  Bootstrapped Newtonian gravity is a non-linear 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 centre. These bounds make vacuum bootstrapped
Newtonian gravity experimentally indistinguishable from General Relativity.
