Authors: Lorenzo Iorio
Publish Date: 2011/02/08
Volume: 43, Issue: 6, Pages: 1697-1706
Abstract
The strategy followed so far in the performed or proposed tests of the general relativistic LenseThirring effect in the gravitational field of the Earth with laserranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions induced by the first even zonal harmonic coefficient J 2 of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed linear combinations of the nodes Ω of more than one spacecraft Actually such a removal does depend on the accuracy with which the coefficients of the combinations adopted can be realistically known Uncertainties of the order of 2 cm in the semimajor axes a and 05 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II entering the expression of the coefficient c 1 of the combination of their nodes used so far yield an uncertainty δc 1 = 130 × 10−8 It gives an imperfectly canceled J 2 signal of 108 milliarcseconds per year corresponding to 23 of the LenseThirring signature Uncertainties of the order of 10–30 microarcseconds in the inclinations yield δc 1 = 79 × 10−9 which corresponds to an uncanceled J 2 signature of 65 milliarcseconds per year ie 14 of the LenseThirring signal Concerning a future LAGEOSLAGEOS IILARES combination with coefficients k 1 and k 2 the same uncertainties in a and the less accurate uncertainties in I as before yield δk 1 = 11 × 10−8 δk 2 = 2 × 10−9 they imply a residual J 2 combined precession of 147 milliarcseconds per year corresponding to 29 of the LenseThirring trend Uncertainties in the inclinations at ≈ 10 microarcseconds level give δk 1 = 5 × 10−9 δk 2 = 2 × 10−9 the uncanceled J 2 effect is 79 milliarcseconds per year ie 16 of the relativistic effect
Keywords: