The impact of the orbital decay of the LAGEOS satellites on the frame-dragging tests

• The semimajor axes a of the LAGEOS-type satellites secularly decrease.
• Such orbital decays are known to σȧ≈0.1–0.01 m yr−1 level.
• a   enters the classical node precession due to the Earth’s oblateness J2J2.
• The errors σȧ cause further residual node shifts δ(ΔΩJ2)δ(ΔΩJ2).
• They are a bias in the frame-dragging tests as large as the GR effect itself.

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 ȧ of the semimajor axes a   of such spacecrafts, recently measured in an independent way to a σȧ≈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 J2J2. Indeed, the systematic bias due to the current measurement errors σȧ 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.