ALMA astrometry of the objects within 0.5 pc of Sagittarius A*

The Atacama Large Millimeter/Submillimeter Array (ALMA) is promising to be a powerful tool for precision astrometry of the area around Sagittarius A* (Sgr A*) because it has a high angular resolution, high sensitivity, and wide field of view. We have observed the area including the Nuclear Star Cluster at 230 GHz with ALMA in 2017 October. The angular resolution is $\sim \!\!{0{^{\prime \prime}_{.}}03}$. We determined the relative positions to Sgr A* of 65 compact objects in the area with an accuracy of $\sim \!\! {0{^{\prime \prime}_{.}}001}$. We also analyzed the similar ALMA archival data obtained in 2019 June and determined the 64 relative positions in these objects. We derived the proper motions relative to Sgr A* by comparing these positions. The derived proper motions are roughly described with both clockwise and counterclockwise rotations around Sgr A*. The rotation velocities are reproduced by Kepler orbits bounded around Sgr A*. Moreover, the proper motions include co-moving clusters, for example IRS13E and IRS13N. The positions and proper motions are almost consistent with those found by previous infrared observations. Therefore the observational demonstrations would prove that ALMA is a powerful tool for precision astrometry of the region.