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Solar system anomalies: Revisiting Hubble's law

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This paper investigates the impact of a new metric recently published [R. Plamondon and C. Ouellet-Plamondon, in On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, edited by K. Rosquist, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2015), p. 1301] for studying the space-time geometry of a static symmetric massive object. This metric depends on a complementary error function (erfc) potential that characterizes the emergent gravitation field predicted by the model. This results in two types of deviations as compared to computations made on the basis of a Newtonian potential: a constant and a radial outcome. One key feature of the metric is that it postulates the existence of an intrinsic physical constant σ , the massive object-specific proper length that scales measurements in its surroundings. Although σ must be evaluated experimentally, we use a heuristic to estimate its value and point out some latent relationships between the Hubble constant, the secular increase in the astronomical unit, and the Pioneers delay. Indeed, highlighting the systematic errors that emerge when the effect of σ is neglected, one can link the Hubble constant H 0 to σ Sun and the secular increase V AU to σ Earth . The accuracy of the resulting numerical predictions, H 0 = 74 . 42 ( 0 . 02 ) ( km / s ) / Mpc and V AU 7 . 8 cm yr - 1 , calls for more investigations of this new metric by specific experts. Moreover, we investigate the expected impacts of the new metric on the flyby anomalies, and we revisit the Pioneers delay. It is shown that both phenomena could be partly taken into account within the context of this unifying paradigm, with quite accurate numerical predictions. A correction for the osculating asymptotic velocity at the perigee of the order of 10 mm/s and an inward radial acceleration of 8 . 34 × 10 - 10 m / s 2 affecting the Pioneer space crafts could be explained by this new model.
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Keywords: Complementary Error Functions (erfc) Potential; Emergent Gravity; Flyby Anomalies; Hubble Constant; Modified Gravity; New Spacetime Metric; Pioneers Delay; Secular Astronomical Unit Increase; Specific Proper Length; Weighted Newton's Law

Document Type: Research Article

Publication date: December 7, 2017

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  • Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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