Best-fit model with . Top: orbits of Kleopatra’s moons plotted in the (u, v) coordinates (blue, green lines), observed absolute astrometry (SKY; black circles), and residuals (red and orange lines for bodies 2 and 3, respectively; i.e., inner and outer satellites). Kleopatra’s shape model for one of the epochs is overplotted in grey. The axes are scaled in km; with a variable viewing geometry, but without a variable distance. The mean semimajor axes of orbits are: a₁ 499 km, a₂ 655 km. Bottom: residuals of (u, v) in arcseconds for the epochs of the three datasets (DESCAMPS, SPHERE2017, SPHERE2018). The uncertainties on astrometric observations were approximately 0.01 arcsec.