If a class of stars orbits the central black hole in our galaxy in short period ( \sim 0.1 year ) , high eccentricity ( \sim 0.9 ) orbits , they will experience precessions of their orbital planes induced by both relativistic frame-dragging and the quadrupolar gravity of the hole , at levels that could be as large as 10 \mu arcseconds per year , if the black hole is rotating faster than 1/2 of its maximum rotation rate .
Astrometric observations of the orbits of at least two such stars can in principle lead to a determination of the angular momentum vector { \bf J } of the black hole and its quadrupole moment Q _ { 2 } .
This could lead to a test of the general relativistic no-hair theorems , which demand that Q _ { 2 } = - J ^ { 2 } / M .
Future high-precision adaptive infrared optics instruments may make such a fundamental test of the black-hole paradigm possible .