Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of trans
its T_D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits, P_obs. The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in P_obs (transit timing variations, TTV) or in T_D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a ~4 year period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.
