Pub Date : 2021-10-01DOI: 10.1017/S1743921321001319
Demétrio Tadeu Ceccatto, N. Callegari, Adrián Rodríguez
Abstract With the success of the Cassini-Huygens mission, the dynamic complexity surrounding natural satellites of Saturn began to be elucidated. New ephemeris could be calculated with a higher level of precision, which made it possible to study in detail the resonant phenomena and, in particular, the 54:53 near mean-motion resonance between Prometheus and Atlas. For this task, we have mapped in details the domains of the resonance with dense sets of initial conditions and distinct ranges of parameters. Our initial goal was to identify possible regions in the phase space of Atlas for which some critical angles, associated with the 54:53 mean motion have a stable libration. Our investigations revealed that there is no possibility for the current Atlas orbital configuration to have any regular behavior since it is in a chaotic region located at the boundary of the 54:53 mean-motion resonance phase space. This result is in accordance with previous works (Cooper et al. 2015; Renner et al. 2016). In this work, we generalize such investigations by showing detailed aspects of the Atlas-Prometheus 54:53 mean-motion resonance, like the extension of the chaotic layers, the thin domain of the center of the 54:53 resonance, the proximity of other neighborhood resonances, among other secondary conclusions. In particular, we have also shown that even in the deep interior of the resonance, it is difficult to map periodic motion of the resonant pair for very long time spans.
随着“卡西尼-惠更斯”任务的成功，土星天然卫星周围的动态复杂性开始被阐明。新的星历表可以以更高的精度计算，这使得详细研究共振现象，特别是普罗米修斯和阿特拉斯之间的54:53近平均运动共振成为可能。对于这项任务，我们详细地映射了具有密集初始条件集和不同参数范围的共振域。我们最初的目标是确定Atlas相空间中可能存在的区域，其中与54:53平均运动相关的某些临界角具有稳定的振动。我们的研究表明，目前的Atlas轨道构型不可能具有任何规则行为，因为它位于54:53平均运动共振相空间边界的混沌区域。这一结果与前人的研究一致(Cooper et al. 2015;Renner et al. 2016)。在这项工作中，我们通过展示阿特拉斯-普罗米修斯54:53平均运动共振的详细方面来概括这些研究，如混沌层的扩展，54:53共振中心的薄域，其他邻近共振的邻近性，以及其他次要结论。特别是，我们还表明，即使在共振的深层内部，也很难在很长的时间跨度内映射共振对的周期运动。
{"title":"The current orbit of Atlas (SXV)","authors":"Demétrio Tadeu Ceccatto, N. Callegari, Adrián Rodríguez","doi":"10.1017/S1743921321001319","DOIUrl":"https://doi.org/10.1017/S1743921321001319","url":null,"abstract":"Abstract With the success of the Cassini-Huygens mission, the dynamic complexity surrounding natural satellites of Saturn began to be elucidated. New ephemeris could be calculated with a higher level of precision, which made it possible to study in detail the resonant phenomena and, in particular, the 54:53 near mean-motion resonance between Prometheus and Atlas. For this task, we have mapped in details the domains of the resonance with dense sets of initial conditions and distinct ranges of parameters. Our initial goal was to identify possible regions in the phase space of Atlas for which some critical angles, associated with the 54:53 mean motion have a stable libration. Our investigations revealed that there is no possibility for the current Atlas orbital configuration to have any regular behavior since it is in a chaotic region located at the boundary of the 54:53 mean-motion resonance phase space. This result is in accordance with previous works (Cooper et al. 2015; Renner et al. 2016). In this work, we generalize such investigations by showing detailed aspects of the Atlas-Prometheus 54:53 mean-motion resonance, like the extension of the chaotic layers, the thin domain of the center of the 54:53 resonance, the proximity of other neighborhood resonances, among other secondary conclusions. In particular, we have also shown that even in the deep interior of the resonance, it is difficult to map periodic motion of the resonant pair for very long time spans.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"166 10 1","pages":"120 - 127"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83330464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001447
E. Pitjeva, D. Pavlov, D. Aksim, Margarita Kan
Abstract We present an updated public version of EPM (Ephemerides of Planets and the Moon). Since the last public version, EPM2017, many improvements were made in both the observational database and the mathematical model. Latest lunar laser ranging observations have been added, as well as radio ranges of Juno spacecraft and more recent ranges of Odyssey and Mars Reconnaissance Orbiter. EPM2021 uses a new improved way to calculate radio signal delays in solar plasma and has a major update in the method of determination of asteroid masses. Also, a delay-capable multistep numerical integrator was implemented for EPM in order to properly account for tide delay in the equations of the motion of the Moon. The improved processing accuracy has allowed to refine existing estimates of the mass of the Sun and its change rate, parameters of the Earth–Moon system, masses of the Main asteroid belt and the Kuiper belt; and also to raise important questions about existing numerical models of solar wind.
{"title":"Planetary and lunar ephemeris EPM2021 and its significance for Solar system research","authors":"E. Pitjeva, D. Pavlov, D. Aksim, Margarita Kan","doi":"10.1017/S1743921321001447","DOIUrl":"https://doi.org/10.1017/S1743921321001447","url":null,"abstract":"Abstract We present an updated public version of EPM (Ephemerides of Planets and the Moon). Since the last public version, EPM2017, many improvements were made in both the observational database and the mathematical model. Latest lunar laser ranging observations have been added, as well as radio ranges of Juno spacecraft and more recent ranges of Odyssey and Mars Reconnaissance Orbiter. EPM2021 uses a new improved way to calculate radio signal delays in solar plasma and has a major update in the method of determination of asteroid masses. Also, a delay-capable multistep numerical integrator was implemented for EPM in order to properly account for tide delay in the equations of the motion of the Moon. The improved processing accuracy has allowed to refine existing estimates of the mass of the Sun and its change rate, parameters of the Earth–Moon system, masses of the Main asteroid belt and the Kuiper belt; and also to raise important questions about existing numerical models of solar wind.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"77 1","pages":"220 - 225"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86184420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S174392132100123X
G. Voyatzis, D. Karydis, K. Tsiganis
Abstract In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction of asymmetries in a gravitational potential may significantly affect the dynamical properties of the families. In this paper, we discuss the effect of the asymmetries in the neighborhood of vertically critical orbits, where, in the symmetric model, bifurcations of 3D periodic orbit families occur. When asymmetries are introduced, we demonstrate that two possible continuation schemes can take place in general. Numerical simulations, using an ellipsoid and a mascon model of 433-Eros, verify the existence of these schemes.
在Karydis et al.(2021)中，我们从一个对称的简单模型开始，引入了形状延拓的方法，以获得不规则形状小行星在复杂引力场中的周期轨道。更重要的是，我们将简单模型的周期轨道族映射到真实小行星模型的族。在重力势中引入不对称性会显著影响族的动力学性质。本文讨论了在对称模型中，三维周期轨道族在垂直临界轨道附近出现分岔的不对称性所产生的影响。当引入不对称时，我们证明了一般情况下可以有两种可能的延续方案。利用椭球和433-Eros的mascon模型进行了数值模拟，验证了这些方案的存在性。
{"title":"Families of periodic orbits around asteroids: From shape symmetry to asymmetry","authors":"G. Voyatzis, D. Karydis, K. Tsiganis","doi":"10.1017/S174392132100123X","DOIUrl":"https://doi.org/10.1017/S174392132100123X","url":null,"abstract":"Abstract In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction of asymmetries in a gravitational potential may significantly affect the dynamical properties of the families. In this paper, we discuss the effect of the asymmetries in the neighborhood of vertically critical orbits, where, in the symmetric model, bifurcations of 3D periodic orbit families occur. When asymmetries are introduced, we demonstrate that two possible continuation schemes can take place in general. Numerical simulations, using an ellipsoid and a mascon model of 433-Eros, verify the existence of these schemes.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"12 1","pages":"246 - 251"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83471940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001265
Valerie Chopovda, W. Sweatman
Abstract We consider four- and five-body problems with symmetrical masses (Caledonian problems). Families of periodic orbits originate from the collinear Schubart orbits. We present and discuss some of these periodic orbits.
{"title":"Four- and five-body periodic Caledonian orbits","authors":"Valerie Chopovda, W. Sweatman","doi":"10.1017/S1743921321001265","DOIUrl":"https://doi.org/10.1017/S1743921321001265","url":null,"abstract":"Abstract We consider four- and five-body problems with symmetrical masses (Caledonian problems). Families of periodic orbits originate from the collinear Schubart orbits. We present and discuss some of these periodic orbits.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"129 1","pages":"140 - 145"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81335622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001368
Rita Mastroianni, C. Efthymiopoulos
Abstract We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.
{"title":"Secular dynamics in extrasolar systems with two planets in mutually inclined orbits","authors":"Rita Mastroianni, C. Efthymiopoulos","doi":"10.1017/S1743921321001368","DOIUrl":"https://doi.org/10.1017/S1743921321001368","url":null,"abstract":"Abstract We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"118 1","pages":"191 - 196"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84072498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001356
I. Cavallari, C. Efthymiopoulos
Abstract We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.
{"title":"Closed-form perturbation theory in the Sun-Jupiter restricted three body problem without relegation","authors":"I. Cavallari, C. Efthymiopoulos","doi":"10.1017/S1743921321001356","DOIUrl":"https://doi.org/10.1017/S1743921321001356","url":null,"abstract":"Abstract We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"11 1","pages":"113 - 119"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89061116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001496
P. Peñarroya, R. Paoli
Abstract Missions to asteroids have been the trend in space exploration for the last years. They provide information about the formation and evolution of the Solar System, contribute to direct planetary defense tasks, and could be potentially exploited for resource mining. Be their purpose as it may, the factor that all these mission types have in common is the challenging dynamical environment they have to deal with. The gravitational environment of a certain asteroid is most of the times not accurately known until very late mission phases when the spacecraft has already orbited the body for some time. Shape models help to estimate the gravitational potential with a density distribution assumption (usually constant value) and some optical measurements of the body. These measurements, unlike the ones needed for harmonic coefficient estimation, can be taken from well before arriving at the asteroid’s sphere of influence, which allows to obtain a better approximation of the gravitational dynamics much sooner. The disadvantage they pose is that obtaining acceleration values from these models implies a heavy computational burden on the on-board processing unit, which is very often too time-consuming for the mission profile. In this paper, the technique developed on [1] is used to create a validated Python-based tool that obtains spherical harmonic coefficients from the shape model of an asteroid or comet, given a certain density for the body. This validated software suite, called AstroHarm, is used to analyse the accuracy of the models obtained and the improvements in computational efficiency in a simulated spacecraft orbiting a small body. The results obtained are shown offering a qualitative comparison between different order spherical harmonic models and the original shape model. Finally, the creation of a catalogue for harmonics is proposed together with some thoughts on complex modelling using this tool.
{"title":"Orbit propagation around small bodies using spherical harmonic coefficients obtained from polyhedron shape models","authors":"P. Peñarroya, R. Paoli","doi":"10.1017/S1743921321001496","DOIUrl":"https://doi.org/10.1017/S1743921321001496","url":null,"abstract":"Abstract Missions to asteroids have been the trend in space exploration for the last years. They provide information about the formation and evolution of the Solar System, contribute to direct planetary defense tasks, and could be potentially exploited for resource mining. Be their purpose as it may, the factor that all these mission types have in common is the challenging dynamical environment they have to deal with. The gravitational environment of a certain asteroid is most of the times not accurately known until very late mission phases when the spacecraft has already orbited the body for some time. Shape models help to estimate the gravitational potential with a density distribution assumption (usually constant value) and some optical measurements of the body. These measurements, unlike the ones needed for harmonic coefficient estimation, can be taken from well before arriving at the asteroid’s sphere of influence, which allows to obtain a better approximation of the gravitational dynamics much sooner. The disadvantage they pose is that obtaining acceleration values from these models implies a heavy computational burden on the on-board processing unit, which is very often too time-consuming for the mission profile. In this paper, the technique developed on [1] is used to create a validated Python-based tool that obtains spherical harmonic coefficients from the shape model of an asteroid or comet, given a certain density for the body. This validated software suite, called AstroHarm, is used to analyse the accuracy of the models obtained and the improvements in computational efficiency in a simulated spacecraft orbiting a small body. The results obtained are shown offering a qualitative comparison between different order spherical harmonic models and the original shape model. Finally, the creation of a catalogue for harmonics is proposed together with some thoughts on complex modelling using this tool.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"39 1","pages":"203 - 210"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88413895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S1743921321001253
Mattia Rossi, C. Efthymiopoulos
Abstract We address the question of identifying the long-term (secular) stability regions in the semi-major axis-eccentricity projected phase space of the Sun-Jupiter planar circular restricted three-body problem in the domains i) below the curve of apsis equal to the planet’s orbital radius (ensuring protection from collisions) and ii) above that curve. This last domain contains several Jupiter’s crossing trajectories. We discuss the structure of the numerical stability map in the (a,e) plane in relation to manifold dynamics. We also present a closed-form perturbation theory for particles with non-crossing highly eccentric trajectories exterior to the planet’s trajectory. Starting with a multipole expansion of the barycentric Hamiltonian, our method carries out a sequence of normalizations by Lie series in closed-form and without relegation. We discuss the applicability of the method as a criterion for estimating the boundary of the domain of regular motion.
{"title":"Characterization of the stability for trajectories exterior to Jupiter in the restricted three-body problem via closed-form perturbation theory","authors":"Mattia Rossi, C. Efthymiopoulos","doi":"10.1017/S1743921321001253","DOIUrl":"https://doi.org/10.1017/S1743921321001253","url":null,"abstract":"Abstract We address the question of identifying the long-term (secular) stability regions in the semi-major axis-eccentricity projected phase space of the Sun-Jupiter planar circular restricted three-body problem in the domains i) below the curve of apsis equal to the planet’s orbital radius (ensuring protection from collisions) and ii) above that curve. This last domain contains several Jupiter’s crossing trajectories. We discuss the structure of the numerical stability map in the (a,e) plane in relation to manifold dynamics. We also present a closed-form perturbation theory for particles with non-crossing highly eccentric trajectories exterior to the planet’s trajectory. Starting with a multipole expansion of the barycentric Hamiltonian, our method carries out a sequence of normalizations by Lie series in closed-form and without relegation. We discuss the applicability of the method as a criterion for estimating the boundary of the domain of regular motion.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"40 1","pages":"232 - 238"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84888548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/S174392132100140X
S. Dermott, Dan Li, A. Christou
Abstract We have shown that in the inner belt the loss of asteroids from the ν6 secular resonance and the 3:1 Jovian mean motion resonance accounts for the observation that the mean size of the asteroids increases with increasing orbital inclination. We have used that observation to constrain the Yarkovsky loss timescale and to show that the family asteroids are embedded in a background population of old ghost families. We argue that all the asteroids in the inner belt originated from a small number of asteroids and that the initial mass of the belt was similar to that of the present belt. We also show that the observed size frequency distribution of the Vesta asteroid family was determined by the action of Yarkovsky forces, and that the age of this family is comparable to the age of the solar system.
{"title":"Dynamical constraints on the evolution of the inner asteroid belt and the sources of meteorites","authors":"S. Dermott, Dan Li, A. Christou","doi":"10.1017/S174392132100140X","DOIUrl":"https://doi.org/10.1017/S174392132100140X","url":null,"abstract":"Abstract We have shown that in the inner belt the loss of asteroids from the ν6 secular resonance and the 3:1 Jovian mean motion resonance accounts for the observation that the mean size of the asteroids increases with increasing orbital inclination. We have used that observation to constrain the Yarkovsky loss timescale and to show that the family asteroids are embedded in a background population of old ghost families. We argue that all the asteroids in the inner belt originated from a small number of asteroids and that the initial mass of the belt was similar to that of the present belt. We also show that the observed size frequency distribution of the Vesta asteroid family was determined by the action of Yarkovsky forces, and that the age of this family is comparable to the age of the solar system.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"35 1","pages":"1 - 19"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85616409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-01DOI: 10.1017/s1743921322000126
A. Perminov, E. Kuznetsov
Abstract The averaged four-planetary motion theory is constructed up to the third order in planetary masses. The equations of motion in averaged elements are numerically integrated for the Solar system’s giant planets for different initial conditions. The comparison of obtained results with the direct numerical integration of Newtonian equations of motion shows an excellent agreement with them. It suggests that this motion theory is constructed correctly. So, we can use this theory to investigate the dynamical evolution of various extrasolar planetary systems with moderate orbital eccentricities and inclinations.
{"title":"The semi-analytical motion theory of the third order in planetary masses for the Sun – Jupiter – Saturn – Uranus –Neptune’s system","authors":"A. Perminov, E. Kuznetsov","doi":"10.1017/s1743921322000126","DOIUrl":"https://doi.org/10.1017/s1743921322000126","url":null,"abstract":"Abstract The averaged four-planetary motion theory is constructed up to the third order in planetary masses. The equations of motion in averaged elements are numerically integrated for the Solar system’s giant planets for different initial conditions. The comparison of obtained results with the direct numerical integration of Newtonian equations of motion shows an excellent agreement with them. It suggests that this motion theory is constructed correctly. So, we can use this theory to investigate the dynamical evolution of various extrasolar planetary systems with moderate orbital eccentricities and inclinations.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"29 1","pages":"211 - 213"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91204732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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