The impact of gravitational lensing in the reconstruction of stellar orbits around Sgr A*

After the amazing discoveries by the GRAVITY collaboration in the last few years on the star S2 orbiting the black hole Sgr A* in the center of the Milky Way, we present a detailed investigation of the impact of gravitational lensing on the reconstruction of stellar orbits around this massive black hole. We evaluate the lensing astrometric effects on the stars S2, S38 and S55 and how these systematically affect the derived orbital parameters. The effect is below current uncertainties, but not negligible. With the addition of more observations on these stars, it will be possible to let the astrometric shift by lensing emerge from the statistical noise and be finally detected. By repeating the analysis on a smaller semimajor axis $a$ and various inclinations $i$, we are able to quantify the lensing effects on a broader range of parameters. As expected, for smaller semimajor axes and for nearly edge-on orbits lensing effects increase by about an order of magnitude.