Detecting General Relativistic Orbital Precession in Transiting Hot Jupiters

Both classical and relativistic weak-field and slow-motion perturbations to planetary orbits can be treated as perturbative corrections to the Keplerian model. In particular, tidal forces and General Relativity (GR) induce small precession rates of the apsidal line. Accurate measurements of these effects in transiting exoplanets could be used to test GR and to gain information about the planetary interiors. Unfortunately, models for transiting planets have a high degree of degeneracy in the orbital parameters that, combined to the uncertainties of photometric transit observations, results in large errors on the determinations of the argument of periastron and precludes a direct evaluation of the apsidal line precession. Moreover, tidal and GR precession time-scales are many order of magnitudes larger than orbital periods, so that on the observational time-spans required to cumulate a precession signal enough strong to be detected, even small systematic errors in transit ephemerides add up to cancel out the tiny variations due to precession. Here we present a more feasible solution to detect tidal and GR precession rates through the observation of variations of the time interval ($\Delta \tau$) between primary and secondary transits of hot Jupiters and propose the most promising target for such detection, WASP-14 b. For this planet we expect a cumulated $\Delta \tau$ $\approx$ -250 s, due to tidal and relativistic precession, since its first photometric observations.