# An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging

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## Abstract

We deal with the attempts to measure the Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES spacecraft. According to general relativity, a central spinning body of mass *M* and angular momentum * S* like the Earth generates a gravitomagnetic field which induces small secular precessions of the orbit of a test particle geodesically moving around it. Extracting this signature from the data is a demanding task because of many classical orbital perturbations having the same pattern as the gravitomagnetic one, like those due to the centrifugal oblateness of the Earth which represents a major source of systematic bias. The first issue addressed here is: are the so far published evaluations of the systematic uncertainty induced by the bad knowledge of the even zonal harmonic coefficients

*J*

_{ ℓ }of the multipolar expansion of the Earth’s geopotential reliable and realistic? Our answer is negative. Indeed, if the differences Δ

*J*

_{ ℓ }among the even zonals estimated in different Earth’s gravity field global solutions from the dedicated GRACE mission are assumed for the uncertainties

*δ*

*J*

_{ ℓ }instead of using their covariance sigmas \(\sigma_{J_{\ell}}\) , it turns out that the systematic uncertainty

*δ*

*μ*in the Lense-Thirring test with the nodes

*Ω*of LAGEOS and LAGEOS II may be up to 3 to 4 times larger than in the evaluations so far published (5–10%) based on the use of the sigmas of one model at a time separately. The second issue consists of the possibility of using a different approach in extracting the relativistic signature of interest from the LAGEOS-type data. The third issue is the possibility of reaching a realistic total accuracy of 1% with LAGEOS, LAGEOS II and LARES, which should be launched in November 2009 with a VEGA rocket. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be likely placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact has been evaluated with the standard Kaula’s approach up to degree

*ℓ*=60 by using Δ

*J*

_{ ℓ }and \(\sigma_{J_{\ell }}\) ; it turns out that it may be as large as some tens percent. The different orbit of LARES may also have some consequences on the non-gravitational orbital perturbations affecting it which might further degrade the obtainable accuracy in the Lense-Thirring test.

## Keywords

Experimental tests of gravitational theories Satellite orbits Harmonics of the gravity potential field## PACS

04.80.Cc 91.10.Sp 91.10.Qm## Preview

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