Reconstruction of stellar orbits close to Sagittarius A*: Possibilities for testing general relativity

We have reconstructed possible orbits for a collection of stars located wit hin 0."5 of Sgr A*. These orbits are constrained by observed stellar positi ons and angular proper motions. The construction of such orbits serves as a baseline from which to search for possible deviations due to the unseen ma ss distribution in the central 1000 AU of the Galaxy. We also discuss the l ikelihood that some of these stars may eventually exhibit detectable relati vistic effects, allowing for interesting tests of general relativity around the 2.6 x 10(6) M. central object.