Orbital perturbations on transiting planets: A possible method to measure stellar quadrupoles and to detect Earth-mass planets

The recent discovery of a planetary transit in the star HD 209458, and the subsequent highly precise observation of the transit lightcurve with Hubble Space Telescope, is encouraging to search for any phenomena that might induce small changes in the light curve. Here we consider the effect of the quadrupole moment of the parent star and of a possible second planet perturbing the orbit of the transiting planet. Both of these cause a precession of the orbital plane and of the periastron of the planet, which result in a long-term variation of the duration and the period of the transits. For a transiting planet at 0.05 AU, either a quadrupole moment similar to that of the Sun or the gravitational tug from an Earth-like planet on an orbit of semimajor axis ~ 0.2 AU and a relative inclination near the optimal 45 degrees would cause a transit duration time derivative of ~ 1 second per year.