semimajor axis and flattening of the primary are the main sources of the uncertainty of the bulk density of the system. In addition to that, the uncertainties of the two parameters are not independent. We therefore stepped $a$ and $(A_1 B_1)^{1/2}/C_1$ on a grid (while all other parameters were fitted at each step) to obtain an uncertainty area of both parameters together. The area is shown in Fig. \[66391\_20Ba\_a\_PrimA\_Rho\] with values of the bulk density for each combination of the parameters indicated.

The mutual orbit and shapes of the binary asteroid components of 1999 KW4 were modeled by Ostro et al. (2006) with radar observations taken in 2001. They report the size of the primary to be close to a tri-axial ellipsoid with axes 1417 $\times$ 1361 $\times$ 1183 m ($1\sigma$ uncertainties of $\pm$ 3%), and the secondary to be a tri-axial ellipsoid with axes 595 $\times$ 450 $\times$ 343 m ($1\sigma$ uncertainties of $\pm$ 5%). The dimensions given are extents of dynamically equivalent equal-volume ellipsoid (DEEVE; a homogeneous ellipsoid having the same moment-of-inertia ratios and volume as the shape model).

They also found the parameters of the mutual orbit to be as follows: orbital period $P_{\rm orb} = 17.422 