An advanced multipole model for (216) Kleopatra triple system
Abstract
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 Nbody 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 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.
Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under program 199.C0074 (PI Vernazza).
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 2021
 DOI:
 10.1051/00046361/202140901
 arXiv:
 arXiv:2105.09134
 Bibcode:
 2021A&A...653A..56B
 Keywords:

 minor planets;
 asteroids: individual: (216) Kleopatra;
 planets and satellites: fundamental parameters;
 astrometry;
 celestial mechanics;
 methods: numerical;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 accepted in A&