The impact of the static part of the Earth's gravity field on some tests of General Relativity with Satellite Laser Ranging

In this paper we calculate explicitly the secular classical precessions of the node \Omega and the perigee \omega of an Earth artificial satellite induced by the static, even zonal harmonics of the geopotential up to degree l=20. Subsequently, their systematic errors induced by the mismodelling in the even zonal geopotential coefficients J_l are compared to the general relativistic secular gravitomagnetic and gravitoelectric precessions of the node and the perigee of the existing laser-ranged geodetic satellites and of the proposed LARES.