Solar system constraints on planetary Coriolis-type effects induced by rotation of distant masses

Abstract

We phenomenologically put local constraints on the rotation of distant masses by using the planets of the solar system. First, we analytically compute the orbital secular precessions induced on the motion of a test particle about a massive primary by a Coriolis-like force, treated as a small perturbation of first order in the rotation, in the case of a constant angular velocity vector \Psi directed along a generic direction in space. The semimajor axis a and the eccentricity e of the test particle do not secularly precess, contrary to the inclination I, the longitude of the ascending node \Omega, the longitude of the pericenter \varpi and the mean anomaly M. Then, we compare our prediction for <\dot\varpi> with the corrections \Delta\dot\varpi to the usual perihelion precessions of the inner planets recently estimated by fitting long data sets with different versions of the EPM ephemerides. We obtain |\Psi_z| <= 0.0006-0.013 arcsec cty^-1, |\Psi_x| <= 0.1-2.7 arcsec cty-1, |\Psi_y| <= 0.3-2.3 arcsec cty^-1. Interpreted in terms of models of space-time involving cosmic rotation, our results are able to yield constraints on cosmological parameters like the cosmological constant \Lambda and the Hubble parameter H_0 not too far from their values determined with cosmological observations and, in some cases, several orders of magnitude better than the constraints usually obtained so far from space-time models not involving rotation. In the case of the rotation of the solar system throughout the Galaxy, occurring clockwise about the North Galactic Pole, our results for \Psi_z are in disagreement with the expected value of it at more than 3-\sigma level.