On testing frame-dragging with LAGEOS and a recently announced geodetic satellite

Abstract

Recently, Ciufolini and coworkers announced the forthcoming launch of a new cannonball geodetic satellite in 2019. It should be injected in an essentially circular path with the same semimajor axis $a$ of LAGEOS, in orbit since 1976, and an inclination $I$ of its orbital plane supplementary with respect to that of its existing cousin. According to their proponents, the sum of the satellites' precessions of the longitudes of the ascending nodes $\Omega$ should allow one to test the general relativistic Lense-Thirring effect to a $\simeq 0.2\%$ accuracy level, with a contribution of the mismodeling in the even zonal harmonics $J_{\ell },\ell =2,4,6,\dots$ of the geopotential to the total error budget as little as $0.1\%$. Actually, such an ambitious goal seems to be hardly attainable because of the direct and indirect impact of, at least, the first even zonal $J_2$. On the one hand, the lingering scatter of the estimated values of such a key geophysical parameter from different recent GRACE/GOCE-based global gravity field solutions is representative of an uncertainty which may directly impact the summed Lense-Thirring node precessions at a $\simeq 70-80\%$ in the worst scenarios, and to a $\simeq 3-10\%$ level in other, more favorable cases. On the other hand, the phenomenologically measured secular decay $\dot{a}$ of the semimajor axis of LAGEOS (and, presumably, of the other satellite as well), currently known at a ${\sigma }_{\dot{a}}\simeq 0.03{\text{m yr}}^{-1}$ level after more than 30 yr, will couple with the sum of the $J_2$-induced node precessions yielding an overall bias as large as $\simeq 20-40\%$ after $5-10$ yr. A further systematic error of the order of $\simeq 2-14\%$ may arise from an analogous interplay of the secular decay of the inclination $\dot{I}$ with the oblateness-driven node precessions.

LaTex2e, 27 pages, 3 tables, 7 figures. Accepted for publication

References in corpus (5)

• Phenomenology of the Lense-Thirring effect in the Solar System
• A new laser-ranged satellite for General Relativity and space geodesy: I. An introduction to the LARES2 space experiment
• Poynting-Robertson drag and solar wind in the space debris problem
• Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the Galactic Center
• A new laser-ranged satellite for General Relativity and Space Geodesy II. Monte Carlo Simulations and covariance analyses of the LARES 2 Experiment

Cited by in corpus (3)

• Gravity Probe Spin: Prospects for measuring general-relativistic precession of intrinsic spin using a ferromagnetic gyroscope
• A tale of analogies: gravitomagnetic effects, rotating sources, observers and all that
• Constraints on ultralight axions, vector gauge bosons, and unparticles from geodetic and frame-dragging measurements