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 (|alpha_2| < 4 x 10^-7, 90% C.L.), but the present bound on the other one is much weaker (|alpha_1| < 5 x 10^-4, 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.