Measuring the De Sitter precession with a new Earth's satellite to the $\mathbf{\simeq 10^{-5}}$ level: a proposal

TL;DR

This paper proposes a new satellite-based method to measure the Earth's de Sitter precession with an accuracy potentially ten times better than current bounds, by optimizing orbital parameters to minimize perturbations.

Contribution

It introduces a novel satellite orbit configuration that suppresses competing perturbations, enabling more precise measurement of the Earth's geodesic precession.

Findings

De Sitter precession of about -7.6 mas/yr can be isolated in polar orbits.

Measurement accuracy of better than 35 microarcseconds over 5 years is required.

Perturbations from Earth's geopotential and tides can be minimized with specific orbital choices.

Abstract

The inclination $I$ of an Earth's satellite in polar orbit undergoes a secular De Sitter precession of $-7.6$ milliarcseconds per year for a suitable choice of the initial value of its non-circulating node $\Omega$. The competing long-periodic harmonic rates of change of $I$ due to the even and odd zonal harmonics of the geopotential vanish for either a circular or polar orbit, while no secular rates occur at all. This may open up, in principle, the possibility of measuring the geodesic precession in the weak-field limit with an accurately tracked satellite by improving the current bound of $9\times 10^{-4}$ from Lunar Laser Ranging, which, on the other hand, may be even rather optimistic, by one order of magnitude, or, perhaps, even better. The most insidious competing effects are due to the solid and ocean components of the $K_1$ tide since their perturbations have nominal huge amplitudes and the same temporal pattern of the De Sitter signature. They vanish for polar orbits. Departures of $\simeq 10^{-5}-10^{-3}~\textrm{deg}$ from the ideal polar geometry allow to keep the $K_1$ tidal perturbations to a sufficiently small level. Most of the other gravitational and non-gravitational perturbations vanish for the proposed orbital configuration, while the non-vanishing ones either have different temporal signatures with respect to the De Sitter effect or can be modeled with sufficient accuracy. In order to meet the proposed goal, the measurement accuracy of $I$ should be better than $\simeq 35~\textrm{microarcseconds}=0.034~\textrm{milliarcseconds}$ over, say, 5 yr.