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Context. The recent estimates of the 3D shape of the M/Xe-type 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 delay-Doppler 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 ± 1.40) km and mass (2.97 ± 0.32) × 10 18 kg (i.e., 56% lower than previously reported) imply a bulk density of (3.38 ± 0.50) g cm −3 . Such a low density for a supposedly metal-rich body indicates a substantial porosity within the primary. This porous structure along with its near equilibrium shape is compatible with a formation scenario including a giant impact followed by reaccumulation. (216) Kleopatra’s current rotation period and dumbbell shape imply that it is in a critically rotating state. The low effective gravity along the equator of the body, together with the equatorial orbits of the moons and possibly rubble-pile structure, opens the possibility that the moons formed via mass shedding. Conclusions. (216) Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. This system certainly deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission, to decipher its entire formation history. 

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 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.C-0074), 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 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, m 1 = (1.49 ± 0.16) × 10 −12 M ⊙ or 2.97 × 10 18 kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body. 

ABSTRACT High angular resolution disc-resolved images of (7) Iris collected by VLT/SPHERE instrument are allowed for the detailed shape modelling of this large asteroid revealing its surface features. If (7) Iris did not suffer any events catastrophic enough to disrupt the body (which is very likely) by studying its topography, we might get insights into the early Solar system’s collisional history. When it comes to internal structure and composition, thoroughly assessing the volume and density uncertainties is necessary. In this work, we propose a method of uncertainty calculation of asteroid shape models based on light curve and adaptive optics (AO) images. We apply this method on four models of (7) Iris produced from independent Shaping Asteroids using Genetic Evolution and All-Data Asteroid Modelling inversion techniques and multiresolution photoclinometry by deformation. Obtained diameter uncertainties stem from both the observations from which the models were scaled and the models themselves. We show that despite the availability of high-resolution AO images, the volume and density of (7) Iris have substantial error bars that were underestimated in the previous studies.