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Anomalous Post-Newtonian terms and the secular increase of the Astronomical Unit

In the last decade a major debate has emerged on the astrophysics community concerning the anomalous behaviour of the astronomical unit, the fundamental scale of distances in the Solar system. Several independent studies have combined radar ranging and optical data from the last four decades to come to the conclusion that the astronomical unit is increasing by several meters per century. It is abundantly clear that General Relativity cannot account for this new effect, although an still undefined angular momentum transfer mechanism could provide the simpler and more conventional explanation. Here we investigate several anomalous post-newtonian terms containing only the product of the mass and angular momentum of the Sun as well as its Schwarzschild radius in order to determine if they could explain the secular increase of the astronomical unit and the recently reported increase of Lunar eccentricity. If these anomalies are confirmed, searching for a modification of General Relativity predicting these terms could have far-reaching consequences.