When the anomalistic, draconitic and sidereal orbital periods do not coincide: the impact of post-Keplerian perturbing accelerations

Abstract

In a purely Keplerian picture, the anomalistic, draconitic and sidereal orbital periods of a test particle orbiting a massive body coincide with each other. Such a degeneracy is removed when a post-Keplerian perturbing acceleration enters the equations of motion yielding generally different corrections to the Keplerian period for the three aforementioned characteristic orbital timescales. They are analytically worked out in the case of the accelerations induced by the general relativistic post-Newtonian gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of the central body as well. The resulting expressions hold for completely general orbital configurations and spatial orientations of the spin axis of the primary. Astronomical systems characterized by extremely accurate measurements of the orbital periods like, e.g., transiting exoplanets and binary pulsars, may offer potentially viable scenarios for measuring such post--Keplerian features of motion, at least in principle. As an example, the sidereal period of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as small as $\simeq 10^{-5}\mathrm{s}$, while its predicted post-Newtonian gravitoelectric correction amounts to $0.07\mathrm{s}$; however, the accuracy with which the Keplerian period can be calculated is just 572 s. For the double pulsar PSR J0737-3039, the largest relativistic correction to the anomalistic period amounts to a few tenths of a second, given a measurement error of such a characteristic orbital timescale as small as $\simeq 10^{-6}\mathrm{s}$. On the other hand, the Keplerian term can be currently calculated just to a $\simeq 9$ s accuracy. In principle, measuring at least two of the three characteristic orbital periods for the same system independently would allow to cancel out their common Keplerian component provided that their difference is taken.

arXiv commentLaTex2e, 29 pages, 17 figures, no tables. Accepted for publication in Time and Space

References in corpus (31)

• The Confrontation between General Relativity and Experiment
• 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
• 55 Cancri (Copernicus): A Multi-Planet System with a Hot Super-Earth and a Jupiter Analogue
• Probing the Interiors of Very Hot Jupiters Using Transit Light Curves
• Long Term Evolution of Close Planets Including the Effects of Secular Interactions
• Gravitoelectromagnetism: A Brief Review
• Observability of the General Relativistic Precession of Periastra in Exoplanets
• Measurements of Transit Timing Variations for WASP-5b
• Periastron Precession Measurements in Transiting Extrasolar Planetary Systems at the Level of General Relativity
• Effects of Secular Interactions in Extrasolar Planetary Systems
• On the (im)possibility of testing new physics in exoplanets using transit timing variations: deviation from inverse-square law of gravity
• Are we far from testing general relativity with the transiting extrasolar planet HD 209458b `Osiris'?
• WD1032+011, an inflated brown dwarf in an old eclipsing binary with a white dwarf
• Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them
• Classical and relativistic long-term time variations of some observables for transiting exoplanets
• Relativistic Effects in Extrasolar Planetary Systems
• Extrasolar planets as a probe of modified gravity
• Constraining the Kehagias-Sfetsos solution in the Horava-Lifshitz gravity with extrasolar planets
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Detecting the General Relativistic Orbital Precession of the Exoplanet HD 80606b
• Probing a $r^{-n}$ modification of the Newtonian potential with Exoplanets
• Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the Galactic Center
• Parametrized Post-Newtonian Orbital Effects in Extrasolar Planets
• Post-Keplerian corrections to the orbital periods of a two-body system and their measurability
• Prospecting transit duration variations in extrasolar planetary systems
• Cyclic Transit Probabilities of Long-Period Eccentric Planets Due to Periastron Precession
• Detecting General Relativistic Orbital Precession in Transiting Hot Jupiters
• The influence of general-relativity effects, dynamical tides and collisions on planet-planet scattering close to the star