Monitoring lensed starlight emitted close to the Galactic Center

We describe the feasibility of detecting the gravitational deflection of light emitted by stars moving under the influence of the massive object at the Galactic center. Light emitted by a star orbiting behind the central mass has a smaller impact parameter than the star itself, and suffers the effect of gravitational lensing, providing a closer probe of the central mass distribution and hence a stricter test of the black hole hypothesis. A mass of $4.3\times {10}^6{M}_{\odot }$ causes a $0.1-2\mathrm{m}\mathrm{a}\mathrm{s}$ deviation in the apparent position of orbiting stars projected within ${10}^{\circ }$ of the line of sight to the galactic center. In addtion, we may uniquely constrain the distance to the center of the galaxy because lensing deflections constrain the ratio $\text{rg}\mathrm{/}{R}_0$ of the Schwarzschild radius to the distance to the black hole, $R_o$, whereas the ratio $\text{rg}\mathrm{/}{R}_o^3$ is obtained by fitting the orbit.