Characterizing the astrometric precision limit for moving targets observed with digital-array detectors

Aims. We investigate the maximum astrometric precision that can be reached on moving targets observed with digital-sensor arrays, and provide an estimate for its ultimate lower limit based on the Cram\'er-Rao bound. Methods. We extend previous work on one-dimensional Gaussian point-spread functions (PSFs) focusing on moving objects and extending the scope to two-dimensional array detectors. In this study the PSF of a stationary point-source celestial body is replaced by its convolution with a linear motion, thus effectively modeling the spread function of a moving target. Results. The expressions of the Cram\'er-Rao lower bound deduced by this method allow us to study in great detail the limit of astrometric precision that can be reached for moving celestial objects, and to compute an optimal exposure time according to different observational parameters such as seeing, detector pixel size, decentering, and elongation of the source caused by its drift. Comparison to simulated and real data shows that the predictions of our simple model are consistent with observations.