&#x0D; On Testing Frame-Dragging with LAGEOS and a Recently Announced Geodetic Satellite&#x0D;

Lorenzo Iorio

doi:10.3390/universe4110113

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 (Laser Geodynamics Satellite), 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 Ω should allow one to test the general relativistic Lense–Thirring effect to a ≃0.2% accuracy level, with a contribution of the mismodeling in the even zonal harmonics Jl, l = 2, 4, 6, . . . 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 J2. On the one hand, the lingering scatter of the estimated values of such a key geophysical parameter from different recent GRACE/GOCE-based (Gravity Recovery and Climate Experiment/Gravity field and steady-state Ocean Circulation Explorer) global gravity field solutions is representative of an uncertainty which may directly impact the summed Lense–Thirring node precessions at a ≃70–80% in the worst scenarios, and to a ≃3–10% level in other, more favorable cases. On the other hand, the phenomenologically measured secular decay à of the semimajor axis of LAGEOS (and, presumably, of the other satellite as well), currently known at a σà≃0.03 m yr–1 level after more than 30 yr, will couple with the sum of the J2-induced node precessions yielding an overall bias as large as '20–40% after 5–10 yr. A further systematic error of the order of ≃2–14% may arise from an analogous interplay of the secular decay of the inclination I˙ with the oblateness-driven node precessions.

Highlights

The cannonball geodetic satellites of the LAGEOS (Laser Geodynamics Satellite) family, i.e., LAGEOS (L), LAGEOS II (L II) and LARES (Laser Relativity Satellite) (LR), entirely covered by passive retroreflectors and tracked on a continuous basis from several ground stations scattered around the world with the Satellite Laser Ranging (SLR) technique [1], are currently used, among other things, to put to the test some predictions of the Einstein’s General Theory of Relativity (GTR) [2,3,4,5,6]
LAGEOS satellite and the future CiufoLares, to be launched in 2019 with a VEGA C rocket, should provide us with a '0.2% test of frame-dragging in the field of the Earth whose imperfectly known even zonal harmonics should contribute just 0.1% of the total error budget. It seems difficult for such an ambitious goal to be reached because of the direct and indirect impact of the competing classical node precessions mainly induced by the first even zonal of the geopotential
On the one hand, according to some of the latest GRACE/GOCE-based global gravity field solutions released by various international institutions in 2016–2017, the lingering scatter of their determinations of such a fundamental geophysical parameter would directly affect the sum of the nodes with an uncancelled mismodelled total precession, which, in some cases, may reach even several dozen percentage points of the total Lense–Thirring effect for departures of the orbital elements of CiufoLares as little as 20 km and 0.5 deg

Summary

Introduction

The cannonball geodetic satellites of the LAGEOS (Laser Geodynamics Satellite) family, i.e., LAGEOS (L), LAGEOS II (L II) and LARES (Laser Relativity Satellite) (LR), entirely covered by passive retroreflectors and tracked on a continuous basis from several ground stations scattered around the world with the Satellite Laser Ranging (SLR) technique [1], are currently used, among other things, to put to the test some predictions of the Einstein’s General Theory of Relativity (GTR) [2,3,4,5,6].One of them is known as1 a Lense–Thirring (LT) effect [10], and its measurement is one of the current goals of the LAGEOS-type satellites in fundamental physics. We will show that, the overall impact of just the first even zonal harmonic of the geopotential, including both its direct effect due to the mismodeling in J2 and the indirect one due to the interplay with the measured secular decay of the semimajor axis, and, perhaps, of the inclination as well, of LAGEOS and, likely, of CL as well, may be up to 200–800 times larger over a data analysis 5–10 yr long.

Results

Conclusion