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The recent discovery of a planetary transit in the star HD 209458, and thesubsequent highly precise observation of the transit lightcurve with HubbleSpace Telescope, is encouraging to search for any phenomena that might inducesmall changes in the light curve. Here we consider the effect of the quadrupolemoment of the parent star and of a possible second planet perturbing the orbitof the transiting planet. Both of these cause a precession of the orbital planeand of the periastron of the planet, which result in a long-term variation ofthe duration and the period of the transits. For a transiting planet at 0.05AU, either a quadrupole moment similar to that of the Sun or the gravitationaltug from an Earth-like planet on an orbit of semimajor axis ~ 0.2 AU and arelative inclination near the optimal 45 degrees would cause a transit durationtime derivative of ~ 1 second per year.Comment: submitted to Ap

Orbital Perturbations of Transiting Planets: A Possible Method to Measure Stellar Quadrupoles and to Detect Earth‐Mass Planets