arXiv:gr-qc/0111086v3 22 May 2002 IL NUOVO CIMENTO Vol. ?, N. ? ? Recent Developments in Testing General Relativity with Satellite Laser Ranging L. Iorio( 1 )( ∗ ) ( 1 ) Dipartimento di Fisica dell’Universit` a di Bari, Via Amendola 173, 70126, Bari, Italy. 1. – Introduction The last decade can be characterized by an impressive diversity of techniques mon- itoring the artificial and natural satellite dynamics, as well as the Earth rotation: im- proved laser technology, renewed Doppler techniques, satellite radar altimetry, massive usage of the Global Positioning System (GPS), etc. Each of these techniques is opti- mally tailored to a specific type of application or scientific problem. For example, it appears that laser tracking (SLR: see on the WEB: http://ilrs.gsfc.nasa.gov) of pas- sive geodynamics satellites (LAGEOS, LAGEOS II, Starlette, Stella, Ajisai, Etalon I and II) over relatively long time intervals provides an excellent method for determin- ing the long-term variations of the geopotential [1] (including tidal effects) and many small non-gravitational phenomena [2]. It turns out that the precision reached in the latest years by such technique in measuring the position of the passive laser-ranged geodetic satellites LAGEOS and LAGEOS II amounts to 1 cm or better( 1 ). See, e.g., http://earth.agu.org/revgeophys/marsha01/node1.html Such astonishing levels of accuracy have disclosed an unexpectedly wide field of re- search in space geodesy, geophysics and fundamental physics. E.g., now it is possible to plan satellite-based experiments devoted to the experimental control even of some tiny post-Newtonian features of the Earth’gravitational field predicted by Einstein’ s General Relativity [3]. They are usually expressed in terms of certain solve-for least squares fits’ parameters. In evaluating the precision of the results of these experiments it must be considered that, in general, the main error does not consist of the standard statistical error of the fits but of the various systematic errors. They are induced by a complete set of other physical effects acting upon the satellites to be employed [4]. Such perturbations are often quite larger than the relativistic effects investigated and induce systematic errors to be correctly evaluated and assessed. Many of these aliasing effects are traditionally investigated by geophysics and space geodesy, so that such experiments are multidisciplinary efforts which cover many scientific areas until now separated [5, 6]. Indeed, the expansion of the SLR network, together with improved system accuracies, has enabled the laser data to contribute directly to improving orbit force models. It allows one to calculate more accurately, among other things, the error budget of many ( * ) E–mail: Lorenzo.Iorio@ba.infn.it ( 1 ) In August 2001 the single-shot accuracy in tracking LAGEOS at Matera amounts to 5 mm c  Societ` a Italiana di Fisica 1