Will LAGEOS and LARES 2 succeed in accurately measuring frame-dragging?

Lorenzo Iorio

doi:10.1140/epjc/s10052-025-13964-x

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 255
https://doi.org/10.1140/epjc/s10052-025-13964-x

Regular Article - Theoretical Physics

Will LAGEOS and LARES 2 succeed in accurately measuring frame-dragging?

Lorenzo Iorio^a

Ministero dell’ Istruzione e del Merito, Viale Unità di Italia 68, 70125, Bari (BA), Italy

^a lorenzo.iorio@libero.it

Received: 19 October 2024
Accepted: 17 February 2025
Published online: 10 March 2025

Abstract

The current LAGEOS–LARES 2 experiment aims to accurately measure the general relativistic Lense–Thirring effect in the gravitomagnetic field of the spinning Earth generated by the latter’s angular momentum $J$ ${\varvec{J}}$ . The key quantity to a priori analytically assess the overall systematic uncertainty is the ratio $R^{J_{2}}$ ${\mathcal {R}}^{J_2}$ of the sum of the classical precessions of the satellites’ nodes $Ω$ $\Omega$ induced by the Earth’s oblateness $J_{2}$ $$J_2$$ to the sum of their post-Newtonian counterparts. In principle, if the sum of the inclinations I of both satellites were exactly $180^{\circ}$ $180^\circ$ , the semimajor axes a and the eccentricities e being identical, $R^{J_{2}}$ ${\mathcal {R}}^{J_2}$ would exactly vanish. Actually, it is not so by a large amount because of the departures of the real satellites’ orbital configurations from the ideal ones. Thus, $J_{2}$ $$J_2$$ impacts not only directly through its own uncertainty, but also indirectly through the errors in all the other physical and orbital parameters entering $R^{J_{2}}$ ${\mathcal {R}}^{J_2}$ . The consequences of this fact are examined in greater details than done so far in the literature. The Van Patten and Everitt’s proposal in 1976 of looking at the sum of the node precessions of two counter-orbiting spacecraft in (low-altitude) circular polar orbits is revamped rebranding it POLAr RElativity Satellites (POLARES). Regardless the specific type of satellite and tracking technologies that may be eventually adopted, it might be conceptually superior to the LAGEOS–LARES 2 one from the point of view of the orbital characteristics since, given the same semimajor axes and eccentricities of the existing laser-ranged cousins, its $R^{J_{2}}$ ${\mathcal {R}}^{J_2}$ is less sensitive to the impact of the deviations from its ideal orbital configuration.

© The Author(s) 2025

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