Abstract
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.
Highlights
Any scientist will agree that Einstein’s general relativity theory (GR) is one of the most mathematically elegant theories invented in the human history
Our motivation for paper emanates from the fact that this work can serve as another possible observational test in setting solar system as well as binary system bounds on graviton mass mgr, where the bound depends on the mass of the source, which in this case is a sun like type of star
We have found that the rate of change of the orbital energy of circular and elliptical orbits w.r.t. the mean motion is a logarithmic function of the mean anomaly n
Summary
Any scientist will agree that Einstein’s general relativity theory (GR) is one of the most mathematically elegant theories invented in the human history. Considering the expression for λ, we obtain a Lambert function that relates the mass of the graviton along the orbit of the secondary to the Yukawa parameters, eccentric anomaly, orbital energy, and eccentricity. This is done using the already derived expression for lambda and substituting it into the corresponding equation for the range of graviton λ and solving for its mass mgr. In Zacharov et al [12], the authors consider Yukawa gravity interactions of S2 star orbits near the galactic plane to improve expectations for graviton mass bounds. Our motivation for paper emanates from the fact that this work can serve as another possible observational test in setting solar system as well as binary system bounds on graviton mass mgr, where the bound depends on the mass of the source, which in this case is a sun like type of star
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