Towards a 1% measurement of the Lense-Thirring effect with LARES?

After the recent approval by the Italian Space Agency (ASI) of the LARES mission, which will be launched at the end of 2008 by a VEGA rocket to measure the general relativistic gravitomagnetic Lense-Thirring effect by combining LARES data with those of the existing LAGEOS and LAGEOS II satellites, it is of the utmost importance to assess if the claimed accuracy \lesssim 1% will be realistically obtainable. A major source of systematic error is the mismodelling \delta J_L in the static part of the even zonal harmonic coefficients J_L, L=2,4,6,.. of the multipolar expansion of the classical part of the terrestrial gravitational potential; such a bias crucially depends on the orbital configuration of LARES. If for \delta J_L the difference between the best estimates of different Earth’s gravity solutions from the dedicated GRACE mission is conservatively taken instead of optimistically considering the statistical covariance sigmas of each model separately, as done so far in literature, it turns out that, since LARES will be likely launched in a low-orbit (semimajor axis a\lesssim 7600 km), the bias due to the geopotential may be up to ten times larger than what claimed, according to a calculation up to degree L=20. Taking into account also the even zonal harmonics with L>20, as required by the relatively low altitude of LARES, may further degrade the total accuracy. Should a nearly polar configuration (inclination to the Earth’s equator i\approx 90 deg) be finally implemented, also other perturbations would come into play, further corrupting the measurement of the Lense-Thirring effect. The orbital configuration of LARES may also have some consequences in terms of non-gravitational perturbations and measurement errors.

💡 Research Summary

The paper critically examines the claim that the upcoming LARES (LAser RElativity Satellite) mission, funded by the Italian Space Agency and slated for launch in late 2008, will be able to measure the general‑relativistic Lense‑Thirring (frame‑dragging) effect with an accuracy of 1 % by combining its laser‑ranged node data with those of the existing LAGEOS and LAGEOS II satellites. The author identifies the dominant source of systematic error as the mismodelling of the static even zonal harmonics (J₂, J₄, J₆, …) of Earth’s geopotential, whose secular node precessions mimic the relativistic signal but are orders of magnitude larger.

The standard approach in earlier studies has been to use the formal covariance sigmas (σ_Jℓ) supplied by individual GRACE‑derived gravity models as the uncertainty on each Jℓ. The author argues that this is overly optimistic because the true model‑to‑model differences are often much larger. Instead, a more conservative estimate is adopted: for each degree ℓ the uncertainty δJℓ is taken as the absolute difference between the best‑fit coefficients of two independent Earth‑gravity solutions (e.g., GGM02S vs. GGM03S, ITG‑Grace02s vs. ITG‑Grace03s, etc.). This “difference‑method” is widely used by gravity‑field specialists and provides a realistic bound on the geopotential error.

The Lense‑Thirring node precession for a satellite is Ω_LT = 2GS/(c²a³(1−e²)^{3/2}). By forming the linear combination Ω_LAGEOS + c₁Ω_LAGEOS II + c₂Ω_LARES (Eq. 2) the coefficients c₁ and c₂ are chosen to cancel the contributions of J₂ and J₄ exactly, leaving higher‑order even zonals as the residual source of bias. The author evaluates the systematic percent error δμ (Eq. 8) for a range of plausible LARES orbital configurations: semimajor axis a = 7600 km (the nominal value) and a = 7000 km (a lower bound), eccentricity e = 0.001, and inclinations i = 60°, 70°, 80°, as well as near‑polar values i = 85°–89°.

Tables and figures (Figs. 1‑5) show that, when only the formal σ_Jℓ from the EIGEN‑GRACE02S model are used, the error budget appears modest (e.g., 1.6 % for i = 70°). However, employing the model‑difference uncertainties dramatically inflates the error: for a = 7600 km and i = 70°, δμ rises to roughly 5 %–8 %, and for near‑polar inclinations it exceeds 10 %. The error grows with decreasing altitude because the sensitivity of the node to a given Jℓ scales roughly as a^{-(ℓ+1)/2}; thus a low‑orbit satellite feels a much stronger influence from higher‑degree zonals. The analysis up to degree ℓ = 20 already yields errors several times larger than the 1 % goal, and the author warns that contributions from ℓ > 20—inevitable at these altitudes—could increase the total bias by another factor of two to three.

Beyond the geopotential, the paper discusses non‑gravitational perturbations (solar‑radiation pressure, Earth albedo, thermal thrust, atmospheric drag, and the K₁ tidal term). In a near‑polar configuration the coefficient c₂ becomes large, amplifying these perturbations and making their control critical. Achieving a non‑gravitational error below 0.1 % of the Lense‑Thirring signal would require stringent design choices (surface material, spin stabilization, precise laser tracking) and possibly additional on‑board instrumentation.

The author concludes that the originally proposed LARES orbit (a ≈ 12 270 km, i ≈ 70°) would indeed allow the even‑zonal error to stay below 1 % if the inclination is kept within about ±1°. However, the presently favored low‑orbit, moderate‑inclination scenario cannot meet the 1 % target; realistic error estimates suggest a systematic bias of at least 5 % and likely closer to 10 %. Consequently, the claim of a 1 % measurement appears overly optimistic unless the mission design is revised, higher‑degree geopotential models are incorporated, and non‑gravitational forces are suppressed to unprecedented levels. The paper calls for a reassessment of the orbital parameters and a more rigorous error‑budget analysis before the LARES mission proceeds.