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An advanced multipole model for (216) Kleopatra triple system

Brož, M. and Marchis, F. and Jorda, L. and Hanuš, J. and Vernazza, P. and Ferrais, M. and Vachier, F. and Rambaux, N. and Marsset, M. and Viikinkoski, M. and Jehin, E. and Benseguane, S. and Podlewska-Gaca, E. and Carry, B. and Drouard, A. and Fauvaud, S. and Birlan, M. and Berthier, J. and Bartczak, P. and Dumas, C. and Dudziński, G. and Ďurech, J. and Castillo-Rogez, J. and Cipriani, F. and Colas, F. and Fetick, R. and Fusco, T. and Grice, J. and Kryszczynska, A. and Lamy, P. and Marciniak, A. and Michalowski, T. and Michel, P. and Pajuelo, M. and Santana-Ros, T. and Tanga, P. and Vigan, A. and Vokrouhlický, D. and Witasse, O. and Yang, B. (2021) An advanced multipole model for (216) Kleopatra triple system. Astronomy and Astrophysics, 653 . A56. ISSN 0004-6361. doi:10.1051/0004-6361/202140901.

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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 C_(ℓm), S_(ℓm) 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Brož, M.0000-0003-2763-1411
Marchis, F.0000-0001-7016-7277
Jorda, L.0000-0001-8735-3308
Hanuš, J.0000-0002-2934-3723
Vernazza, P.0000-0002-2564-6743
Ferrais, M.0000-0002-0535-652X
Vachier, F.0000-0002-4289-4466
Marsset, M.0000-0001-8617-2425
Viikinkoski, M.0000-0001-8601-9164
Jehin, E.0000-0001-8923-488X
Carry, B.0000-0001-5242-3089
Castillo-Rogez, J.0000-0003-0400-1038
Fetick, R.0000-0002-1329-7603
Vigan, A.0000-0002-5902-7828
Additional Information:© ESO 2021. Article published by EDP Sciences. Received 26 March 2021; Accepted 28 April 2021; Published online 09 September 2021. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under program 199.C-0074 (PI Vernazza). We thank an anonymous referee for valuable comments. 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. The data presented herein were obtained partially at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.
Group:Thirty Meter Telescope
Funding AgencyGrant Number
Czech Science Foundation21-11058S
Czech Science Foundation20-08218S
Charles UniversityUNCE/SCI/023
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
Institut national des sciences de l'Univers (INSU)UNSPECIFIED
Programme National de Planétologie (PNP)UNSPECIFIED
Generalitat ValencianaAPOSTD/2019/046
Ministerio de Economía, Industria y Competitividad (MINECO)RTI2018-095076-B-C21
Australian Research CouncilUNSPECIFIED
Wallonia-Brussels FederationUNSPECIFIED
Fond National de la Recherche Scientifique (FNRS)FRFC 2.5.594.09.F
University of LiègeUNSPECIFIED
W. M. Keck FoundationUNSPECIFIED
Subject Keywords:minor planets, asteroids: individual: (216) Kleopatra – planets and satellites: fundamental parameters – astrometry – celestial mechanics – methods: numerical
Record Number:CaltechAUTHORS:20211006-224130190
Persistent URL:
Official Citation:An advanced multipole model for (216) Kleopatra triple system. M. Brož, F. Marchis, L. Jorda, J. Hanuš, P. Vernazza, M. Ferrais, F. Vachier, N. Rambaux, M. Marsset, M. Viikinkoski, E. Jehin, S. Benseguane, E. Podlewska-Gaca, B. Carry, A. Drouard, S. Fauvaud, M. Birlan, J. Berthier, P. Bartczak, C. Dumas, G. Dudziński, J. Ďurech, J. Castillo-Rogez, F. Cipriani, F. Colas, R. Fetick, T. Fusco, J. Grice, A. Kryszczynska, P. Lamy, A. Marciniak, T. Michalowski, P. Michel, M. Pajuelo, T. Santana-Ros, P. Tanga, A. Vigan, D. Vokrouhlický, O. Witasse and B. Yang. A&A, 653 (2021) A56; DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111258
Deposited By: Tony Diaz
Deposited On:07 Oct 2021 16:02
Last Modified:07 Oct 2021 16:02

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