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Effects in the anomalistic period of celestial bodies due to a logarithmic correction to the Newtonian gravitational potential

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Abstract

We study the motion of a secondary celestial body under the influence of the logarithmic corrected gravitational force of a primary one. This kind of correction was introduced by Fabris and Campos (Gen. Relativ. Gravit. 41(1):93, 2009). We derive two equations to compute the rate of change of the anomalistic period with respect to the eccentric anomaly and its total variation over one revolution. In a kinematical sense, this influence produces an apsidal motion. We perform numerical estimations for some celestial bodies. We also compare our results to those obtained by considering a Yukawa correction.

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Acknowledgements

The authors would like to thank the anonymous reviewer for his valuable comments and suggestions that helped to improve this manuscript considerably.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, 26504, Patras, Greece

    Omiros Ragos

  2. Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Ioannis Haranas

  3. Departments of Mathematics and Biomedical Physics, East Carolina University, 124 Austin Building, East Fifth Street Greenville, Greenville, NC, 27858-4353, USA

    Ioannis Gkigkitzis

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  1. Omiros Ragos
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  2. Ioannis Haranas
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Correspondence to Ioannis Haranas.

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Ragos, O., Haranas, I. & Gkigkitzis, I. Effects in the anomalistic period of celestial bodies due to a logarithmic correction to the Newtonian gravitational potential. Astrophys Space Sci 345, 67–72 (2013). https://doi.org/10.1007/s10509-013-1377-6

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  • DOI: https://doi.org/10.1007/s10509-013-1377-6

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