A reassessment of the systematic gravitational error in the LARES mission

In this letter we reexamine the evaluation of the error due to the even zonal harmonics of the geopotential in some proposed tests of relativistic gravitomagnetism with existing and proposed laser-ranged LAGEOS-like satellites in the gravitational field of the Earth. It is particularly important because the error due to the even zonal harmonics of the geopotential is one of the major sources of systematic errors in this kind of measurements. A conservative, although maybe pessimistic, approach is followed by using the diagonal part only of the covariance matrix of the EGM96 Earth's gravity model up to degree l=20. It turns out that, within this context and according to the present level of knowledge of the terrestrial gravitational field, the best choice would be the use of a recently proposed combination which involves the nodes Omega of LAGEOS, LAGEOS II and LARES and the perigees omega of LAGEOS II and LARES. Indeed, it turns out that the unavoidable orbital injection errors in the inclination of LARES would not affect the gravitational error which would also be insensitive to the correlations among the even zonal harmonics of geopotential.