  According to General Relativity, as distinct from Newtonian gravity, motion
under gravity is treated by a theory that deals, initially, only with test
particles. At the same time, satellite measurements deal with extended bodies.
We discuss the correspondence between geodesic motion in General Relativity and
the motion of an extended body by means of the Ehlers-Geroch theorem, and in
the context of the recently launched LAser RElativity Satellite (LARES). Being
possibly the highest mean density orbiting body in the Solar system, this
satellite provides the best realization of a test particle ever reached
experimentally and provides a unique possibility for testing the predictions of
General Relativity.
