Astrometric eccentricity dependence of distance and magnitude detection limits for Δχ² = 100 for a G2V star and a 10 M_J BD with P = 4 yr. The black point at e = 0 corresponds to the black point in the middle panel of Fig. A.2. Sky-detection fractions of 50 percentile (thick line) and 10–90 percentile (shaded region) illustrate that the detection threshold for such a (randomly oriented) system varies by ±25%, depending on sky position.