We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive , young stars located within 3 \farcs 5 ( 0.14 pc ) of the supermassive black hole at the Galactic Center .
Our proper motion measurements have uncertainties of only 0.07 mas yr ^ { -1 } ( 3 km s ^ { -1 } ) , which is \gtrsim 7 times better than previous proper motion measurements for these stars , and enables us to measure accelerations as low as 0.2 mas yr ^ { -2 } ( 7 km s ^ { -1 } yr ^ { -1 } ) .
Using these measurements , line-of-sight velocities from the literature , and 3D velocities for additional young stars in the central parsec , we constrain the true orbit of each individual star and directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed .
Analysis of the stellar orbits reveals only one of the previously proposed disks of young stars using a method that is capable of detecting disks containing at least 7 stars .
The detected disk contains 50 % of the young stars , is inclined by \sim 115 ^ { \circ } from the plane of the sky , and is oriented at a position angle of \sim 100 ^ { \circ } East of North .
Additionally , the on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger projected radii as \propto r ^ { -2 } .
The disk has an out-of-the-disk velocity dispersion of 28 \pm 6 km s ^ { -1 } , which corresponds to a half-opening angle of 7 ^ { \circ } \pm 2 ^ { \circ } , and several candidate disk members have eccentricities greater than 0.2 .
Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple , thin circular disk .