[Paper Review] An improved measurement of the Lense-Thirring precession on the orbits of laser-ranged satellites with an accuracy approaching the 1% level

David Lucchesi, M. Visco+6 more|arXiv (Cornell University)|Oct 4, 2019

Geophysics and Sensor Technology4 references4 citations

TL;DR

This paper presents a high-precision measurement of the Lense-Thirring precession using laser-ranged satellites LAGEOS, LAGEOS II, and LARES, achieving an accuracy of approximately 1.6% by leveraging improved Earth gravitational field models from the GRACE mission. The result, μ = 1.0015 ± 0.0074 ± 0.016, is consistent with general relativity predictions and represents a significant reduction in systematic errors from gravitational and non-gravitational perturbations.

ABSTRACT

We present a new measurement of the Lense-Thirring effect on the orbits of the geodetic satellites LAGEOS, LAGEOS II and LARES. This secular precession is a general relativity effect produced by the gravitomagnetic field of the Earth generated by its rotation. The effect is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein's theory of gravitation. This measurement stands out, compared to previous measurements in the same context, for its precision ($\simeq7.4 imes10^{-3}$) and accuracy ($\simeq16 imes10^{-3}$), i.e. for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. For this new measurement, we have largely exploited the results of GRACE mission to significantly improve the description of the gravitational field of the Earth, by also modeling its time dependence. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects.

Motivation & Objective

• To improve the measurement accuracy of the Lense-Thirring effect in Earth's gravitational field using laser-ranged satellite data.
• To reduce systematic errors arising from uncertainties in Earth's gravitational field, particularly zonal harmonic coefficients.
• To minimize biases from unmodeled periodic perturbations in orbital residuals.
• To validate general relativity by testing the Lense-Thirring precession with a precision approaching 1%.
• To demonstrate the effectiveness of modeling time-dependent gravitational field coefficients via linear trends in orbit determination.

Proposed method

• Utilized cumulative residuals from laser-ranged satellite orbits to isolate the secular Lense-Thirring precession signal.
• Incorporated time-dependent zonal harmonic coefficients (up to ℓ = 20) from GRACE monthly solutions into orbit determination.
• Applied linear fitting to cumulative residuals to estimate the relativistic parameter μ, minimizing overfitting.
• Simultaneously estimated corrections to the quadrupole (δC̄₂₀) and octupole (δC̄₄₀) gravitational coefficients to account for mismodeling.
• Quantified correlations between μ and gravitational coefficient corrections to assess parameter degeneracy.
• Performed error budgeting considering static gravity field, ocean tides, periodic effects, and de Sitter precession uncertainties.

Experimental results

Research questions

• RQ1 Can the Lense-Thirring precession be measured with an accuracy approaching 1% using laser-ranged satellites?
• RQ2 How do uncertainties in Earth's zonal harmonic coefficients affect the precision of Lense-Thirring measurements?
• RQ3 To what extent can time-dependent gravitational field modeling reduce systematic errors in relativistic tests?
• RQ4 What is the impact of unmodeled periodic perturbations on the estimation of the relativistic parameter μ?
• RQ5 How do correlations between μ and gravitational coefficient corrections influence the reliability of the measurement?

Key findings

• The measured Lense-Thirring parameter μ is 1.0015, consistent with the general relativity prediction of μ = 1 within uncertainties.
• The precision of the measurement is δμ = 0.0074 at the 2σ level, corresponding to a fractional uncertainty of about 0.74%.
• The total accuracy, including systematic error contributions, is estimated at 1.6%, with the dominant components being static gravity field (≈1.0%), ocean tides (≤0.6%), and periodic effects (≈1.0%).
• The results from four different gravitational field models (GGM05S, EIGEN-GRACE02S, ITU_GRACE16, Tonji-Grace02s) are consistent with GR, with μ values ranging from 0.9996 to 1.0053.
• The use of time-dependent zonal harmonic modeling significantly reduced systematic errors compared to previous studies.
• Correlations between μ and gravitational coefficient corrections were reduced compared to earlier analyses, improving parameter stability.