2021MNRAS.502.3761L

The Galactic Centre (Sgr A*), hosting a supermassive black hole, carries sufficient potential for testing gravitational theories. Existing astrometric facilities on Very Large Telescope (VLT) and the Keck Telescope have enabled astronomers to study stellar orbits near Sgr A* and perform new astronomical tests of gravitational theories. These observations have provided strong field tests of gravity (ph/c² ∼ 10^–3, which is much greater than ph/c² for the Solar system). In this work, we have estimated magnitudes of various contributions to the periastron shift of compact stellar orbits near Sgr A* for pericentre distance in the range r_p = (0.3 - 50)au at a fixed orbital inclination, i = 90°. We take the spin of the black hole as χ = 0.1, 0.44, and 0.9 and eccentricities of the orbit as e = 0.9. The relativistic effects including orders beyond 1PN and spin induced effects are incorporated in the contributions. Effect of tidal distortion on periastron shift has also been added into the estimation by considering gravitational Love numbers for polytropic models of the stars. For the tidal effect, we have considered updated mass-radii relations for low-mass stars and high-mass stars. It has been found that the tidal effect on periastron shift arising from stars represented by polytropes of indices n = 1 and n = 3 terminate above r_p ∼ 2 au and r_p ∼ 1 au, respectively. The periastron shift angle for the stars has been compared with the astrometric capabilities of existing large telescopes and upcoming extremely large telescopes. Challenges and prospects associated with the estimations are highlighted.