Speaker
Description
Using a geocentric ecliptical coordinate system to analyze the data of a proposed new Earth's satellite, provisionally named ELXIS, in a circular orbit perpendicular to both the equator and the reference direction of the Vernal Equinox should allow, in principle, to measure the general relativistic Lense-Thirring and De Sitter effects on the satellite's inclination $I$ and node $\Omega$ to a relative accuracy of $\simeq 10^{-2},~10^{-5}$, respectively. Indeed, the long-term perturbations on $I,~\Omega$, referred to the ecliptic, due to the zonal harmonic coefficients $J_\ell,~\ell=2,3,4,5,\ldots$ of the geopotential vanish for $e=0,~I = \Omega = 90\deg$. Departures $\Delta I=\Delta\Omega\simeq 0.01-0.1\deg$ from such an ideal orbital configuration would not compromise the stated accuracy goals. The most insidious competing perturbations are due to the ocean component of the $K_1$ tide of degree $\ell=2$ and order $m=1$: they do not vanish for $I = \Omega = 90\deg$, and our knowledge of its tidal height $C_{2,1,K_1}^{+}$ is relatively inaccurate. A suitable linear combination of the rates of change of $I,~\Omega$ allows to cancel out them and enforce the De Sitter effect. By assuming a relative uncertainty of the order of $\simeq 10^{-3}$ in $C_{2,1,K_1}^{+}$ from a comparison of some rather recent global ocean tide models, the resulting systematic bias on each of the Lense-Thirring precessions would be at the percent level. Other sources of potential systematic uncertainties like the 3rd-body perturbations due to the Moon and the non-gravitational accelerations allow to meet the desired accuracy levels.
Summary
ELXIS is a concept study for a satellite-based mission to measure the De Sitter and Lense-Thirring precessions in the field of the Earth to a $\simeq 10^{-5}$ and $\simeq 10^{-2}$ relative accuracy, respectively.
