The laser-tracked geodetic satellites LAGEOS , LAGEOS II and LARES are currently employed , among other things , to measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth with the hope of providing a more accurate test of such a prediction of the Einstein ’ s theory of gravitation than the existing ones .
The secular decay \dot { a } of the semimajor axes a of such spacecrafts , recently measured in an independent way to a \sigma _ { \dot { a } } \approx 0.1 - 0.01 m yr ^ { -1 } accuracy level , may indirectly impact the proposed relativistic experiment through its connection with the classical orbital precessions induced by the Earth ’ s oblateness J _ { 2 } . Indeed , the systematic bias due to the current measurement errors \sigma _ { \dot { a } } is of the same order of magnitude of , or even larger than , the expected relativistic signal itself ; moreover , it grows linearly with the time span T of the analysis . Therefore , the parameter-fitting algorithms must be properly updated in order to suitably cope with such a new source of systematic uncertainty .
Otherwise , an improvement of one-two orders of magnitude in measuring the orbital decay of the satellites of the LAGEOS family would be required to reduce this source of systematic uncertainty to a percent fraction of the Lense-Thirring signature .