The mystery of why some objects don't seem to follow known physical laws regarding gravitational attraction is getting deeper. A research paper posted on the Arxiv astrophysics database discusses some of these bizarre events, including the so-called Pioneer Anomaly, in which two spacecraft started unexpectedly accelerating, and the Allais pendulum experiments. In the paper, Dutch researcher Chris P. Duif reviews the history of conventional explanations for the phenomena and argues that each of them has failed.  Some researchers have invoked them to claim there's a need for a completely new theory of physics. Duif argues that some conventional explanation will probably turn out to work, but that some exotic ones -- including that the sun influences the galactic flow of dark matter -- are possible.

As Duif writes in his paper, which he submitted to the proceedings of a conference on the Pioneer anomaly:

"Conventional explanations for observations of anomalous behaviour of mechanical systems during solar eclipses are critically reviewed. These observations include the work of Allais with paraconical pendula, those of Saxl and Allen with a torsion pendulum and measurements with gravimeters. Attempts of replications of these experiments and recent gravimeter results are discussed and unpublished data by Latham and by Saxl et al. is presented. Some of the data are summarized and reanalyzed. Especially, attention is paid to observations of tilt of the vertical, which seems to play an important role in this matter. Recommendations for future research are given and its possible relevance to the Pioneer Anomaly is discussed. It is concluded that all the proposed conventional explanations either qualitatively or quantitatively fail to explain the observations."