Tidal contributions to neutron star orbital precession around Sgr $A^*$

We investigate tidal contributions to the orbital precession of neutron stars around the supermassive black hole Sgr A*, using stellar configurations described by the Tolman - Oppenheimer - Volkoff equations. We examine the dependence of tidal precession on stellar compactness, pericentre distance, and the quadrupolar tidal Love number $k_2$, and compare its magnitude with general relativistic orbital precession. The calculated tidal angular shift decreases strongly with increasing pericentre distance and, for the stellar configurations considered, with increasing compactness. Larger Love numbers enhance the tidal contribution. This behaviour reflects the strong dependence of tidal precession on the stellar-radius-to-pericentre-distance ratio, $(R/r_p)^5$. Despite the enhancement during closer encounters, the predicted tidal shifts remain extremely small, reaching approximately $3.5 \times 10^{-18},μas$ within the displayed parameter range. The ratio of tidal to general relativistic precession spans approximately $10^{-33}$ - $10^{-28}$, indicating that relativistic precession overwhelmingly dominates. Our results suggest that direct detection of the neutron-star tidal contribution through orbital precession around Sgr A* would be exceptionally challenging under the assumptions of the adopted model.