Revisiting the 2PN pericentre precession in view of possible future measurements of it

Abstract

At the second post-Newtonian (2PN) order, the secular pericentre precession ${\dot{\omega }}^{2PN}$ of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computing ${\dot{\omega }}^{2PN}$ in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration ${\mathbf{A}}^{2PN}$, and also an indirect part arising from the self-interaction of the 1PN acceleration ${\mathbf{A}}^{1PN}$ in the orbital average accounting for the instantaneous shifts induced by ${\mathbf{A}}^{1PN}$ itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity $e$. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericentre precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

arXiv commentLatex2e, 25 pages, 2 figures, no tables. Accepted for publication in Universe

References in corpus (25)

• Closest Star Seen Orbiting the Supermassive Black Hole at the Centre of the Milky Way
• Tests of general relativity from timing the double pulsar
• An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system
• A Double-Pulsar System - A Rare Laboratory for Relativistic Gravity and Plasma Physics
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• General Relativity and Cosmology: Unsolved Questions and Future Directions
• Authenticating the Presence of a Relativistic Massive Black Hole Binary in OJ 287 Using its General Relativity Centenary Flare: Improved Orbital Parameters
• Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
• On incorporating post-Newtonian effects in N-body dynamics
• A new general relativistic contribution to Mercury's perihelion advance
• Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft
• Relativistic orbits around spinning supermassive black holes. Secular evolution to 4.5 post-Newtonian order
• Future measurements of the Lense-Thirring effect in the Double Pulsar
• On Relativistic Multipole Moments of Stationary Spacetimes
• Pericenter advance in general relativity: Comparison of approaches at high post-Newtonian orders
• Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body
• Spinning compact binary dynamics and chameleon orbits
• Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method
• Spinning compact binary inspiral II: Conservative angular dynamics
• Effects on satellite orbits in the gravitational field of an axisymmetric central body with a mass monopole and arbitrary spin multipole moments
• A simple exact series representation for relativistic perihelion advance
• Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars
• Periastron Advance in Neutron Star - Black Hole Binaries

Cited by in corpus (4)

• Chaos in self-gravitating many-body systems: Lyapunov time dependence of $N$ and the influence of general relativity
• The Orbital Pericenter Precession in the 2PN Approximation
• On the 2PN pericentre precession in the general theory of relativity and the recently discovered fast orbiting S-stars in Sgr A${}^{\ast }$
• Orbital precession of stars in the Galactic center