  We consider the feasibility of using the Galileo Navigation Satellite System
to constrain possible extensions or modifications to General Relativity, by
assessing the impact of the related additions to the Newtonian potential and
comparing with the available observables: the relative frequency shift and the
time delay of light propagation. We address the impact of deviations from
General Relativity based on the parameterized Post-Newtonian parameters due to
the presence of a Cosmological Constant, of a constant acceleration like the
putative Pioneer anomaly, a Yukawa potential term due to massive scalar fields
and a power-law potential term, which can arise from Ungravity or f(R)
theories.
