Change in orbit fit quality due to the nonspherical shapes of Haumea’s satellites. In this plot, ﹩{\rm{\Delta }}{\chi }^{2}={\sum }^{i}({x}_{i,{J}_{2}}-{x}_{i,{J}_{2}=0})/{\sigma }_{i,\mathrm{obs}}﹩, where ﹩{x}_{i,{J}_{2}}﹩ and ﹩{x}_{i,{J}_{2}=0}﹩ are synthetic astrometric measurements from models including satellite J ₂ and those without. σ _i,obs are the true measurement uncertainties for the system as tabulated in Table 1. This formulation allows us to directly determine whether the satellites’ J ₂ values produce detectable changes in the system relative astrometry, given our current observations (HST+Keck). The parameters for the models used were taken from the best fit of our orbit fits. The rotational poles of the satellites were chosen to have high obliquities (with respect to their Haumea-centric orbits) to enhance the effect of J ₂. The three separate lines show each satellite’s individual contribution, as well as a comparison where both satellites have (the same) J ₂. For reasonable values, J ₂ ≲ 0.5, very little change in fit quality is found, although for extremely nonspherical shapes, Hi’iaka’s J ₂ could begin to alter the fit.