Bootstrapped Newtonian gravity is a nonlinear version of Newton's law, which can be lifted to a fully geometric theory of gravity starting from a modified potential. Here, we study geodesics in the bootstrapped Newtonian effective metric in vacuum and obtain bounds on a free parameter from Solar System data and S-star orbits near our Galaxy center. These bounds make vacuum bootstrapped Newtonian gravity experimentally indistinguishable from General Relativity.
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