  We present the first measurement of the proper motion of the young, compact
Arches cluster near the Galactic center from near-infrared adaptive optics (AO)
data taken with the recently commissioned laser-guide star (LGS) at the Keck
10-m telescope. The excellent astrometric accuracy achieved with LGS-AO
provides the basis for a detailed comparison with VLT/NAOS-CONICA data taken
4.3 years earlier. Over the 4.3 year baseline, a spatial displacement of the
Arches cluster with respect to the field population is measured to be 24.0 +/-
2.2 mas, corresponding to a proper motion of 5.6 +/- 0.5 mas/yr or 212 +/- 29
km/s at a distance of 8 kpc. In combination with the known line-of-sight
velocity of the cluster, we derive a 3D space motion of 232 +/- 30 km/s of the
Arches relative to the field. The large proper motion of the Arches cannot be
explained with any of the closed orbital families observed in gas clouds in the
bar potential of the inner Galaxy, but would be consistent with the Arches
being on a transitional trajectory from x1 to x2 orbits. We investigate a
cloud-cloud collision as the possible origin for the Arches cluster. The
integration of the cluster orbit in the potential of the inner Galaxy suggests
that the cluster passes within 10 pc of the supermassive black hole only if its
true GC distance is very close to its projected distance. A contribution of
young stars from the Arches cluster to the young stellar population in the
inner few parsecs of the GC thus appears increasingly unlikely. The measurement
of the 3D velocity and orbital analysis provides the first observational
evidence that Arches-like clusters do not spiral into the GC. This confirms
that no progenitor clusters to the nuclear cluster are observed at the present
epoch.
