Some considerations on the present-day results for the detection of frame-dragging after the final outcome of GP-B

TL;DR

This paper critically examines the current methods for detecting Earth's frame-dragging effect using LAGEOS satellites, highlighting uncertainties and proposing more reliable approaches after analyzing the final results of the Gravity Probe B experiment.

Contribution

It reveals the limitations of previous assumptions in canceling Earth's J2 harmonic and suggests alternative, more trustworthy methods for measuring the Lense-Thirring effect.

Findings

Uncertainty in Earth's spin axis affects J2 cancellation accuracy.

A systematic 20% uncertainty in gravitomagnetic signal prediction.

Proposes a new approach focusing on directly observable quantities.

Abstract

The cancelation of the first even zonal harmonic coefficient J2 of the multipolar expansion of the Newtonian part of the Earth's gravitational potential from the linear combination f(2L) of the nodes of LAGEOS and LAGEOS II used in the latest tests of the general relativistic Lense-Thirring effect cannot be perfect, as assumed so far. It is so, among other things, because of the uncertainties in the spatial orientation of the terrestrial spin axis as well. As a consequence, the coefficient c1 entering f(2L), which is not a solve-for parameter being theoretically computed from the analytical expressions of the classical node precessions due to J2, is, on average, uncertain at a 10-8 level over multi-decadal time spans DT comparable to those used in the data analyses performed so far. A further \simeq 20% systematic uncertainty in the theoretically predicted gravitomagnetic signal, thus, occurs. The shift due to the gravitomagnetic frame-dragging on the station-spacecraft range is numerically computed over DT = 15 d and DT = 1 yr. The need of looking at such a directly observable quantity is pointed out, along with some critical remarks concerning the methodology used so far to measure the Lense-Thirring effect with the LAGEOS satellites. Suggestions for a different, more trustable and reliable approach are offered.