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 and the inclination 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 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 due to the even and odd zonal harmonics of the geopotential ideally vanish. Moreover, a suitable linear combination of would be able to cancel out the solid and ocean tidal perturbations induced by the tide and, at the same time, enforce the geodetic precessions yielding a secular trend of , thus strengthening the goal of a test of the de Sitter effect recently proposed in the literature in the case of an equatorial coordinate system. Relatively mild departures from the ideal orbital configuration with are allowed. Present-day levels of relative accuracy in testing the geodetic and the gravitomagnetic effects in the field of the Sun and the Earth, respectively, are (lunar laser ranging) and (Gravity Probe B) for the de Sitter precessions, and for the Pugh–Schiff rates of change of gyroscopes (gravity probe B). Other tests of the Lense–Thirring effect with the LAGEOS type satellites are ongoing in the field of the Earth; their overall accuracy is currently debated.