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

In this paper, we investigate the possibility of measuring the general relativistic gravitoelectric correction P(GE) to the orbital period P of the transitting exoplanet HD 209458b 'Osiris'. It turns out that the predicted magnitude of such an effect is ∼0.1 s, while the most recent determinations of the orbital period of HD 209458b with the photometric transit method are accurate to ∼0.01 s. It turns out that the major limiting factor is the error in the measurement of the projected semiamplitude of the star's radial velocity KM. 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 ∼8 s. However, the present situation may change if future 1-2 orders of magnitude improvements in the Doppler spectroscopy technique will occur.