The Galactic center offers us a unique opportunity to test General Relativity(GR) with the orbits of stars around a supermassive black hole. Observations ofthese stars have been one of the great successes of adaptive optics on 8-10 mtelescopes, driving the need for the highest angular resolution and astrometricprecision. New tests of gravitational physics in the strong gravity regime withstellar orbits will be made possible through the leap in angular resolution andsensitivity from the next generation of extremely large ground-basedtelescopes. We present new simulations of specific science cases such as thedetection of the GR precession of stars, the measurement of extended dark mass,and the distance to the Galactic center. We use realistic models of theadaptive optics system for TMT and the IRIS instrument to simulate thesescience cases. In additions, the simulations include observational issues suchas the impact of source confusion on astrometry and radial velocities in thedense environment of the Galactic center. We qualitatively show howimprovements in sensitivity, astrometric and spectroscopic precision, andincreasing the number of stars affect the science with orbits at the Galacticcenter. We developed a tool to determine the constraints on physical modelsusing a joint fit of over 100 stars that are expected to be observable withTMT. These science cases require very high astrometric precision and stability,thus they provide some of the most stringent constraints on the plannedinstruments and adaptive optics systems.
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