryos of the Earth and the Moon could be about 0.01ME, if we take into account the growth of the angular momentum of the embryos with growth of their masses. The Moon embryo could get by an order of magnitude more material ejected from the Earth embryo than that fell directly onto the Moon embryo.
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We compared the number of lunar craters with diameters greater than 15 km with age less than 1.1 Gyr in the region of the Oceanus Procellarum with the estimates of the number of craters made based on the number of near-Earth objects and... more
We compared the number of lunar craters with diameters greater than 15 km with age less than 1.1 Gyr in the region of the Oceanus Procellarum with the estimates of the number of craters made based on the number of near-Earth objects and on the characteristic times elapsed before collisions of near-Earth objects with the Moon. Our estimates allow the increase of the number of near-Earth objects after a recent catastrophic disruption of a large main-belt asteroid. However, destruction of some old craters and variations in orbital distribution of near-Earth objects with time could allow that the mean number of near-Earth objects during the last billion years could be close to the present value.
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Research Interests: Migration, Computer Simulation, Celestial Mechanics, Numerical Integration, Solar System, and 12 morePlanetary system formation, Planetesimals, Cambridge University, Embryos, Terrestrial planet formation, Near Earth Objects, Terrestrial Planets, Main Belt Asteroids, Kuiper Belt, Transneptunian Objects, Ice Giant Planets, and Trans Neptunian Objects
We studied the orbital evolution of objects with initial orbits close to those of Jupiter-family comets (JFCs), Halley-type comets (HTCs), and long-period comets, and the probabilities of their collisions with the planets. In our runs the... more
We studied the orbital evolution of objects with initial orbits close to those of Jupiter-family comets (JFCs), Halley-type comets (HTCs), and long-period comets, and the probabilities of their collisions with the planets. In our runs the probability of a collision of one object with the Earth could be greater than the sum of probabilities for thousands of other objects. Even without the contribution of such a few objects, the probability of a collision of a former JFC with the Earth during the dynamical lifetime of the comet was greater than 4×10−6. This probability is enough for delivery of all the water to Earth's oceans during the formation of the giant planets. The ratios of probabilities of collisions of JFCs and HTCs with Venus and Mars to the mass of the planet usually were not smaller than that with Earth. Among 30,000 considered objects with initial orbits close to those of JFCs, a few objects got Earth-crossing orbits with semimajor axes a<2 AU and aphelion distanc...
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Our results are consistent with an initial mass of the protoplanetary cloud of MN ~0.04-0.1 Ms ( Ms is the mass of the Sun) assumed by many authors. More icy and stony matter may have entered the core and shell of Jupiter than any other... more
Our results are consistent with an initial mass of the protoplanetary cloud of MN ~0.04-0.1 Ms ( Ms is the mass of the Sun) assumed by many authors. More icy and stony matter may have entered the core and shell of Jupiter than any other planet. The total mass of bodies penetrating into the asteroid belt from the zones of the giant planets could have been tens of times the mass of the Earth. The system of giant planets expanded during accumulation of these planets. In order for Jupiter and Saturn to have their current eccentricities and their present periods of axial rotation and inclinations of the axes of rotation, nuclei of unformed planets with masses equal to several times the mass of the Earth must have existed in their feed zones. The nuclei of Uranus and Neptune with initial masses equal to several times the mass of the Earth could have migrated from the zone of Saturn, moving along slightly elliptical orbits. The same conclusion can be made for the migration from the zone of Jupiter of the nucleus of Saturn with a mass equal to several dozen times the mass of the Earth. In addition to the nuclei of Uranus and Neptune, other smaller objects could have migrated in the same way from the zones of Jupiter and Saturn into the zones of Uranus and Neptune. The total mass of bodies reaching beyond Neptune&#39;s orbit could have reached tens of times the mass of the Earth. Planetesimals could exist at the present time in the zone of Neptune, moving along eccentric and inclined orbits [4]. The average eccentricity of the orbits of bodies migrating into the trans-Neptune belt from the zones of the giant planets is larger than the average eccentricity of bodies formed in the trans-Neptune belt. At the present time bodies could migrate to the Earth&#39;s orbit from the asteroid and trans-Neptune belts, and also from the zones of Uranus and Neptune and from the Oort and Hills clouds.
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ABSTRACT
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ABSTRACT
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Investigations of the planet formation from the disk of planetesimals are mainly based on the results of computer simulation of evolving disks initially consisted of hundreds of gravitating bodies, moving around the Sun. Efficient methods... more
Investigations of the planet formation from the disk of planetesimals are mainly based on the results of computer simulation of evolving disks initially consisted of hundreds of gravitating bodies, moving around the Sun. Efficient methods have been worked out for a choice of pairs of contacting objects in the evolving disk. It was shown that intensive mixing of initial bodies had occurred during the accumulation of terrestrial planets. Some planetesimals from the zones of Uranus and Neptune migrated to Jupiter with subsequent ejection of most bodies into hyperbolic orbits under the action of Jupiter. If embryos of Uranus and Neptune were initially located near Saturn's orbit, then they could increase their semimajor axes to the present values due to the interactions with the migrating planetesimals.
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The outer boundaries of the maximum region of initial values of semi-major axes and eccentricities for which fictitious asteroids cross the orbit of Mars during their evolution coincide with the boundaries of the 5/2 Kirkwood gap.
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Formulas for calculation of the characteristic time elapsed before a collision of two celestial bodies orbiting the Sun were considered. Most of planetesimals collided with the Earth in 100 Myr and with Neptune in 1 Gyr.
Research Interests: Planets and Solar System
ABSTRACT
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Ejection of material after the Deep Impact collision with Comet Tempel 1 was studied based on analysis of the images made by the Deep Impact cameras during the first 13 minutes after impact. Analysis of the images shows that there was a... more
Ejection of material after the Deep Impact collision with Comet Tempel 1 was studied based on analysis of the images made by the Deep Impact cameras during the first 13 minutes after impact. Analysis of the images shows that there was a local maximum of the rate of ejection at time of ejection ~10 s with typical velocities ~100 m/s. At the same time, a considerable excessive ejection in a few directions began, the direction to the brightest pixel changed by ~50 deg, and there was a local increase of brightness of the brightest pixel. The ejection can be considered as a superposition of the normal ejection and the longer triggered outburst.
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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... 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.
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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... 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 as a part of the state assignments of the Vernadsky Institute of RAS № 0137-2021-0004.
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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... 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.
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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... 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”.
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”.
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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... 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.
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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... 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.
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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.
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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... 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.
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Bodies ejected from the Earth and the Moon at impacts of bodies-impactors could move in the zone of the terrestrial planets for up to a few hundred million years. The fraction of such bodies that fall back onto the Earth was about... more
Bodies ejected from the Earth and the Moon at impacts of bodies-impactors could move in the zone of the terrestrial planets for up to a few hundred million years. The fraction of such bodies that fall back onto the Earth was about 0.15-0.2. The probability of collisions of such bodies with the Moon in its present orbit was about 0.006-0.008. A large Moon embryo should be formed close to the Earth in order to accumulate material rich in iron.
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The values of the probability of a collision of a planetesimal with the Earth were typically greater for smaller distancesR from the Sun at 3< R <40 AU. The probability varied from about 10-6 at R~30-40 AU to 10-3 −10-2 at R about 3.2-3.3... more
The values of the probability of a collision of a planetesimal with the Earth were typically greater for smaller distancesR from the Sun at 3< R <40 AU. The probability varied from about 10-6 at R~30-40 AU to 10-3 −10-2 at R about 3.2-3.3 AU. Though only one of several hundreds of planetesimals from the zone of exoplanetcin the Proxima Centauri system reached the inner exoplanet b, it often collides with the planet b. The probability of a collision of such planetesimal with the exoplanet b could be about several 10−4. A lot of icy material could be delivered to inner exoplanets b and d in the Proxima Centauri system.
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The amounts of material from different parts of the zone from 0.7 to 1.5 AU from the Sun, which entered into almost formed the Earth and Venus, differed for these planets by no more than 3 times. For the TRAPPIST exoplanetary system, the... more
The amounts of material from different parts of the zone from 0.7 to 1.5 AU from the Sun, which entered into almost formed 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 were located, to the fraction of planetesimals collided with the neighbouring planet was typically less than 4. Embryos of the Earth and the Moon with a total mass equaled to about 0.01-0.1 Earth mass could be formed as a result of compression of a rarefied condensation. The fraction of material ejected from the Earth’s embryo and acquired by the Moon’s embryo could exceed by an order of magnitude the sum of the total mass of the planetesimals acquired by the Moon’s embryo and of the initial mass of the Moon’s embryo.
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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. The amount of water delivered to Proxima Centauri b probably exceeded the mass of water in Earth’s oceans. After... more
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. The amount of water delivered to Proxima Centauri b probably exceeded the mass of water in Earth’s oceans. 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.
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The fraction of bodies ejected from the Earth and the Moon at impacts of bodies-impactors that fall back onto the Earth was about 0.2. The probability of collisions of such bodies with the Moon moved in its present orbit was about 0.01.... more
The fraction of bodies ejected from the Earth and the Moon at impacts of bodies-impactors that fall back onto the Earth was about 0.2. The probability of collisions of such bodies with the Moon moved in its present orbit was about 0.01. The bodies ejected from the Earth and the Moon could move in the zone of the terrestrial planets for up to a few hundred million years. A large Moon embryo should be formed close to the Earth in order to accumulate material less rich in iron.
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Migration of planetesimals to the Earth from the zone beyond the orbit of Jupiter was considered by us e.g. in [1-3]. References to papers of several other authors on migration of bodies to the Earth were presented in [1]. In [1] we... more
Migration of planetesimals to the Earth from the zone beyond the orbit of Jupiter was considered by us e.g. in [1-3]. References to papers of several other authors on migration of bodies to the Earth were presented in [1]. In [1] we considered migration of planetesimals from the zone from 4.5 to 12 AU. In [2-3] migration of planetesimals with initial semi-major axes a0 of their orbits between 5 and 40 AU was considered. Below I also consider migration of planetesimals with a0 between 3 and 5 AU to the Earth. Migration of planetesimals under the gravitational influence of 7 planets (from Venus to Neptune) or 5 planets (from Venus to Saturn) was calculated with the use of the symplectic code from [4]. The. In each variant of the calculations, the initial values of semimajor axes of orbits of planetesimals varied from amin to amax=amin+da, the initial eccentricities were equal to eo, and the initial inclinations equaled to eo/2 rad. Orbital elements of the migrated planetesimals were recorded in computer memory with a step of 500 years. Based on these arrays of orbital elements, I calculated the probabilities of collisions of planetesimals with the Earth, and for some runs I also calculated the probabilities of collisions of the planetesimals with other terrestrial planets, the Moon and their embryos. The calculations were made similar to those in [1-3, 5-7]. In the series of calculations considered in [2-3], da=2.5 AU, and amin took values from 2.5 to 40 AU in increments of 2.5 AU. The initial eccentricities equaled to 0.3 or 0.05. In each calculation variant, 250 planetesimals were considered, but for the same values of amin, da, and eo, several (up to 8) calculation variants were performed. So the total number of considered planetesimals for a set with fixed values of amin, da and e0 could reach 2000. Some calculations were made for da=0. In the recent series of calculations, da=0.
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Migration of planetesimals and probabilities of their collisions with exoplanets were studied for the Proxima Centaury planetary system.
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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,... 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.