Testing for preferred-frame effects in gravity with artificial earth satellites

As gravity is a long-range force, one might $a$ priori expect the Universe's global matter distribution to select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, two parameters suffice to describe the phenomenology of preferred-frame effects. One of them has already been very tightly constrained ($\left|{\alpha }_2\right|<\mathrm{}4\mathrm{}\times {10}^{-7\mathrm{}}$, 90% C.L.), but the present bound on the other one is much weaker ($\left|{\alpha }_1\right|<\mathrm{}5\mathrm{}\times {10}^{-4\mathrm{}}$, 90% C.L.). It is pointed out that the observation of particular orbits of artificial Earth satellites has the potential of improving the ${\alpha }_1$ limits by a couple of orders of magnitude, thanks to the appearance of small divisors which enhance the corresponding preferred-frame effects. There is a discrete set of inclinations which lead to arbitrarily small divisors, while, among zero-inclination (equatorial) orbits, geostationary ones are near optimal. The main ${\alpha }_1$-induced effects are (i) a complex secular evolution of the eccentricity vector of the orbit, describable as the vectorial sum of several independent rotations, and (ii) a yearly oscillation in the longitude of the satellite.