  In this proceeding, we show how observations of Solar System Objects with
Gaia can be used to test General Relativity and to constrain modified
gravitational theories. The high number of Solar System objects observed and
the variety of their orbital parameters associated with the impressive
astrometric accuracy will allow us to perform local tests of General
Relativity. In this communication, we present a preliminary sensitivity study
of the Gaia observations on dynamical parameters such as the Sun quadrupolar
moment and on various extensions to general relativity such as the parametrized
post-Newtonian parameters, the fifth force formalism and a violation of Lorentz
symmetry parametrized by the Standard-Model extension framework. We take into
account the time sequences and the geometry of the observations that are
particular to Gaia for its nominal mission (5 years) and for an extended
mission (10 years).
