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Department of Physics and Computer Science


Research on gravitational theories involves several contemporary modified models that predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. In this paper we consider a Yukawa potential and we calculate the time rate of change of the orbital energy as a function of the orbital mean motion for circular and elliptical orbits. In both cases we find that there is a logarithmic dependence of the orbital energy on the mean motion. Using that, we derive an expression for the mean motion as a function of the Yukawa orbital energy, as well as specific Yukawa potential parameters. Furthermore, various special cases are examined. Lastly, expressions for the Yukawa range πœ† and coupling constant 𝛼 are also derived. Finally, an expression for the mass of the graviton π‘šπ‘”π‘Ÿ mediating the interaction is calculated using the expression its Compton wavelength (i.e., the potential range πœ†).Numerical estimates for the mass of the graviton mediating the interaction are finally obtained at various eccentricity values and in particular at the perihelion and aphelion points of Mercury’s orbit around the sun.


Copyright Β© 2019 Connor Martz et al. This is an open access article distributed under the Creative Commons 4.0 Attribution License, which permits unrestricted use, distribution, and reproduction in any medium. This article originally appeared in Advances in Mathematical Physics, vol. 2019, Article ID 6765827, 10 pages, DOI: 10.1155/2019/6765827