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The strategy followed so far in the performed or proposed tests of thegeneral relativistic Lense-Thirring effect in the gravitational field of theEarth with laser-ranged satellites of LAGEOS type relies upon the cancelationof the disturbing huge precessions induced by the first even zonal harmoniccoefficient J_2 of the multipolar expansion of the Newtonian part of theterrestrial gravitational potential by means of suitably designed linearcombinations of the nodes \Omega of more than one spacecraft. Actually, such aremoval does depend on the accuracy with which the coefficients of thecombinations adopted can be realistically known. Uncertainties of the order of2 cm in the semimajor axes a and 0.5 milliarcseconds in the inclinations I ofLAGEOS and LAGEOS II, entering the expression of the coefficient c_1 of thecombination of their nodes used so far, yield an uncertainty \delta c_1 = 1.3010^-8. It gives an imperfectly canceled J_2 signal of 10.8 milliarcseconds peryear corresponding to 23% of the Lense-Thirring signature. Uncertainties of theorder of 10-30 microarcseconds in the inclinations yield \delta c_1=7.9 10^-9which corresponds to an uncanceled J_2 signature of 6.5 milliarcseconds peryear, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOSII-LARES combination with coefficients k_1 and k_2, the same uncertainties in aand the less accurate uncertainties in I as before yield \delta k_1=1.1 10^-8,\delta k_2=2 10^-9; they imply a residual J_2 combined precession of 14.7milliarcseconds per year corresponding to 29% of the Lense-Thirring trend.Uncertainties in the inclinations at about 10 microarcseconds level give \deltak_1=5 10^-9, \delta k_2 = 2 10^-9; the uncanceled J_2 effect is 7.9milliarcseconds per year, i.e. 16% of the relativistic effect.

How accurate is the cancelation of the first even zonal harmonic of the geopotential in the present and future LAGEOS-based Lense-Thirring tests?