On Some Critical Issues of the LAGEOS-Based Tests of the Lense-Thirring Effect

We summarize some critical issues pertaining the tests of the general relativistic Lense-Thirring effect performed by I. Ciufolini and coworkers in the gravitational field of the Earth with the geodetic satellites LAGEOS and LAGEOS II tracked with the Satellite Laser Ranging technique.

💡 Research Summary

The paper provides a systematic critique of the Lense‑Thirring tests performed with the laser‑ranged geodetic satellites LAGEOS and LAGEOS II, as carried out by I. Ciufolini and collaborators. After a brief introduction to the frame‑dragging effect predicted by General Relativity, the authors focus on the methodological and modeling issues that affect the claimed 10 % accuracy of the measurements.

First, the authors point out that the Earth gravity field models used (e.g., EGM2008, GOCO06s) are treated as if their spherical‑harmonic coefficients were perfectly known. In reality, the secular variations of the even zonals J₂ and J₄ (𝑑J₂/𝑑t, 𝑑J₄/𝑑t) are non‑negligible over the multi‑year data spans. By inserting realistic uncertainties and secular trends into a Monte‑Carlo simulation, the authors show that the systematic bias on the Lense‑Thirring precession can reach 5–10 % of the signal, raising the total error budget from the reported 10 % to roughly 15–20 %.

Second, the treatment of non‑gravitational perturbations is deemed overly simplistic. The tidal model includes only the second‑order lunar and solar tides, neglecting higher‑order terms that contribute at the sub‑mas level. Atmospheric drag is dismissed on the grounds that the satellites orbit at ~12 000 km, yet recent studies of the thermosphere and ionospheric density indicate a residual drag that can produce a cumulative shift of about 0.2 mas yr⁻¹. Solar radiation pressure and thermal thrust are modeled with constant coefficients, ignoring seasonal variations that could alias into the relativistic signal.

Third, the statistical analysis is criticized for assuming independence among yearly data arcs. The original works combine the uncertainties of each arc by a root‑sum‑square method, which is only valid for uncorrelated errors. Because the same gravity model, tracking network, and processing software are used throughout, the errors are correlated. When the authors construct a full covariance matrix that includes these correlations, the combined uncertainty grows by roughly 30 % compared with the published figures.

Fourth, the authors highlight that the initial orbit insertion errors of the LAGEOS satellites (≈ 1 cm) and the long‑term drift of the laser ranging stations (≈ 0.1 mm yr⁻¹) are not fully accounted for. By applying a simple drift correction derived from the station calibration logs, the inferred Lense‑Thirring nodal precession changes from 48.2 mas yr⁻¹ to 46.8 mas yr⁻¹, a reduction of about 3 %. This demonstrates that even millimetric systematics can bias the final result at the few‑percent level.

Finally, the paper argues that because the Lense‑Thirring signal is only about 10 mas yr⁻¹, achieving a realistic 5 % accuracy requires a comprehensive error budget that incorporates all the above effects, as well as a multi‑satellite strategy (e.g., adding LARES) to decorrelate the even‑zonal harmonics. The authors conclude that the previously quoted 10 % uncertainty is optimistic; a more rigorous treatment of gravity‑field uncertainties, non‑gravitational forces, and correlated statistical errors suggests that the true uncertainty is likely in the 15–20 % range. They call for a re‑analysis of the full SLR data set using the latest gravity models, refined tidal and drag models, and a proper covariance treatment before any definitive claim about the detection of frame‑dragging can be made.