Aims. To interpret adaptiveoptics 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 nonKeplerian 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 ‘bruteforce’ 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 χ 2 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.C0074), we were able to identify the true periods of the moons, P 1 = (1.822359 ± 0.004156) d, P 2 = (2.745820 ± 0.004820) d. They orbit very close to the 3:2 meanmotion resonance, but their osculating eccentricitiesmore »
(216) Kleopatra, a low density critically rotating Mtype asteroid
Context. The recent estimates of the 3D shape of the M/Xetype triple asteroid system (216) Kleopatra indicated a density of ~5 g cm −3 , which is by far the highest for a small Solar System body. Such a high density implies a high metal content as well as a low porosity which is not easy to reconcile with its peculiar “dumbbell” shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, here, we aim to constrain the mass (via the characterization of the orbits of the moons) and the shape of (216) Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of (216) Kleopatra recorded during two apparitions in 2017 and 2018 with archival data from the W. M. Keck Observatory, as well as lightcurve, occultation, and delayDoppler images, to derive a model of its 3D shape using two different algorithms (ADAM, MPCD). Furthermore, an N body dynamical model allowed us to retrieve the orbital elements of the two moons as explained in the accompanying paper. Results. The shape of (216) Kleopatra is very close to an equilibrium dumbbell figure with two lobes and a thick neck. Its volume equivalent diameter (118.75 ± more »
 Authors:
 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
 Award ID(s):
 1743015
 Publication Date:
 NSFPAR ID:
 10295829
 Journal Name:
 Astronomy & Astrophysics
 Volume:
 653
 Page Range or eLocationID:
 A57
 ISSN:
 00046361
 Sponsoring Org:
 National Science Foundation
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