S-star dynamics through a Yukawa–like gravitational potential

Abstract

We use S-stars observations to constrain a phenomenological Yukawa-like gravitational potential whose deviations from General Relativity are parametrized by two couplings, the strength of the potential, δ, and its length scale, λ. In order to constrain their value using the data of S-stars orbit, we adopt a fully relativistic approach which consists of solving the geodesic equations instead of just putting the modified gravitational potential in the standard Newton’s law. As a result, we do not detect any significant departure from GR, even using more stars simultaneously.