A new approach for investigating secular variations of the low-degree geopotential coefficients

Recent tests aimed at the detection of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS and LAGEOS II satellites have proved to be affected, among other things, by the corrupting impact of the secular variations J̇4 and J̇6 of the second and third even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential. Unfortunately, they are, at present, poorly known so that their impact on the performed measurement is ∼ 13% over 11 years. Also the impact of the static part of J4 and J6 is relevant inducing a systematic bias of 4-9% according to different gravity models. Moreover, the currently available values for them may retain an a priori ‘memory’ effect of the Lense-Thirring effect itself. In this paper we suggest a novel method to determine J2, J4, J6 along with their secular variations J̇2, J̇4, J̇6. Our approach is based on the use of three linear combinations of the nodes of LAGEOS, LAGEOS II and Ajisai and the perigee of LAGEOS II. The retrieved values for the even zonal harmonics of interest are, by construction, independent of each other and of the post-Newtonian precessions. The so obtained mini-model could subsequently be used in order to enhance the accuracy and the reliability of the measurements of the Lense-Thirring effect by means of LAGEOS and LAGEOS II satellites. Moreover, it would also allow for a clearer investigation of possible seasonal and interannual variations of J4 and J6.