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Extended gravity is widely constrained in different astrophysical andastronomical systems. Since these different systems are based on differentscales it is not trivial to get a combined constraint that is based ondifferent phenomenology. Here, for the first time (to the best of ourknowledge), we combine constraints for $f(R)$ gravity from late time Cosmologyand the orbital motion of the stars around the galactic center. $f(R)$ gravitymodels give different potentials that are tested directly in the galacticcenter. The cosmological data set includes the type Ia supernova and baryonacoustic oscillations. For the galactic star center data set we use thepublished orbital measurements of the S2 star. The constraints on the universalparameter $\beta$ from the combined system give: $\beta_{HS}=0.154 \pm 0.109$for the Hu-Sawicki model, while $\beta_{St}= 0.309 \pm 0.19 $ for theStarobinsky dark energy model. These results improve on the cosmologicalresults we obtain. The results show that {{\it combined constraint}} fromdifferent systems yields a stronger constraint for different theories underconsideration. Future measurements from the galactic center and from cosmologywill give better constraints on models with $f(R)$ gravity.

Strengthening extended Gravity constraints with combined systems: $f(R)$ bounds from Cosmology and the Galactic Center