Gravitational signatures beyond Newton: Exploring hierarchical three-body dynamics

Hierarchical three-body systems offer a compelling framework to explore the subtle interplay between Newtonian and relativistic gravitational effects in astrophysical environments. In this work, we investigate post-Newtonian corrections to the periastron shift within such systems, focusing on the impact of orbital eccentricity. Modeling the secondary body's influence as a quadrupolar perturbation, we compare Newtonian, Schwarzschild, and post-Newtonian quadrupolar contributions to orbital precession. Our analysis demonstrates that Newtonian quadrupolar effects could be observable, for a long monitoring time, in the orbit of the S87 star around Sagittarius A* if an intermediate-mass black hole is present, under the assumptions of our model. Additionally, post-Newtonian quadrupolar corrections may influence the dynamics of small Solar System bodies in the presence of massive companions. Although the predicted effects are minute and require long monitoring periods to be measurable, our analysis clarifies how relativistic corrections enter the dynamics of the third body and outlines the conditions under which future observations could reveal them.