Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them

WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit with semi-major axis a = 0.02 au and eccentricity provisionally set to e = 0. The quadrupole mass moment J_2 and the proper angular momentum S of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and relativistic non-Keplerian orbital effects should take place in such a system. In this paper we investigate the perspectives in detecting them (Abridged)