  In this paper we investigate the classical non-relativistic limit of the
Eddington-inspired Born-Infeld theory of gravity. We show that strong bounds on
the value of the only additional parameter of the theory \kappa, with respect
to general relativity, may be obtained by requiring that gravity plays a
subdominant role compared to electromagnetic interactions inside atomic nuclei.
We also discuss the validity of the continuous fluid approximation used in this
and other astrophysical and cosmological studies. We argue that although the
continuous fluid approximation is expected to be valid in the case of
sufficiently smooth density distributions, its use should eventually be
validated at a quantum level.
