Coupling between corotation and Lindblad resonances in the elliptic planar three-body problem

We investigate the dynamics of two satellites with masses $\mu_s$ and $\mu'_s$ orbiting a massive central planet in a common plane, near a first order mean motion resonance $m$+1:$m$ ($m$ integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degree of freedom system, associated with the two critical resonant angles $\phi= (m+1)\lambda' -m\lambda - \varpi$ and $\phi'= (m+1)\lambda' -m\lambda - \varpi'$, where $\lambda$ and $\varpi$ are the mean longitude and longitude of periapsis of $\mu_s$, respectively, and where the primed quantities apply to $\mu'_s$. We consider the special case where $\mu_s \rightarrow 0$ (restricted problem). The symmetry between the two angles $\phi$ and $\phi'$ is then broken, leading to two different kinds of resonances, classically referred to as Corotation Eccentric resonance (CER) and Lindblad Eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance $D$ between the CER and LER, and a forcing parameter $\epsilon_L$ that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for $D=0$ the system is integrable, for $D$ of order unity, it exhibits prominent chaotic regions, while for $D$ large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances : Aegaeon, Methone and Anthe

The dynamics of rings around Centaurs and Trans-Neptunian Objects

Since 2013, dense and narrow rings are known around the small Centaur object Chariklo and the dwarf planet Haumea. Dense material has also been detected around the Centaur Chiron, although its nature is debated. This is the first time ever that rings are observed elsewhere than around the giant planets, suggesting that those features are more common than previously thought. The origins of those rings remain unclear. In particular, it is not known if the same generic process can explain the presence of material around Chariklo, Chiron, Haumea, or if each object has a very different history. Nonetheless, a specific aspect of small bodies is that they may possess a non-axisymmetric shape (topographic features and or elongation) that are essentially absent in giant planets. This creates strong resonances between the spin rate of the object and the mean motion of ring particles. In particular, Lindblad-type resonances tend to clear the region around the corotation (or synchronous) orbit, where the particles orbital period matches that of the body. Whatever the origin of the ring is, modest topographic features or elongations of Chariklo and Haumea explain why their rings should be found beyond the outermost 1/2 resonance, where the particles complete one revolution while the body completes two rotations. Comparison of the resonant locations relative to the Roche limit of the body shows that fast rotators are favored for being surrounded by rings. We discuss in more details the phase portraits of the 1/2 and 1/3 resonances, and the consequences of a ring presence on satellite formation.Comment: Chapter to be published in the book "The Transneptunian Solar System", Dina Prialnik, Maria Antonietta Barucci, Leslie Young Eds. Elsevie

Cupid Is Not Doomed Yet: On the Stability of the Inner Moons of Uranus

Some of the small inner moons of Uranus have very closely-spaced orbits. Multiple numerical studies have found that the moons Cressida and Desdemona, within the Portia sub-group, are likely to collide in less than 100 Myr. The subsequent discovery of three new moons (Cupid, Perdita, and Mab) made the system even more crowded. In particular, it has been suggested that the Belinda group (Cupid, Belinda, and Perdita) will become unstable in as little as 10$^5$ years. Here we revisit the issue of the stability of the inner moons of Uranus using updated orbital elements and considering tidal dissipation. We find that the Belinda group can be stable on $10^8$-year timescales due to an orbital resonance between Belinda and Perdita. We find that tidal evolution cannot form the Belinda-Perdita resonance, but convergent migration could contribute to the long-term instability of the Portia group. We propose that Belinda captured Perdita into the resonance during the last episode of disruption and re-accretion among the inner moons, possibly hundreds of Myr ago.Comment: 11 pages, 4 figures, accepted for A

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn

The Cassini spacecraft collects high resolution images of the saturnian satellites and reveals the surface of these new worlds. The shape and rotation of the satellites can be determined from the Cassini Imaging Science Subsystem data, employing limb coordinates and stereogrammetric control points. This is the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap is essential to introduce explicitly into rotational models. During its journey in the saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by Erdi (1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form

Constraints on the structure and seasonal variations of Triton's atmosphere from the 5 October 2017 stellar occultation and previous observations

Context. A stellar occultation by Neptune's main satellite, Triton, was observed on 5 October 2017 from Europe, North Africa, and the USA. We derived 90 light curves from this event, 42 of which yielded a central flash detection. Aims. We aimed at constraining Triton's atmospheric structure and the seasonal variations of its atmospheric pressure since the Voyager 2 epoch (1989). We also derived the shape of the lower atmosphere from central flash analysis. Methods. We used Abel inversions and direct ray-tracing code to provide the density, pressure, and temperature profiles in the altitude range similar to 8 km to similar to 190 km, corresponding to pressure levels from 9 mu bar down to a few nanobars. Results. (i) A pressure of 1.18 +/- 0.03 mu bar is found at a reference radius of 1400 km (47 km altitude). (ii) A new analysis of the Voyager 2 radio science occultation shows that this is consistent with an extrapolation of pressure down to the surface pressure obtained in 1989. (iii) A survey of occultations obtained between 1989 and 2017 suggests that an enhancement in surface pressure as reported during the 1990s might be real, but debatable, due to very few high S/N light curves and data accessible for reanalysis. The volatile transport model analysed supports a moderate increase in surface pressure, with a maximum value around 2005-2015 no higher than 23 mu bar. The pressures observed in 1995-1997 and 2017 appear mutually inconsistent with the volatile transport model presented here. (iv) The central flash structure does not show evidence of an atmospheric distortion. We find an upper limit of 0.0011 for the apparent oblateness of the atmosphere near the 8 km altitude.J.M.O. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) and the European Social Fund (ESF) through the PhD grant SFRH/BD/131700/2017. The work leading to these results has received funding from the European Research Council under the European Community's H2020 2014-2021 ERC grant Agreement nffi 669416 "Lucky Star". We thank S. Para who supported some travels to observe the 5 October 2017 occultation. T.B. was supported for this research by an appointment to the National Aeronautics and Space Administration (NASA) Post-Doctoral Program at the Ames Research Center administered by Universities Space Research Association (USRA) through a contract with NASA. We acknowledge useful exchanges with Mark Gurwell on the ALMA CO observations. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. J.L.O., P.S.-S., N.M. and R.D. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709), they also acknowledge the financial support by the Spanish grant AYA-2017-84637-R and the Proyecto de Excelencia de la Junta de Andalucia J.A. 2012-FQM1776. The research leading to these results has received funding from the European Union's Horizon 2020 Research and Innovation Programme, under Grant Agreement no. 687378, as part of the project "Small Bodies Near and Far" (SBNAF). P.S.-S. acknowledges financial support by the Spanish grant AYA-RTI2018-098657-J-I00 "LEO-SBNAF". The work was partially based on observations made at the Laboratorio Nacional de Astrofisica (LNA), Itajuba-MG, Brazil. The following authors acknowledge the respective CNPq grants: F.B.-R. 309578/2017-5; R.V.-M. 304544/2017-5, 401903/2016-8; J.I.B.C. 308150/2016-3 and 305917/2019-6; M.A. 427700/20183, 310683/2017-3, 473002/2013-2. This study was financed in part by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior -Brasil (CAPES) -Finance Code 001 and the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). G.B.R. acknowledges CAPES-FAPERJ/PAPDRJ grant E26/203.173/2016 and CAPES-PRINT/UNESP grant 88887.571156/2020-00, M.A. FAPERJ grant E26/111.488/2013 and A.R.G.Jr. FAPESP grant 2018/11239-8. B.E.M. thanks CNPq 150612/2020-6 and CAPES/Cofecub-394/2016-05 grants. Part of the photometric data used in this study were collected in the frame of the photometric observations with the robotic and remotely controlled telescope at the University of Athens Observatory (UOAO; Gazeas 2016). The 2.3 m Aristarchos telescope is operated on Helmos Observatory by the Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing of the National Observatory of Athens. Observations with the 2.3 m Aristarchos telescope were carried out under OPTICON programme. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 730890. This material reflects only the authors views and the Commission is not liable for any use that may be made of the information contained therein. The 1. 2m Kryoneri telescope is operated by the Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing of the National Observatory of Athens. The Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA) is managed by the Fondazione Clement Fillietroz-ONLUS, which is supported by the Regional Government of the Aosta Valley, the Town Municipality of Nus and the "Unite des Communes valdotaines Mont-Emilius". The 0.81 m Main Telescope at the OAVdA was upgraded thanks to a Shoemaker NEO Grant 2013 from The Planetary Society. D.C. and J.M.C. acknowledge funds from a 2017 'Research and Education' grant from Fondazione CRT-Cassa di Risparmio di Torino. P.M. acknowledges support from the Portuguese Fundacao para a Ciencia e a Tecnologia ref. PTDC/FISAST/29942/2017 through national funds and by FEDER through COMPETE 2020 (ref. POCI010145 FEDER007672). F.J. acknowledges Jean Luc Plouvier for his help. S.J.F. and C.A. would like to thank the UCL student support observers: Helen Dai, Elise Darragh-Ford, Ross Dobson, Max Hipperson, Edward Kerr-Dineen, Isaac Langley, Emese Meder, Roman Gerasimov, Javier Sanjuan, and Manasvee Saraf. We are grateful to the CAHA, OSN and La Hita Observatory staffs. This research is partially based on observations collected at Centro Astronomico HispanoAleman (CAHA) at Calar Alto, operated jointly by Junta de Andalucia and Consejo Superior de Investigaciones Cientificas (IAA-CSIC). This research was also partially based on observation carried out at the Observatorio de Sierra Nevada (OSN) operated by Instituto de Astrofisica de Andalucia (CSIC). This article is also based on observations made with the Liverpool Telescope operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council. Partially based on observations made with the Tx40 and Excalibur telescopes at the Observatorio Astrofisico de Javalambre in Teruel, a Spanish Infraestructura Cientifico-Tecnica Singular (ICTS) owned, managed and operated by the Centro de Estudios de Fisica del Cosmos de Aragon (CEFCA). Tx40 and Excalibur are funded with the Fondos de Inversiones de Teruel (FITE). A.R.R. would like to thank Gustavo Roman for the mechanical adaptation of the camera to the telescope to allow for the observation to be recorded. R.H., J.F.R., S.P.H. and A.S.L. have been supported by the Spanish projects AYA2015-65041P and PID2019-109467GB-100 (MINECO/FEDER, UE) and Grupos Gobierno Vasco IT1366-19. Our great thanks to Omar Hila and their collaborators in Atlas Golf Marrakech Observatory for providing access to the T60cm telescope. TRAPPIST is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant PDR T.0120.21. TRAPPIST-North is a project funded by the University of Liege, and performed in collaboration with Cadi Ayyad University of Marrakesh. E.J. is a FNRS Senior Research Associate

Dynamique des petits satellites de Saturne

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