Pub Date : 2021-10-01DOI: 10.1017/S1743921322000035
M. Sommer, P. Pokorný, H. Yano, R. Srama
Abstract Circumstellar discs are known to exist in great variety, from gas-rich discs around the youngest stars to evolved debris discs such as the solar system’s zodiacal cloud. Through gravitational interaction, exoplanets embedded in these discs can generate density variations, imposing potentially observable structural features on the disc such as rings or gaps. Here we report on a mirrored double crescent pattern arising in simulations of discs harbouring a small, moderately eccentric planet - such as Mars. We show that the structure is a result of a directed apsidal precession occurring in particles that migrate the planet’s orbital region under Poynting-Robertson drag. We further analyze the strength of this effect with respect to planet and particle parameters.
{"title":"Apsidal alignment in migrating dust - Crescent features caused by eccentric planets","authors":"M. Sommer, P. Pokorný, H. Yano, R. Srama","doi":"10.1017/S1743921322000035","DOIUrl":"https://doi.org/10.1017/S1743921322000035","url":null,"abstract":"Abstract Circumstellar discs are known to exist in great variety, from gas-rich discs around the youngest stars to evolved debris discs such as the solar system’s zodiacal cloud. Through gravitational interaction, exoplanets embedded in these discs can generate density variations, imposing potentially observable structural features on the disc such as rings or gaps. Here we report on a mirrored double crescent pattern arising in simulations of discs harbouring a small, moderately eccentric planet - such as Mars. We show that the structure is a result of a directed apsidal precession occurring in particles that migrate the planet’s orbital region under Poynting-Robertson drag. We further analyze the strength of this effect with respect to planet and particle parameters.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"83 1","pages":"259 - 261"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91156156","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/S1743921321001484
P. Di Cintio, L. Casetti
Abstract By means of numerical simulations we study the radial-orbit instability in anisotropic self-gravitating N–body systems under the effect of noise. We find that the presence of additive or multiplicative noise has a different effect on the onset of the instability, depending on the initial value of the orbital anisotropy.
{"title":"Noise, friction and the radial-orbit instability in anisotropic stellar systems: stochastic N–body simulations","authors":"P. Di Cintio, L. Casetti","doi":"10.1017/S1743921321001484","DOIUrl":"https://doi.org/10.1017/S1743921321001484","url":null,"abstract":"Abstract By means of numerical simulations we study the radial-orbit instability in anisotropic self-gravitating N–body systems under the effect of noise. We find that the presence of additive or multiplicative noise has a different effect on the onset of the instability, depending on the initial value of the orbital anisotropy.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"27 1","pages":"152 - 157"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75738618","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/S1743921321001411
R. Malhotra
Abstract Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called “low-eccentricity resonant bridges” connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some – though not necessarily entire – resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.
{"title":"New results on orbital resonances","authors":"R. Malhotra","doi":"10.1017/S1743921321001411","DOIUrl":"https://doi.org/10.1017/S1743921321001411","url":null,"abstract":"Abstract Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called “low-eccentricity resonant bridges” connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some – though not necessarily entire – resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"14 1","pages":"85 - 101"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74993928","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/S1743921322000552
A. Celletti, E. Karampotsiou, C. Lhotka, G. Pucacco, M. Volpi
Abstract The Laplace resonance is a configuration that involves the commensurability between the mean motions of three small bodies revolving around a massive central one. This resonance was first observed in the case of the three inner Galilean satellites, Io, Europa, and Ganymede. In this work the Laplace resonance is generalised by considering a system of three satellites orbiting a planet that are involved in mean motion resonances. These Laplace-like resonances are classified in three categories: first-order (2:1&2:1, 3:2&3:2, 2:1&3:2), second-order (3:1&3:1) and mixed-order resonances (2:1&3:1). In order to study the dynamics of the system we implement a model that includes the gravitational interaction with the central body, the mutual gravitational interactions of the satellites, the effects due to the oblateness of the central body and the secular interaction of a fourth satellite and a distant star. Along with these contributions we include the tidal interaction between the central body and the innermost satellite. We study the survival of the Laplace-like resonances and the evolution of the orbital elements of the satellites under the tidal effects. Moreover, we study the possibility of capture into resonance of the fourth satellite.
{"title":"Evolution and stability of Laplace-like resonances under tidal dissipation","authors":"A. Celletti, E. Karampotsiou, C. Lhotka, G. Pucacco, M. Volpi","doi":"10.1017/S1743921322000552","DOIUrl":"https://doi.org/10.1017/S1743921322000552","url":null,"abstract":"Abstract The Laplace resonance is a configuration that involves the commensurability between the mean motions of three small bodies revolving around a massive central one. This resonance was first observed in the case of the three inner Galilean satellites, Io, Europa, and Ganymede. In this work the Laplace resonance is generalised by considering a system of three satellites orbiting a planet that are involved in mean motion resonances. These Laplace-like resonances are classified in three categories: first-order (2:1&2:1, 3:2&3:2, 2:1&3:2), second-order (3:1&3:1) and mixed-order resonances (2:1&3:1). In order to study the dynamics of the system we implement a model that includes the gravitational interaction with the central body, the mutual gravitational interactions of the satellites, the effects due to the oblateness of the central body and the secular interaction of a fourth satellite and a distant star. Along with these contributions we include the tidal interaction between the central body and the innermost satellite. We study the survival of the Laplace-like resonances and the evolution of the orbital elements of the satellites under the tidal effects. Moreover, we study the possibility of capture into resonance of the fourth satellite.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"45 1","pages":"128 - 133"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78841965","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/S1743921321001241
R. Machado Oliveira, O. Winter, R. Sfair, G. Valvano, T. Moura, G. Borderes-Motta
Abstract Didymos and Dimorphos are primary and secondary, respectively, asteroids who compose a binary system that make up the set of Near Earth Asteroids (NEAs). They are targets of the Double Asteroid Redirection Test (DART), the first test mission dedicated to study of planetary defense, for which the main goal is to measure the changes caused after the secondary body is hit by a kinect impactor. The present work intends to conduct a study, through numerical integrations, on the dynamics of massless particles distributed in the vicinity of the two bodies. An approximate shape for the primary body was considered as a model of mass concentrations (mascons) and the secondary was considered as a massive point. Our results show the location and size of stable regions, and also their lifetime.
{"title":"Dynamics around the binary system (65803) Didymos","authors":"R. Machado Oliveira, O. Winter, R. Sfair, G. Valvano, T. Moura, G. Borderes-Motta","doi":"10.1017/S1743921321001241","DOIUrl":"https://doi.org/10.1017/S1743921321001241","url":null,"abstract":"Abstract Didymos and Dimorphos are primary and secondary, respectively, asteroids who compose a binary system that make up the set of Near Earth Asteroids (NEAs). They are targets of the Double Asteroid Redirection Test (DART), the first test mission dedicated to study of planetary defense, for which the main goal is to measure the changes caused after the secondary body is hit by a kinect impactor. The present work intends to conduct a study, through numerical integrations, on the dynamics of massless particles distributed in the vicinity of the two bodies. An approximate shape for the primary body was considered as a model of mass concentrations (mascons) and the secondary was considered as a massive point. Our results show the location and size of stable regions, and also their lifetime.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"1 1","pages":"197 - 202"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75734948","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/S1743921321001332
E. Pilat-Lohinger, S. Clees, M. Zimmermann, B. Loibnegger
Abstract Recent GAIA observations revealed that the K-type star Gliese 710 will cross the Oort cloud in a distance between approximately 4000 and 12000 au in about 1.3 Myrs. This occurrence motivated us to study the influence of a stellar encounter on comets in the outer region of the solar system. Even if the Oort cloud extends to 100000 au from the sun, we restrict our study to the region between 30 and 25000 au where 25 million objects are distributed randomly. Comets at larger distances are not taken into account as they hardly enter the observable region after a single stellar fly-by. An overview of all objects that are scattered towards the sun for the different fly-by distances at 4000, 8000 and 12000 au shows that only a handful of objects are moving towards the sun immediately after the stellar encounter. However, a subsequent long-term study of all objects that are moved into highly eccentric motion by the stellar fly-by shows a significant increase of comets crossing Jupiter’s orbit and entering into the observable region. In addition, our study shows the first comets crossing the orbit of Earth only about 2.5 Myrs after the stellar fly-by. Thus, the impact risk for the Earth increases only some million years after the stellar fly-by.
{"title":"On the scattering and dynamical evolution of Oort cloud comets caused by a stellar fly-by","authors":"E. Pilat-Lohinger, S. Clees, M. Zimmermann, B. Loibnegger","doi":"10.1017/S1743921321001332","DOIUrl":"https://doi.org/10.1017/S1743921321001332","url":null,"abstract":"Abstract Recent GAIA observations revealed that the K-type star Gliese 710 will cross the Oort cloud in a distance between approximately 4000 and 12000 au in about 1.3 Myrs. This occurrence motivated us to study the influence of a stellar encounter on comets in the outer region of the solar system. Even if the Oort cloud extends to 100000 au from the sun, we restrict our study to the region between 30 and 25000 au where 25 million objects are distributed randomly. Comets at larger distances are not taken into account as they hardly enter the observable region after a single stellar fly-by. An overview of all objects that are scattered towards the sun for the different fly-by distances at 4000, 8000 and 12000 au shows that only a handful of objects are moving towards the sun immediately after the stellar encounter. However, a subsequent long-term study of all objects that are moved into highly eccentric motion by the stellar fly-by shows a significant increase of comets crossing Jupiter’s orbit and entering into the observable region. In addition, our study shows the first comets crossing the orbit of Earth only about 2.5 Myrs after the stellar fly-by. Thus, the impact risk for the Earth increases only some million years after the stellar fly-by.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"57 1","pages":"214 - 219"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74950801","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/S1743921322000461
U. Locatelli, Chiara Caracciolo, M. Sansottera, M. Volpi
Abstract We revisit the problem of the existence of KAM tori in extrasolar planetary systems. Specifically, we consider the υ Andromedæ system, by modelling it with a three-body problem. This preliminary study allows us to introduce a natural way to evaluate the robustness of the planetary orbits, which can be very easily implemented in numerical explorations. We apply our criterion to the problem of the choice of a suitable orbital configuration which exhibits strong stability properties and is compatible with the observational data that are available for the υ Andromedæ system itself.
{"title":"A numerical criterion evaluating the robustness of planetary architectures; applications to the υ Andromedæ system","authors":"U. Locatelli, Chiara Caracciolo, M. Sansottera, M. Volpi","doi":"10.1017/S1743921322000461","DOIUrl":"https://doi.org/10.1017/S1743921322000461","url":null,"abstract":"Abstract We revisit the problem of the existence of KAM tori in extrasolar planetary systems. Specifically, we consider the υ Andromedæ system, by modelling it with a three-body problem. This preliminary study allows us to introduce a natural way to evaluate the robustness of the planetary orbits, which can be very easily implemented in numerical explorations. We apply our criterion to the problem of the choice of a suitable orbital configuration which exhibits strong stability properties and is compatible with the observational data that are available for the υ Andromedæ system itself.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"36 1","pages":"65 - 84"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91261872","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/S1743921321001423
Anne-Sophie Libert
Abstract The Lidov-Kozai (LK) resonance is one of the most widely discussed topics since the discovery of exoplanets in eccentric orbits. It constitutes a secular protection mechanism for systems with high mutual inclinations, although large variations in eccentricity and inclination are observed. This review aims to illustrate how the LK resonance influences the dynamics of the three-body problem at different scales, namely i) for two-planet extrasolar systems where the orbital variations occur in a coherent way such that the system remains stable, ii) for inclined planets in protoplanetary discs where the LK cycles are produced by the gravitational force exerted by the disc on the planet, iii) for migrating planets in binary star systems, whose dynamical evolution is strongly affected by the LK resonance even without experiencing a resonance capture, and iv) for triple-star systems for which the migration through LK cycles combined with tidal friction is a possible explanation for the short-period pile-up observed in the distribution of multiple stars.
{"title":"The Lidov-Kozai resonance at different scales","authors":"Anne-Sophie Libert","doi":"10.1017/S1743921321001423","DOIUrl":"https://doi.org/10.1017/S1743921321001423","url":null,"abstract":"Abstract The Lidov-Kozai (LK) resonance is one of the most widely discussed topics since the discovery of exoplanets in eccentric orbits. It constitutes a secular protection mechanism for systems with high mutual inclinations, although large variations in eccentricity and inclination are observed. This review aims to illustrate how the LK resonance influences the dynamics of the three-body problem at different scales, namely i) for two-planet extrasolar systems where the orbital variations occur in a coherent way such that the system remains stable, ii) for inclined planets in protoplanetary discs where the LK cycles are produced by the gravitational force exerted by the disc on the planet, iii) for migrating planets in binary star systems, whose dynamical evolution is strongly affected by the LK resonance even without experiencing a resonance capture, and iv) for triple-star systems for which the migration through LK cycles combined with tidal friction is a possible explanation for the short-period pile-up observed in the distribution of multiple stars.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"5 1","pages":"52 - 64"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81586813","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}
Abstract The objective of this paper is to carry out periodic orbital propagation and bifurcations detection around asteroid 433 Eros. Specifically, we propose to exploit a frequency-domain method, the harmonic balance method, as an efficient alternative to the usual time integration. The stability and bifurcations of the periodic orbits are also assessed thanks to the Floquet exponents. Numerous periodic orbits are found with various periods and shapes. Different bifurcations, including period doubling, tangent, real saddle and Neimark-Sacker bifurcations, are encountered during the continuation process. Resonance phenomena are highlighted as well.
{"title":"Multiple bifurcations around 433 Eros with Harmonic Balance Method","authors":"Leclère Nicolas, Kerschen Gaëtan, Dell’Elce Lamberto","doi":"10.1017/S1743921322000734","DOIUrl":"https://doi.org/10.1017/S1743921322000734","url":null,"abstract":"Abstract The objective of this paper is to carry out periodic orbital propagation and bifurcations detection around asteroid 433 Eros. Specifically, we propose to exploit a frequency-domain method, the harmonic balance method, as an efficient alternative to the usual time integration. The stability and bifurcations of the periodic orbits are also assessed thanks to the Floquet exponents. Numerous periodic orbits are found with various periods and shapes. Different bifurcations, including period doubling, tangent, real saddle and Neimark-Sacker bifurcations, are encountered during the continuation process. Resonance phenomena are highlighted as well.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"15 1","pages":"171 - 177"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76268670","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/S174392132100137X
Irene De Blasi, A. Celletti, C. Efthymiopoulos
Abstract A powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J 2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the eccentricity and the inclination. We finally discuss the applicability of Nekhoroshev’s theorem on the exponential stability of the action variables. To this end, we investigate the non-degeneracy properties of the J 2 and geolunisolar models. We obtain that the J 2 model satisfies a “three-jet” non-degeneracy condition, while the geolunisolar model is quasi-convex non-degenerate.
{"title":"Satellites’ orbital stability through normal forms","authors":"Irene De Blasi, A. Celletti, C. Efthymiopoulos","doi":"10.1017/S174392132100137X","DOIUrl":"https://doi.org/10.1017/S174392132100137X","url":null,"abstract":"Abstract A powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J 2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the eccentricity and the inclination. We finally discuss the applicability of Nekhoroshev’s theorem on the exponential stability of the action variables. To this end, we investigate the non-degeneracy properties of the J 2 and geolunisolar models. We obtain that the J 2 model satisfies a “three-jet” non-degeneracy condition, while the geolunisolar model is quasi-convex non-degenerate.","PeriodicalId":20590,"journal":{"name":"Proceedings of the International Astronomical Union","volume":"6 1","pages":"146 - 151"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83252951","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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