Einstein is still right: new tests of gravitational dynamics in the field of the Earth

It is presented and discussed here a recent analysis of LAGEOS II laser tracking data, which led to the first direct verification of the gravitoelectric relativistic precession in the field of the Earth, and to the simultaneous measurement of the Lense-Thirring and de Sitter effects. Emphasis is given on the analysis strategy and the modelization issues. It is also shown a further result, consisting in a new limit, much more stringent than the previous ones, on a possible non-Newtonian (Yukawa-like) interaction, acting at the scale of the system semimajor axis.