O ct 2 00 4 How to reach a few percent level in deter - mining the Lense - Thirring effect ?

In this paper we explore the possibility of suitably combining the nodes Ω of the existing geodetic LAGEOS, LAGEOS II and Ajisai laser-ranged satellites and of the radar altimeter Jason–1 satellite in order to increase the accuracy in testing the general relativistic gravitomagnetic Lense–Thirring secular effect in the gravitational field of the Earth. The proposal of introducing Ajisai and Jason–1 in such a combination comes from the expected benefits which could be obtained in reducing the aliasing secular impact of the classical part of the terrestrial gravitational field. According to the recently released EIGEN-CG01C combined GRACE+CHAMP+terrestrial gravimetry/altimetry Earth gravity model, the impact of the static part of the mismodelled even zonal harmonics of geopotential, which represent the major source of systematic error, amounts to 1.6%, at 1−σ level. It is better than the error which could be obtained with a two-node LAGEOS-LAGEOS II only combination (6% at 1−σ). Moreover, the proposed combination would be insensitive also to the secular variations of the lowdegree even zonal harmonics, contrary to the LAGEOS-LAGEOS II only combination. Such variations could be a serious limiting factor over observational time spans many years long. The price to be paid for this improvements of the systematic error of gravitational origin is represented by the non–conservative forces introduced along with the new orbital elements. However, they would induce periodic perturbations, contrary to the gravitational noise. A major concern would be the assessment of the impact of the non–conservative accelerations on the Jason–1 node. According to the present–day force models, the mismodelling in the non–conservative forces would, at worst, induce an aliasing periodic signal with an amplitude of 4% of the Lense-Thirring effect over a time span of 2 years. However, an observational time