The impact of the orbital decay of the LAGEOS satellites on the frame-dragging tests

Significance Statement

The passive geodetic satellites LAGEOS, LAGEOS II and LARES, tracked from Earth-based stations with the Satellite Laser Ranging (SLR) technique, are  currently used, among other things, to put to the test one of the predictions of the General Theory of Relativity by Einstein known as Lense-Thirring effect or frame dragging. It consists of small secular orbital precessions caused by the so-called gravitomagnetic component of the Earth’s gravitational field arising, at the post-Newtonian level, because of the rotation of our planet. In 2011, a dedicated experiment, known as Gravity Probe B (GP-B) and lasted for several decades since the original proposal until the release of the final results, measured successfully another gravitomagnetic effect in the terrestrial space environment, the Pugh-Schiff precession of a gyroscope, although with an accuracy (19%) worse than expected. At present, despite its great complexity, the GP-B’s results have not yet been criticized in the peer-reviewed literature. The proponents of the concurrent LAGEOS/LARES experiment aim to reach a 1% overall accuracy in measuring the Lense-Thirring effect, although various concerns have been raised so far in the literature. A major obstacle resides in the much larger competing orbital precessions induced by the Newtonian component of the expansion of the Earth’s gravitational potential in multipoles Jdue to its centrifugal oblateness. While LAGEOS and LAGEOS II orbit at about 6000 km from the  Earth’s surface, the height of LARES is just 1450 km, making it potentially more sensitive than the LAGEOSs to the high degree multipoles of the Earth’s field. The resulting systematic uncertainty in the Lense-Thirring signal, not to be confused with the internal precision of the data reduction procedure, is difficult to be reliably assessed a priori because different computational techniques do not yet converge to a unique result, yielding instead a spread of figures which are in some cases far from the expected 1% level. A further source of systematic bias lies in the observed secular decay da/dt of the semimajor axis a of the satellites considered, which is currently known with an error as large as 0.1-0.01 m/yr. Indeed, a enters the analytical formula of the orbital precession due to the largest multipole J2, causing a further source of uncertainty if not properly accounted for. This paper deals with such a new, subtle dynamical effect which, in conjunction with other systematics, may further hamper to finally reach the desired level of accuracy.


  1. Ciufolini, I. et al., Fundamental Physics and General Relativity with the LARES and LAGEOS satellites, Nuclear Physics B Proceedings Supplements, Volume 243, p. 180-193, 2013
  2. Iorio, L. et al., Phenomenology of the Lense-Thirring effect in the solar system, Astrophysics and Space Science, Volume 331, Issue 2, pp.351-395, 2011
  3. Renzetti, G. History of the attempts to measure orbital frame-dragging with artificial satellites, Open Physics, Volume 11, Issue 5, pp.531-544, 2013. 

Advances in Engineering

About the author

Lorenzo Iorio

Born in Bari, Italy, in 1971, Dr. Lorenzo Iorio, Ph.D is an italian physicist working in general relativity, gravitation, astrophysics and cosmology. He received two habilitations as Associate Professor in both Theoretical Physics and Astronomy & Astrophysics by the Italian Ministry of University and Research (MIUR). Author of about 200 articles in peer-reviewed journals, among which there are two invited reviews, according to the SAO/NASA Astrophysics Data System (ADS) he has about 2650 citations (self-citations excluded) and a h-index of 36 as of May 2016. He is listed among the Top Italian Scientists (TIS) by the VIA-Academy.

He is Editor-in-Chief of the international peer-reviewed journal Universe, published by MDPI. He is also Associate Editor of the journal Galaxies, published by MDPI, and for the specialty Cosmology of the journals Frontiers in Astronomy and Space Sciences and Frontiers in Physics, published by Frontiers. The journal New Astronomy, published by Elsevier, awarded him two Top Cited Author Awards in 2010, and featured him as most valued reviewer for the years 2013 and 2014. Two papers of him were highlighted by the journal International Journal of Modern Physics D in 2015.


Journal Reference

Advances in Space Research, Volume 57, Issue 1, 2016, Pages 493–498. 

Lorenzo Iorio 

Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Fellow of the Royal Astronomical Society (F.R.A.S.), Italy


The laser-tracked geodetic satellites LAGEOS, LAGEOS II and LARES are currently employed, among other things, to measure the general relativistic Lense–Thirring effect in the gravitomagnetic field of the spinning Earth with the hope of providing a more accurate test of such a prediction of the Einstein’s theory of gravitation than the existing ones. The secular decay  of the semimajor axes a of such spacecrafts, recently measured in an independent way to a 1-s2.0-S0273117715007322-si33 m yr−1 accuracy level, may indirectly impact the proposed relativistic experiment through its connection with the classical orbital precessions induced by the Earth’s oblateness J2. Indeed, the systematic bias due to the current measurement errors  1-s2.0-S0273117715007322-si21 is of the same order of magnitude of, or even larger than, the expected relativistic signal itself; moreover, it grows linearly with the time span T of the analysis. Therefore, the parameter-fitting algorithms must be properly updated in order to suitably cope with such a new source of systematic uncertainty. Otherwise, an improvement of one-two orders of magnitude in measuring the orbital decay of the satellites of the LAGEOS family would be required to reduce this source of systematic uncertainty to a percent fraction of the Lense–Thirring signature.

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