Eccentricities of the Galactic orbits of the BNSs determined by applying Eq. (6) to the Monte Carlo estimated orbits of each binary, assuming either GC isotropy (left panel) or LSR isotropy (right panel), and shown in 2D histograms with ẽ bins of 0.025. For each BNS, we computed ẽ for the trajectories integrated back up to t_max = 200 Myr (as shown in Fig. 8), and also for the trajectories with t_max = 1 Gyr (as used in Sect. 2.2), and compare both ẽ-distributions (t_max = 200 Myr first, and then t_max = 1 Gyr below).