Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/6765827 |
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| author | Connor Martz Sheldon Van Middelkoop Ioannis Gkigkitzis Ioannis Haranas Ilias Kotsireas |
| author_facet | Connor Martz Sheldon Van Middelkoop Ioannis Gkigkitzis Ioannis Haranas Ilias Kotsireas |
| author_sort | Connor Martz |
| collection | DOAJ |
| description | 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 λ and coupling constant α are also derived. Finally, an expression for the mass of the graviton mgr mediating the interaction is calculated using the expression its Compton wavelength (i.e., the potential range λ). 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. |
| format | Article |
| id | doaj-art-3b4a6f8b43f34c03a018473a307c6887 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3b4a6f8b43f34c03a018473a307c68872025-02-03T01:26:43ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/67658276765827Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial BodiesConnor Martz0Sheldon Van Middelkoop1Ioannis Gkigkitzis2Ioannis Haranas3Ilias Kotsireas4University of Waterloo, Department of Physics and Astronomy, Waterloo, ON, N2L-3G1, CanadaUniversity of Western Ontario, Department of Physics and Astronomy, London, ON N6A-3K7, CanadaNOVA, Department of Mathematics, 8333 Little River Turnpike, Annandale, VA 22003, USAWilfrid Laurier University, Department of Physics and Computer Science, Waterloo, ON, N2L-3C5, CanadaWilfrid Laurier University, Department of Physics and Computer Science, Waterloo, ON, N2L-3C5, CanadaResearch 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 λ and coupling constant α are also derived. Finally, an expression for the mass of the graviton mgr mediating the interaction is calculated using the expression its Compton wavelength (i.e., the potential range λ). 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.http://dx.doi.org/10.1155/2019/6765827 |
| spellingShingle | Connor Martz Sheldon Van Middelkoop Ioannis Gkigkitzis Ioannis Haranas Ilias Kotsireas Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies Advances in Mathematical Physics |
| title | Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies |
| title_full | Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies |
| title_fullStr | Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies |
| title_full_unstemmed | Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies |
| title_short | Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies |
| title_sort | yukawa potential orbital energy its relation to orbital mean motion as well to the graviton mediating the interaction in celestial bodies |
| url | http://dx.doi.org/10.1155/2019/6765827 |
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