Revisiting the two-body problem in Yukawa gravity and in a gravitational extension of the Buckingham potential

Abstract

We revisit the Keplerian-like parametrization of the two-body problem in Yukawa gravity studied in the literature. Some inconsistencies, which spoil Bertrand's theorem, observed in the $\eta$ parametrization of the true anomaly $\theta$ and in the formulae for the pericenter's advance are resolved. Moreover, inspired in this kind of study, we couple the Buckingham potential, a variation of the Lennard-Jones intermolecular potential, with the gravitational Newtonian potential and find a Keplerian-like parametrization for the solution of the two-body problem in this sort of gravity. The outcomes for the advance of the pericenter in both types of gravity are corroborated by using the Landau and Lifshitz's method. We also tested the expressions thus obtained against Solar System and S2 star data. The result for both models is that while some deviation from general relativity (GR) is allowed, GR cannot be discarded by the current analysis.

arXiv comment24 pages, 4 figures

References in corpus (18)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• emcee: The MCMC Hammer
• Extended Theories of Gravity
• On the Origin of Gravity and the Laws of Newton
• Tests of general relativity with GW150914
• The large-scale structure of the Universe
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Graviton Mass Bounds
• Mass for the graviton
• Galaxy rotation curves in $f(R,\varphi )$-gravity
• Constraining Extended Gravity Models by S2 star orbits around the Galactic Centre
• Observational constraints on Yukawa cosmology and connection with black hole shadows
• Constraints on Yukawa gravity parameters from observations of bright stars
• Testing modified gravity via Yukawa potential in two body problem: Analytical solution and observational constraints
• Dark Universe Phenomenology from Yukawa Potential?
• The conservation of energy-momentum and the mass for the graviton
• Visser's Massive Gravity Bimetric Theory Revisited