An Empirical Explanation of the Anomalous Increases in the Astronomical Unit and the Lunar Eccentricity

Abstract

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 the 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 v r of the particle-body relative motion. The results show that non-vanishing secular variations ȧ and ė occur. If the magnitude of the coefficient of proportionality of the extra-acceleration is of the same order of magnitude of the Hubble parameter H 0 = 7.47 × 10 −11 yr −1 at the present epoch, they are able to explain both the 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 extraacceleration 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. Anyway, further data analyses should confirm or disproof the existence of both the astrometric anomalies as genuine physical phenomena.

Gravitational anomalies in the solar system?

“…In Ref. 159, it was shown that an empirical acceleration proportional to the the orbiter's radial velocity v r through a multiplicative coefficient of the same order of magnitude of the current value of the Hubble parameter H 0 is able to cause an average rate of change of the eccentricity of the right magnitude to explain the Selenian anomaly. However, it must be pointed out that it has not yet been possible to derive such an ad-hoc acceleration from first principles pointing towards some viable physical mechanism; in Ref.…”

“…As in the case of the PA and, to a lesser extent so far, the FA, also such an alleged anomaly motivated many researches to find viable explanations in terms of various either conventional or unconventional physical mechanisms. 159,206,[282][283][284][285][286][287][288][289][290][291][292][293][294][295][296] The various attempts 154,[279][280][281] to investigate it have been performed so far within the framework of the International Astronomical Union (IAU) 1976 System of Astronomical Constants, available on the Internet at http://www.iau.org/static/resolutions/ IAU1976_French.pdf, which, in turn, is reminiscent of pre-relativistic eras when, among other things, only relative distances (expressed in astronomical units) in the Solar system could be determined since absolute ones could not be estimated with high accuracy. More precisely, the IAU 1976 system prescribed to measure the masses in units of Solar masses, the durations in days D (made of 86400 seconds), and the distances in astronomical units of length.…”

On the possible onset of the Pioneer anomaly

“…This "acceleration" term is of a similar form as the empirical solution proposed in Ref. 65 to resolve the anomalous secular increases of the astronomical unit and the eccentricity of the lunar orbit. These predictions from (44) eccentricity, why then would our larger clock-drift term not be apparent in these analyses?…”

On the secular recession of the Earth-Moon system as an azimuthal gravitational phenomenon

“…Iorio 2011b). Researchers (Williams et al 2004;Iorio 2011aIorio , 2011bIorio , 2014bXin 2011;Riofrio 2012;Acedo 2013aAcedo , 2013bZiefle 2013;Nyambuya 2014e) have proposed various mechanisms to explain this seemingly observation.…”

“…Even the Moon has been found by Williams et al (2004Williams et al ( , 2014; Williams and Boggs (2009) to be receding from the Earth (cf. Iorio 2011aIorio , 2011b at a rate of about 38 mm/yr.…”