Measuring general relativistic dragging effects in the Earth's gravitational field with ELXIS: a proposal

Abstract

In a geocentric kinematically rotating ecliptical coordinate system in geodesic motion through the deformed spacetime of the Sun, both the longitude of the ascending node $\Omega$ and the inclination $I$ of an artificial satellite of the spinning Earth are affected by the post-Newtonian gravitoelectric De Sitter and gravitomagnetic Lense-Thirring effects. By choosing a circular orbit with $I=\Omega =90°$ for a potential new spacecraft, which we propose to name ELXIS, it would be possible to measure each of the gravitomagnetic precessions separately at a percent level, or, perhaps, even better depending on the level of accuracy of the current and future global ocean tide models since the competing classical long-term perturbations on $I,\Omega$ due to the even and odd zonal harmonics $J_{\ell },\ell =2,3,4,\dots$ of the geopotential vanish. Moreover, a suitable linear combination of $I,\Omega$ would be able to cancel out the solid and ocean tidal perturbations induced by the $K_1$ tide and, at the same time, enforce the geodetic precessions yielding a secular trend of $-8.3\text{milliarcseconds per year}$, thus strengthening the goal of a $\simeq 10^{-5}$ test of the De Sitter effect recently proposed in the literature in the case of an equatorial coordinate system. Relatively mild departures $\Delta I=\Delta \Omega \simeq 0.01-0.1°$ from the ideal orbital configuration with $I=\Omega =90°$ are allowed. [Abridged]

LaTex2e, 40 pages, 2 tables, 11 figures. Two figures and one table added. Typo corrected (0 deg -> 90 deg) at pag. 3 of this draft and pag. 2 of the published version. Definition of the Sun's ecliptic longitude added in Appendix A

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Cited by in corpus (2)

• On the equivalence between rotation and gravity: "Gravitational" and "cosmological" redshifts in the laboratory
• Measuring the De Sitter precession with a new Earth's satellite to the $\simeq 10^{-5}$ level: a proposal