(14.10.2018)
In 2004 Krasinsky and Brumberg indicated that the analysis of all available radiometric measurements of distances between the Earth and the planets, and also the observations of martian landers and orbiters, showed that the Astronomical Unit is increasing at a rate 15 ± 4 meters per century [14]. Later on, a more careful analysis by Standish has shown that the secular rate is closer to 7 ± 2 meters per century [26]. Anyway, this is by far too large to be explained by the loss of solar mass due to solar wind and electromagnetic radiation. An explanation based upon tidal friction caused by the bulge produced by Earth gravity on the Sun has been proposed [17]. However, this model has not been validated and the detailed mechanism for this tidal friction is hypothetical. A secular effect on the eccentricity of planetary motions have been also unveiled by the recent detailed analysis of the Lunar orbit. The secular increase of the eccentricity is very small but, however, is clearly within the range of precision of Lunar laser ranging. This kind of unexplained observations,
after discarding any possible conventional explanation, could give rise to an arena where the status of General Relativity as a complete theory of gravity (at least, at the macroscopic level) could be tested.
In this paper we have assumed that a conventional explanation is not possible and that an extra force term is necessary in order to incorporate this behaviour in the post-newtonian formalism.