  The pericenter shift of a binary system represents a suitable observable to
test for possible deviations from the Newtonian inverse-square law in favor of
new weak interactions between macroscopic objects. We analyzed 13 years of
tracking data of the LAGEOS satellites with GEODYN II software but with no
models for general relativity. From the fit of LAGEOS II pericenter residuals
we have been able to obtain a 99.8% agreement with the predictions of
Einstein's theory. This result may be considered as a 99.8% measurement in the
field of the Earth of the combination of the {\gamma} and {\beta} parameters of
general relativity, and it may be used to constrain possible deviations from
the inverse-square law in favor of new weak interactions parametrized by a
Yukawa-like potential with strength {\alpha} and range {\lambda}. We obtained
|{\alpha}|\lesssim1\times10-11, a huge improvement at a range of about 1 Earth
radius.
