Positional offsets of ten randomly chosen astrometric sources, as produced by two GWs propagating in the same direction and having the same frequency, but with different strain parameters $h_{+}^{\text{c}},h_{+}^{\text{s}},h_{\times }^{\text{c}}$, and $h_{\times }^{\text{s}}$. Top: for a GW with randomly chosen strain parameters, yielding the (random) axis ratio ≃0.24 (corresponding to e ≃ 0.97). Bottom: for a GW with $h_{+}^{\text{c}}=h_{+}^{\text{s}}=h_{\times }^{\text{c}}=h_{\times }^{\text{s}}$, yielding an axis ratio = 0 (corresponding to e = 1). The offsets are shown in the local tangential coordinates of respective source, normalised by Δ_max, and colour-coded by time normalised to the mission duration T. The GW period is P_gw = 6T. The grey lines show the complete path that would be traced for T ≥ P_gw . None of the randomly selected sources is exactly at 90^◦ angle from the GW source, so none of the ellipses attains the maximum semimajor axis Δ_max . (The Rømer correction was neglected in these plots, but would hardly be visible if it were included.)