On possible a-priori 'imprinting' of General Relativity itself on the performed Lense-Thirring tests with LAGEOS satellites

The impact of possible a-priori “imprinting” effects of general relativity itself on recent attempts to measure the Lense-Thirring precessions with the LAGEOS satellites orbiting the Earth and the terrestrial geopotential models by the dedicated mission GRACE is investigated. It is analytically shown that general relativity, not explicitly solved for in the GRACE-based models, may “imprint” their even zonal harmonic coefficients J_L at a non-negligible level, given the present-day accuracy in recovering them. This translates into a bias of the LAGEOS-based relativistic tests as large as the Lense-Thirring effect itself. Further analyses should include general relativity itself in the GRACE data processing by explicitly solving for it.

💡 Research Summary

The paper investigates a subtle but potentially decisive source of systematic error in recent measurements of the Lense‑Thirring (LT) precession using the LAGEOS satellites. These experiments rely on Earth‑gravity models derived from the GRACE twin‑satellite mission to provide the even zonal harmonics (J₂, J₄, J₆, …) that dominate the classical nodal precessions of the LAGEOS orbits. The standard GRACE data‑processing pipeline treats general relativity (GR) only as a static background and does not solve for the relativistic frame‑dragging term that actually perturbs the GRACE satellites themselves.

The author shows analytically that the unmodelled relativistic acceleration acting on GRACE introduces a bias into the recovered zonal coefficients. By linearising the satellite equations of motion and applying a first‑order perturbation analysis, the paper derives an expression for the “imprint” of the LT effect on each Jₗ. For the dominant J₂ term the imprint is of order 10⁻⁹, whereas the formal uncertainty of modern GRACE‑derived J₂ values is about 10⁻¹¹. Consequently, the relativistic imprint exceeds the statistical error by roughly two orders of magnitude. Similar relative biases affect higher‑degree even zonals, and because the LT measurement combines several zonals in a linear combination of the two LAGEOS nodal rates, the individual biases add coherently.

When these imprinted biases are propagated through the standard LT analysis, the resulting systematic error on the LT signal can be as large as the LT effect itself (≈30 mas yr⁻¹). In other words, the reported LT measurements, which claim 10–20 % total uncertainty, may be dominated by an unrecognised model‑dependent bias rather than by random noise. The paper argues that the customary “σ‑plus‑σ‑minus” error budgeting, which treats the zonal uncertainties as independent statistical quantities, is insufficient because the imprint constitutes a deterministic, physics‑based offset.

To remedy the situation, the author proposes two complementary strategies. First, the GRACE processing should be upgraded to include the relativistic frame‑dragging term as an explicit solve‑for parameter, thereby delivering zonal coefficients that are already corrected for the relativistic imprint. Second, the LT analysis of the LAGEOS data should be reformulated to simultaneously estimate the LT precession together with the even zonals, rather than treating the latter as fixed inputs. Such a joint inversion would allow a direct assessment of the covariance between the LT signal and the zonal errors, eliminating the hidden systematic.

The paper concludes that, without incorporating GR explicitly into the GRACE data reduction, any claim of an independent verification of the Lense‑Thirring effect using LAGEOS satellites remains questionable. The “self‑imprinting” of GR into the Earth‑gravity models represents a previously overlooked source of bias that can mimic or mask the very relativistic effect the experiments aim to detect. Future work must therefore adopt a fully relativistic processing chain for both the GRACE mission and the LAGEOS LT analyses to achieve a truly unbiased test of frame‑dragging.