Solar System Constraints on the Yukawa Potential in f(R) Gravity

<p>The gravity theory is a modification of general relativity that yields a Yukawa gravitational potential in the weak-field limit. This potential modifies the Newtonian potential by adding an exponential term that depends on the parameters and . In this study, we test the consistency of the Yukawa potential with observational data on the perihelion precession of planets in the solar system. Using observational data from the planets, we estimate the parameters and that are consistent with observations. Additionally, we analyze the constraints imposed by the Parametrized Post-Newtonian (PPN) formalism on these parameters. The results indicate that the parameter can be taken within the range , with a relatively small value of . Observational constraints from the Cassini and MESSENGER missions also provide tight bounds on the PPN parameters and . These findings suggest that the Yukawa potential in gravity can explain gravitational phenomena on the scale of the solar system without violating existing observational constraints.</p>