Historical research guide · 0538 · 2017
A comment on “A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model”, by I. Ciufolini et al.
Lorenzo Iorio
In one minute
In 2016 Ciufolini and colleagues measured how the spinning Earth drags spacetime around with it, using laser ranging to the LARES and two LAGEOS satellites, and reported 0.994 of Einstein’s predicted value with a five percent systematic error. Lorenzo Iorio’s comment asks how firm that five percent is. His subject is the shape of the Earth. The planet’s gravity field is written as a series of terms, and the three-satellite combination the measurement uses is built to cancel the first two of them; everything from degree six upward stays in the signal, and those coefficients still differ from one modern gravity model to the next. Iorio takes four recent models built by different institutions from GRACE and GOCE data, compares them pair by pair, and converts each disagreement into an error on the frame-dragging figure — up to 15 percent from degree six, 6 percent from degree eight and 36 percent from degree ten. He proposes quoting the budget across an ensemble of models, and using the same satellite combination to solve for the gravity-field corrections as a consistency check.
Connection
Frame-dragging is the one place where a spinning mass twisting the metric has actually been measured in orbit, which is why the measurement it comments on sits in chapter 4 and chapter 11. This comment is the site’s worked example of chapter 1’s evidence ladder: the measurement sheet at /library/stm-e79ea933f1 reports 0.994 with a five percent systematic error, Iorio’s model-to-model comparison puts a larger figure on the table, and both authors name the same next step — more gravity models, longer LARES arcs, and an independent analysis.
From the source
The observable used in the LARES and LAGEOS test is a linear combination of the three satellites’ node rates that cancels the first two even zonal harmonics of the Earth’s gravity field, leaving every harmonic of degree six and above inside the signal.Sect. 2.1, Eqs. (2)–(10)
For the LAGEOS, LAGEOS II and LARES orbits the general-relativistic nodal precessions are 30.7, 31.5 and 118.1 milliarcseconds per year, and the combined Lense–Thirring signature of the three-satellite combination is 50.2 milliarcseconds per year.Table 1; Eq. (16)
The scatter between four recent Earth gravity models in the uncancelled coefficients of degree 6, 8 and 10 corresponds, for certain pairs of models, to systematic uncertainties of up to 15, 6 and 36 percent of the combined Lense–Thirring signal, which is the open question this comment raises about the reported five percent budget.Tables 4, 6, 8 and Table 9; Sect. 3
A realistic error budget should be built from an ensemble of independently produced gravity models rather than a single solution, calibrating each model’s formal sigmas by the Wagner and McAdoo scaling procedure, which here returns values close to the plain differences between models.Sect. 2.2, Eqs. (29)–(30); Sect. 2.2.1
The same linear-combination approach can be turned around to solve for the corrections to the second and fourth even zonals themselves, and comparing those against the GRACE and GOCE global solutions would be a consistency test of the method; that test has not yet been carried out.Sect. 2.3; Sect. 3, closing recommendations
Twenty years after the first LAGEOS tests and four years after the LARES launch, no genuinely independent analysis of the Lense–Thirring effect with these geodetic satellites had been published in the peer-reviewed literature by a group outside the original teams.Sect. 3, final paragraph
The way in
https://doi.org/10.1140/epjc/s10052-017-4607-1How to cite it
Lorenzo Iorio (2017) A comment on “A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model”, by I. Ciufolini et al. doi:10.1140/epjc/s10052-017-4607-1