Constraining the Preferred-Frame $\alpha_1$, $\alpha_2$ parameters from Solar System planetary precessions

Understand

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the PPN parameters $\alpha_1$, $\alpha_2$.

• A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a-priori bias of unmodelled/mismodelled standard effects such as the general relativistic Lense-Thirring precessions and the classical rates due to the Sun's oblateness $J_2$, allows to infer $|\alpha_1| \leq 6\times 10^{-6}, |\alpha_2| \leq 3.5\times 10^{-5}$.
• Such bounds should be improved in the near future after processing the data that are being collected by the MESSENGER spacecraft, currently orbiting Mercury.
• Further improvements may come in the mid-future from the approved BepiColombo mission to Mercury.