  The accuracy reached in the past few years by Satellite Laser Ranging (SLR)
allows for measuring even tiny features of the Earth's gravitational field
predicted by Einstein's General Relativity by means of artificial satellites.
The gravitomagnetic dragging of the orbit of a test body is currently under
measurement by analyzing a suitable combination of the orbital residuals of
LAGEOS and LAGEOS II. The lower bound of the error in this experiment amount to
12.92%. It is due to the mismodeling in the even zonal harmonics of the
geopotential which are the most important sources of systematic error. A
similar approach could be used in order to measure the relativistic
gravitoelectric pericenter shift in the field of the Earth with a lower bound
of the systematic relative error of 0.6% due to the even zonal harmonics as
well. The inclusion of the ranging data to the Japanese passive geodetic
satellite Ajisai would improve such limits to 10.78% and 0.08% respectively and
would allow to improve the accuracy in the determination of the PPN parameters
beta and gamma.
