Predicted motions of the background stars for the events by Luyten 143-23 in 2018 (top), in 2021 (middle), and by Ross 322 in 2018 (bottom). The origin of the coordinate system is the background star’s J2015.5 position. The thin green lines show the unaffected motions of the background stars, the expected paths are shown as thick blue/thin red lines (red parts indicate the epochs at which the star is not observable). δθ_c is the difference between both lines at the same epoch. The black dots indicate equal time intervals of 3 months.