Post-Keplerian corrections to the orbital periods of a two-body system and their measurability

摘要: The orbital motion of a binary system is characterized by various characteristic temporal intervals which, definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in Keplerian case. Such degeneracy removed, general, when post-Keplerian acceleration present. We analytically work out corrections to such otherwise periods which induced general relativity (Schwarzschild Lense-Thirring) and, at Newtonian level, quadrupole primary. In many astronomical astrophysical systems, like exoplanets, one most accurately determined quantities just time span characterizing revolution, often measured independently with techniques transit photometry radial velocities. Thus, our results could be useful, principle, either constrain physical properties central body and/or perform new tests relativity, especially no other standard observables like, e.g., precessions accessible observations. difference two would cancel common term leaving correction. Furthermore, comparing theoretically predicted expressions $T^{(\textrm{pK})}$ experimental accuracy $\sigma_{T_\textrm{exp}}$ measuring period(s) it possible identify those systems whose observations should re-processed genuine models if $T^{(\textrm{pK})}>\sigma_{T_\textrm{exp}}$. It seems case for WASP-33 b since $\sigma_{T_\textrm{exp}}=0.04$ s, while $3$ s$\leq T_\textrm{dra}^{(J_2)}\leq 9.5$ $T_\textrm{dra}^{(\textrm{GE)}}=0.36$ s.