Number of stars with a magnitude range in the G-band of 12 ≤ G ≤ 20 per square degree versus the cumulative distribution of each of their proper motion as seen on the sky, listed in seven directions as given by the galactic coordinates (l, b). The values (l, b) are listed at the right in the same sequence as the curves are seen. The red dashed line at μ = 0.3 mas/yr represents the estimated error of the proper motions from Gaia at G = 20 mag. The red dotted line at μ = 0.03 mas/yr represents the estimated error of the proper motions derived from the positions obtained from Gaia and the proposed Gaia successor mission, also at G = 20 mag.