2 Construction of the physical ephemeris

Radar observations provide the spin-axis direction $(72^\circ; 27^\circ)$ in ecliptic B1950 coordinates, and the topographic model of Kleopatra. The zero rotational phase is calculated in this work in order to match the positions of observed lightcurve extrema. The resulting orientation of the body agrees within a few degrees with the November 1999 radar observations (Fig. 2 of Ostro et al. 2000). From this, the body's physical ephemeris, or apparent shape and size in the plane-of-sky-view, can easily be obtained for any given epoch of observation.

Predicted lightcurves can then be computed from the physical ephemeris. However, radar images do not carry information about the photometric properties in the optical domain of a body's surface. These light-scattering properties can, on the other hand, be constrained from observed lightcurves (Lagerkvist et al. 1996). We have introduced different scattering laws, i.e. normalized brightness distributions: uniform brightness I=1, Lambert $I=\mu_0$, Lommel-Seeliger $I=\mu_0/(\mu+\mu_0)$, Minnaert $I=\mu_0^k~\mu^{k-1}$, where $\mu_0$ and $\mu$ are cosines of the angles of emission and incidence, respectively. Among these scattering laws the parameterized Minnaert law (Minnaert 1941) with $k=0.6\pm0.1$ better reproduces the lightcurves of Kleopatra observed at moderate aspect and solar-phase angles. This means that Kleopatra appears with a moderate center-to-limb darkening, in agreement with Hestroffer & Mignard (1997), Hestroffer (1998) or Ragazzoni et al. (2000). Once the physical ephemeris, albedo variation, and light-scattering are set, it is possible to model the image and brightness distribution at visible wavelengths at any epoch.