Are we far from testing general relativity with the transiting extrasolar planet HD 209458b `Osiris'?

TL;DR

This paper assesses the feasibility of detecting general relativistic effects in the orbital period of exoplanet HD 209458b, concluding current measurement precision is insufficient but could improve with technological advances.

Contribution

It evaluates the potential to measure relativistic effects in exoplanet orbits, highlighting current limitations and future prospects for detection.

Findings

Relativistic gravitoelectric effect magnitude is ~0.1 s.

Current measurement accuracy is ~0.01 s, insufficient for detection.

Radial velocity measurement sensitivity limits the analysis.

Abstract

In this paper we investigate the possibility of measuring the general relativistic gravitoelectric contribution P^(GE) to the orbital period P of the transiting exoplanet HD 209458b 'Osiris'. It turns out that the predicted magnitude of such an effect is \sim 0.1 s, while the most recent determinations of the orbital period of HD 209458b with the photometric transit method are accurate to \sim 0.01 s. The present analysis shows that the major limiting factor is the \sim 1 m s^-1 sensitivity in the measurement of the projected semiamplitude of the star's radial velocity K. Indeed, it affects the determination of the mass m of the planet which, in turn, induces a systematic error in the Keplerian period P^(0) of \sim 8 s. It is of crucial importance because P^(0) should be subtracted from the measured period in order to extract the relativistic correction. The present-day uncertainty in $m$ does not yet make necessary the inclusion of relativistic corrections in the data-reduction process of the determination of the system's parameters. The present situation could change only if improvements of one-two orders of magnitude in the ground-based Doppler spectroscopy technique occurred.