1. An advanced multipole model for (216) Kleopatra triple system
- Author
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Laurent Jorda, Josef Hanus, François Colas, Alexis Drouard, J. Grice, Julie Castillo-Rogez, Patrick Michel, Philippe Lamy, Pierre Vernazza, Josef Ďurech, Miroslav Brož, Bin Yang, Matti Viikinkoski, Franck Marchis, Tadeusz Michalowski, Marin Ferrais, Fabrice Cipriani, Thierry Fusco, Nicolas Rambaux, Olivier Witasse, Przemyslaw Bartczak, Arthur Vigan, David Vokrouhlický, Emmanuel Jehin, E. Podlewska-Gaca, Toni Santana-Ros, Frédéric Vachier, M. Pajuelo, Paolo Tanga, S. Benseguane, Romain Fétick, Christophe Dumas, Grzegorz Dudziński, Mirel Birlan, Agnieszka Kryszczyńska, S. Fauvaud, Anna Marciniak, Benoit Carry, J. Berthier, Michael Marsset, Institute of Astronomy [Prague], Charles University [Prague] (CU), Search for Extraterrestrial Intelligence Institute (SETI), Laboratoire d'Astrophysique de Marseille (LAM), Aix Marseille Université (AMU)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National d'Études Spatiales [Toulouse] (CNES)-Centre National de la Recherche Scientifique (CNRS), Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Department of Earth, Atmospheric and Planetary Sciences [MIT, Cambridge] (EAPS), Massachusetts Institute of Technology (MIT), Tampere University of Technology [Tampere] (TUT), Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal, Space Sciences, Technologies and Astrophysics Research Institute (STAR), Université de Liège, SETI Institute, Ondřejov Observatory of the Prague Astronomical Institute, Czech Academy of Sciences [Prague] (CAS), Observatoire de la Côte d'Azur (OCA), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Observatoire du Bois de Bardon, Astronomical Institute of Romanian Academy, Romanian Academy, Thirty Meter Telescope Observatory, Jet Propulsion Laboratory (JPL), NASA-California Institute of Technology (CALTECH), European Space Research and Technology Centre (ESTEC), Agence Spatiale Européenne = European Space Agency (ESA), DOTA, ONERA, Université Paris Saclay [Châtillon], ONERA-Université Paris-Saclay, School of Physical Sciences [Milton Keynes], Faculty of Science, Technology, Engineering and Mathematics [Milton Keynes], The Open University [Milton Keynes] (OU)-The Open University [Milton Keynes] (OU), PLANETO - LATMOS, Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Pontificia Universidad Católica del Perú = Pontifical Catholic University of Peru (PUCP), Universidad de Alicante, Institut de Ciencies del Cosmos (ICCUB), Universitat de Barcelona (UB), European Southern Observatory [Santiago] (ESO), European Southern Observatory (ESO), Czech Science Foundation, Charles University (Czech Republic), National Science Foundation (US), National Aeronautics and Space Administration (US), Generalitat Valenciana, Ministerio de Ciencia, Innovación y Universidades (España), Fédération Wallonie-Bruxelles, and Belgian Science Policy Office
- Subjects
010504 meteorology & atmospheric sciences ,fundamental parameters [Planets and satellites] ,Library science ,FOS: Physical sciences ,Astrophysics ,01 natural sciences ,methods: numerical ,Física Aplicada ,0103 physical sciences ,Celestial mechanics ,planets and satellites: fundamental parameters ,010303 astronomy & astrophysics ,0105 earth and related environmental sciences ,Physics ,Earth and Planetary Astrophysics (astro-ph.EP) ,[PHYS]Physics [physics] ,numerical [Methods] ,[SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph] ,Minor planets ,Astronomy and Astrophysics ,Astrometry ,celestial mechanics ,asteroids: individual: (216) Kleopatra ,individual: (216) Kleopatra [Asteroids] ,Space and Planetary Science ,individual: (216) Kleopatra [Minor planets, asteroids] ,minor planets ,astrometry ,TRAPPIST ,Christian ministry ,Earth and Planetary Astrophysics ,Astrophysics::Earth and Planetary Astrophysics ,Astrophysics - Earth and Planetary Astrophysics - Abstract
[Aims] To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons orbiting an extremely irregular body and include their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. [Methods] Consequently, we used a modified N-body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order ℓ = 10. Its convergence was verified against the 'brute-force' algorithm. We computed the coefficients Cℓ m, Sℓ m for Kleopatra's shape, assuming a constant bulk density. For Solar System applications, it was also necessary to implement a variable distance and geometry of observations. Our χ2 metric then accounts for the absolute astrometry, the relative astrometry (second moon with respect to the first), angular velocities, and silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra's two moons. [Results] Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons, P1 = (1.822359 ± 0.004156) d, P2 = (2.745820 ± 0.004820) d. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), meaning that regular librations of the critical argument are not present. The resulting mass of Kleopatra, m1 = (1.49 ± 0.16) × 10-12 M· or 2.97 × 1018 kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body., Broz, M. et al., This work has been supported by the Czech Science Foundation through grant 21-11058S (M. Brož, D. Vokrouhlický), 20-08218S (J. Hanuš, J. Ďurech), and by the Charles University Research program No. UNCE/SCI/023. This material is partially based upon work supported by the National Science Foundation under Grant No. 1743015. P.V., A.D., M.F. and B.C. were supported by CNRS/INSU/PNP. M.M. was supported by the National Aeronautics and Space Administration under grant No. 80NSSC18K0849 issued through the Planetary Astronomy Program. The work of TSR was carried out through grant APOSTD/2019/046 by Generalitat Valenciana (Spain). This work was supported by the MINECO (Spanish Ministry of Economy) through grant RTI2018-095076-B-C21 (MINECO/FEDER, UE). The research leading to these results has received funding from the ARC grant for Concerted Research Actions, financed by the Wallonia-Brussels Federation. TRAPPIST is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F. TRAPPIST-North is a project funded by the University of Liège, and performed in collaboration with Cadi Ayyad University of Marrakesh. E. Jehin is a FNRS Senior Research Associate.
- Published
- 2021
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