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 $I = \Omega = 90\deg$ 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 $J_\ell,~\ell=2,~3,~4,\ldots$ 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 $-8.3~\textrm{milliarcseconds~per~year}$, 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 $\Delta I = \Delta\Omega\simeq 0.01-0.1\deg$ from the ideal orbital configuration with $I = \Omega = 90\deg$ are allowed. [Abridged]