ALMA Astrometry of the Objects within 0.5 pc of Sagittarius A$^\ast$
  Atacama Large Millimeter/Submillimeter Array (ALMA) is promising to be a
powerful 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 Star
Cluster 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 in
the area with the accuracy of 0.001". We also analyzed the similar ALMA
archival data obtained in June 2019 and determined the 64 relative positions in
these objects. We derived the proper motions relative to Sgr A$^\ast$ by
comparing these positions. The derived proper motions are roughly described
with both clockwise and counterclockwise rotations around Sgr A$^\ast$. The
rotation velocities are reproduced by Kepler orbits bounded around Sgr
A$^\ast$. Moreover, the proper motions include co-moving clusters for example
IRS13E and IRS13N. The positions and proper motions are almost consistent with
those by previous infrared observations. Therefore the observational
demonstrations would prove that ALMA is a powerful tool for precision
astrometry of the region.
