The subject of this paper is the empirically determined anomalous secular increases of the astronomical unit, of the order of some cm?yr–1, and of the eccentricity of the lunar orbit, of the order of 10–12?yr–1. The aim is to find an empirical explanation of both anomalies as far as their orders of magnitude are concerned. The methods employed are working out perturbatively with the Gauss equations the secular effects on the semi-major axis a and the eccentricity e of a test particle orbiting a central body acted upon by a small anomalous radial acceleration A proportional to the radial velocity vr of the particle-body relative motion. The results show that non-vanishing secular variations and ? occur. If the magnitude of the coefficient of proportionality of the extra-acceleration is of the same order of magnitude as the Hubble parameter H 0 = 7.47 × 10–11?yr–1 at the present epoch, they are able to explain both astrometric anomalies without contradicting other existing observational determinations for the Moon and the other planets of the solar system. Finally, it is concluded that the extra-acceleration might be of cosmological origin, provided that the relative radial particle-body motion is accounted for in addition to that due to the cosmological expansion only. Further data analyses should confirm or disprove the existence of both astrometric anomalies as genuine physical phenomena.
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