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Atacama Large Millimeter/Submillimeter Array (ALMA) is promising to be apowerful tool for precision astrometry of the area around Sagittarius A$^\ast$(Sgr A$^\ast$) because it has the high angular resolution, high sensitivity,and wide field of view. We have observed the area including the Nuclear StarCluster at 230 GHz with ALMA in October 2017. The angular resolution is ~0.03".We determined the relative positions to Sgr A$^\ast$ of 65 compact objects inthe area with the accuracy of 0.001". We also analyzed the similar ALMAarchival data obtained in June 2019 and determined the 64 relative positions inthese objects. We derived the proper motions relative to Sgr A$^\ast$ bycomparing these positions. The derived proper motions are roughly describedwith both clockwise and counterclockwise rotations around Sgr A$^\ast$. Therotation velocities are reproduced by Kepler orbits bounded around SgrA$^\ast$. Moreover, the proper motions include co-moving clusters for exampleIRS13E and IRS13N. The positions and proper motions are almost consistent withthose by previous infrared observations. Therefore the observationaldemonstrations would prove that ALMA is a powerful tool for precisionastrometry of the region.

ALMA Astrometry of the Objects within 0.5 pc of Sagittarius A$^\ast$