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ADM tetrad gravity is an Hamiltonian reformulation of General Relativitywhich gives new insight to the Dark Matter Problem. We impose constraints onthe parameter space of ADM tetrad gravity with a Yukawa-like ansatz for thetrace of the extrinsic curvature of the 3D hypersurfaces by fitting the orbitof the S2 star around the Black Hole in the Galactic center and using theperihelia of some of the planets of the Solar System. We find very thightconstraints on the \emph{strength} of the coupling, $4.2 \,\times \, 10^{-4} \,\text{AU}\,\lesssim \, \delta \, \lesssim \, 4.6 \, \times \, 10^{-4} \,\text{AU}$, and an upper limit for the (inverse) scale length, $\mu \, \lesssim\, 3.5 \, \times \, 10^{-6} \, \text{AU}^{-1}$.

Constraints on ADM tetrad gravity parameter space from S2 star in the center of the Galaxy and from the Solar System