1203.1844 (P. Castelo Ferreira)
P. Castelo Ferreira
In this work are computed analytical solutions for orbital motion on a background described by an Expanding Locally Anisotropic (ELA) metric ansatz. This metric interpolates between the Schwarzschild metric near the central mass and the Robertson-Walker metric describing the expanding cosmological background far from the central mass allowing for a fine-tuneable covariant parameterization of gravitational interactions corrections in between these two asymptotic limits. Assuming a non-varying gravitational constant, 'dG/dt=0', it is discussed the variation of the Astronomical Unit (AU) obtained from numerical analysis of the Solar System dynamics, being shown that the corrections to the orbital periods on the Solar System due to the decrease of the Sun's mass by radiation emission plus the General Relativity corrections due to the ELA metric background with respect to Schwarzschild backgrounds can be mapped to the reported yearly increase of the AU through the corrections to Kepler's third law. Based on the value of the heuristic fit to the parameter 'dAU/dt' corresponding to the more recent ephemerides of the Solar System are derived bounds for the value of a constant parameter 'alpha_0' for the ELA metric as well as the maximal corrections to orbital precession and orbital radius variation within this framework. Hence it is shown that employing the ELA metric as a functional covariant parameterization to model gravitational interactions corrections within the Solar system allows to avoid the need for a varying AU and/or varying gravitational constant G.
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http://arxiv.org/abs/1203.1844
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