Some comments about a recent paper on the measurement of the general relativistic Lense-Thirring in the gravitational field of the Earth with the laser-ranged LAGEOS and LAGEOS II satellites

In this brief note some comments about the observable used in a recently published paper on the measurement of the general relativistic Lense-Thirring in the gravitational field of the Earth are presented. It turns out that, among other things, the authors might have yielded an optimistic evaluation of the error budget because of an underestimation of the impact of the secular variations of the even zonal harmonics of the geopotential. More realistic evaluations point towards a 15-45% error at 1-3σ level, respectively. 1 On the adopted observable In a recently published paper [1], submitted 2 June 2004 and accepted 10 September 2004, a measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the laser-ranged satellites LAGEOS and LAGEOS II is reported. The claimed total accuracy is 5 − 10%. The observable used in the analysis is the following linear combination of the residuals of the longitudes of the ascending nodes Ω of LAGEOS and LAGEOS II δΩ̇ + c1δΩ̇ LAGEOS II ∼ μLT48.2, (1) in which c1 = 0.546 and μLT is a scaling parameter which is 1 in the Einstein’s General Theory of Relativity and 0 in the Newtonian mechanics. Eq. (1) allows to cancel out all the static and time-dependent contributions of the first even zonal harmonic coefficient J2 of the multipolar expansion of the Earth gravitational potential which represents one of the major sources of